algorithm method of problem solving

Smart. Open. Grounded. Inventive. Read our Ideas Made to Matter.

Which program is right for you?

Through intellectual rigor and experiential learning, this full-time, two-year MBA program develops leaders who make a difference in the world.

A rigorous, hands-on program that prepares adaptive problem solvers for premier finance careers.

A 12-month program focused on applying the tools of modern data science, optimization and machine learning to solve real-world business problems.

Earn your MBA and SM in engineering with this transformative two-year program.

Combine an international MBA with a deep dive into management science. A special opportunity for partner and affiliate schools only.

A doctoral program that produces outstanding scholars who are leading in their fields of research.

Bring a business perspective to your technical and quantitative expertise with a bachelor’s degree in management, business analytics, or finance.

A joint program for mid-career professionals that integrates engineering and systems thinking. Earn your master’s degree in engineering and management.

An interdisciplinary program that combines engineering, management, and design, leading to a master’s degree in engineering and management.

Executive Programs

A full-time MBA program for mid-career leaders eager to dedicate one year of discovery for a lifetime of impact.

This 20-month MBA program equips experienced executives to enhance their impact on their organizations and the world.

Non-degree programs for senior executives and high-potential managers.

A non-degree, customizable program for mid-career professionals.

Boston Fed CEO sees interest rates staying put for now

Why this tech consultant and executive coach embraces being a B student

6 ways to transform KPIs

Credit: Alejandro Giraldo

Ideas Made to Matter

How to use algorithms to solve everyday problems

Kara Baskin

May 8, 2017

How can I navigate the grocery store quickly? Why doesn’t anyone like my Facebook status? How can I alphabetize my bookshelves in a hurry? Apple data visualizer and MIT System Design and Management graduate Ali Almossawi solves these common dilemmas and more in his new book, “ Bad Choices: How Algorithms Can Help You Think Smarter and Live Happier ,” a quirky, illustrated guide to algorithmic thinking. 

For the uninitiated: What is an algorithm? And how can algorithms help us to think smarter?

An algorithm is a process with unambiguous steps that has a beginning and an end, and does something useful.

Algorithmic thinking is taking a step back and asking, “If it’s the case that algorithms are so useful in computing to achieve predictability, might they also be useful in everyday life, when it comes to, say, deciding between alternative ways of solving a problem or completing a task?” In all cases, we optimize for efficiency: We care about time or space.

Note the mention of “deciding between.” Computer scientists do that all the time, and I was convinced that the tools they use to evaluate competing algorithms would be of interest to a broad audience.

Why did you write this book, and who can benefit from it?

All the books I came across that tried to introduce computer science involved coding. My approach to making algorithms compelling was focusing on comparisons. I take algorithms and put them in a scene from everyday life, such as matching socks from a pile, putting books on a shelf, remembering things, driving from one point to another, or cutting an onion. These activities can be mapped to one or more fundamental algorithms, which form the basis for the field of computing and have far-reaching applications and uses.

I wrote the book with two audiences in mind. One, anyone, be it a learner or an educator, who is interested in computer science and wants an engaging and lighthearted, but not a dumbed-down, introduction to the field. Two, anyone who is already familiar with the field and wants to experience a way of explaining some of the fundamental concepts in computer science differently than how they’re taught.

I’m going to the grocery store and only have 15 minutes. What do I do?

Do you know what the grocery store looks like ahead of time? If you know what it looks like, it determines your list. How do you prioritize things on your list? Order the items in a way that allows you to avoid walking down the same aisles twice.

For me, the intriguing thing is that the grocery store is a scene from everyday life that I can use as a launch pad to talk about various related topics, like priority queues and graphs and hashing. For instance, what is the most efficient way for a machine to store a prioritized list, and what happens when the equivalent of you scratching an item from a list happens in the machine’s list? How is a store analogous to a graph (an abstraction in computer science and mathematics that defines how things are connected), and how is navigating the aisles in a store analogous to traversing a graph?

Nobody follows me on Instagram. How do I get more followers?

The concept of links and networks, which I cover in Chapter 6, is relevant here. It’s much easier to get to people whom you might be interested in and who might be interested in you if you can start within the ball of links that connects those people, rather than starting at a random spot.

You mention Instagram: There, the hashtag is one way to enter that ball of links. Tag your photos, engage with users who tag their photos with the same hashtags, and you should be on your way to stardom.

What are the secret ingredients of a successful Facebook post?

I’ve posted things on social media that have died a sad death and then posted the same thing at a later date that somehow did great. Again, if we think of it in terms that are relevant to algorithms, we’d say that the challenge with making something go viral is really getting that first spark. And to get that first spark, a person who is connected to the largest number of people who are likely to engage with that post, needs to share it.

With [my first book], “Bad Arguments,” I spent a month pouring close to $5,000 into advertising for that project with moderate results. And then one science journalist with a large audience wrote about it, and the project took off and hasn’t stopped since.

What problems do you wish you could solve via algorithm but can’t?

When we care about efficiency, thinking in terms of algorithms is useful. There are cases when that’s not the quality we want to optimize for — for instance, learning or love. I walk for several miles every day, all throughout the city, as I find it relaxing. I’ve never asked myself, “What’s the most efficient way I can traverse the streets of San Francisco?” It’s not relevant to my objective.

Algorithms are a great way of thinking about efficiency, but the question has to be, “What approach can you optimize for that objective?” That’s what worries me about self-help: Books give you a silver bullet for doing everything “right” but leave out all the nuances that make us different. What works for you might not work for me.

Which companies use algorithms well?

When you read that the overwhelming majority of the shows that users of, say, Netflix, watch are due to Netflix’s recommendation engine, you know they’re doing something right.

Related Articles

What is Problem Solving Algorithm?, Steps, Representation

Table of Contents

• 1 What is Problem Solving Algorithm?
• 2 Definition of Problem Solving Algorithm
• 3.1 Analysing the Problem
• 3.2 Developing an Algorithm
• 3.4 Testing and Debugging
• 4.1 Flowchart
• 4.2 Pseudo code

What is Problem Solving Algorithm?

Computers are used for solving various day-to-day problems and thus problem solving is an essential skill that a computer science student should know. It is pertinent to mention that computers themselves cannot solve a problem. Precise step-by-step instructions should be given by us to solve the problem.

Thus, the success of a computer in solving a problem depends on how correctly and precisely we define the problem, design a solution (algorithm) and implement the solution (program) using a programming language.

Thus, problem solving is the process of identifying a problem, developing an algorithm for the identified problem and finally implementing the algorithm to develop a computer program.

Definition of Problem Solving Algorithm

These are some simple definition of problem solving algorithm which given below:

Steps for Problem Solving

When problems are straightforward and easy, we can easily find the solution. But a complex problem requires a methodical approach to find the right solution. In other words, we have to apply problem solving techniques.

Problem solving begins with the precise identification of the problem and ends with a complete working solution in terms of a program or software. Key steps required for solving a problem using a computer.

For Example: Suppose while driving, a vehicle starts making a strange noise. We might not know how to solve the problem right away. First, we need to identify from where the noise is coming? In case the problem cannot be solved by us, then we need to take the vehicle to a mechanic.

The mechanic will analyse the problem to identify the source of the noise, make a plan about the work to be done and finally repair the vehicle in order to remove the noise. From the example, it is explicit that, finding the solution to a problem might consist of multiple steps.

Following are Steps for Problem Solving :

Analysing the Problem

Developing an algorithm, testing and debugging.

It is important to clearly understand a problem before we begin to find the solution for it. If we are not clear as to what is to be solved, we may end up developing a program which may not solve our purpose.

Thus, we need to read and analyse the problem statement carefully in order to list the principal components of the problem and decide the core functionalities that our solution should have. By analysing a problem, we would be able to figure out what are the inputs that our program should accept and the outputs that it should produce.

It is essential to device a solution before writing a program code for a given problem. The solution is represented in natural language and is called an algorithm. We can imagine an algorithm like a very well-written recipe for a dish, with clearly defined steps that, if followed, one will end up preparing the dish.

We start with a tentative solution plan and keep on refining the algorithm until the algorithm is able to capture all the aspects of the desired solution. For a given problem, more than one algorithm is possible and we have to select the most suitable solution.

After finalising the algorithm, we need to convert the algorithm into the format which can be understood by the computer to generate the desired solution. Different high level programming languages can be used for writing a program. It is equally important to record the details of the coding procedures followed and document the solution. This is helpful when revisiting the programs at a later stage.

The program created should be tested on various parameters. The program should meet the requirements of the user. It must respond within the expected time. It should generate correct output for all possible inputs. In the presence of syntactical errors, no output will be obtained. In case the output generated is incorrect, then the program should be checked for logical errors, if any.

Software industry follows standardised testing methods like unit or component testing, integration testing, system testing, and acceptance testing while developing complex applications. This is to ensure that the software meets all the business and technical requirements and works as expected.

The errors or defects found in the testing phases are debugged or rectified and the program is again tested. This continues till all the errors are removed from the program. Once the software application has been developed, tested and delivered to the user, still problems in terms of functioning can come up and need to be resolved from time to time.

The maintenance of the solution, thus, involves fixing the problems faced by the user, answering the queries of the user and even serving the request for addition or modification of features.

Representation of Algorithms

Using their algorithmic thinking skills, the software designers or programmers analyse the problem and identify the logical steps that need to be followed to reach a solution. Once the steps are identified, the need is to write down these steps along with the required input and desired output.

There are two common methods of representing an algorithm —flowchart and pseudocode. Either of the methods can be used to represent an algorithm while keeping in mind the following:

• It showcases the logic of the problem solution, excluding any implementational details.
• It clearly reveals the flow of control during execution of the program.

A flowchart is a visual representation of an algorithm . A flowchart is a diagram made up of boxes, diamonds and other shapes, connected by arrows. Each shape represents a step of the solution process and the arrow represents the order or link among the steps.

A flow chart is a step by step diagrammatic representation of the logic paths to solve a given problem. Or A flowchart is visual or graphical representation of an algorithm .

The flowcharts are pictorial representation of the methods to b used to solve a given problem and help a great deal to analyze the problem and plan its solution in a systematic and orderly manner. A flowchart when translated in to a proper computer language, results in a complete program.

Advantages of Flowcharts:

• The flowchart shows the logic of a problem displayed in pictorial fashion which felicitates easier checking of an algorithm
• The Flowchart is good means of communication to other users. It is also a compact means of recording an algorithm solution to a problem.
• The flowchart allows the problem solver to break the problem into parts. These parts can be connected to make master chart.
• The flowchart is a permanent record of the solution which can be consulted at a later time.

Differences between Algorithm and Flowchart

Pseudo code.

The Pseudo code is neither an algorithm nor a program. It is an abstract form of a program. It consists of English like statements which perform the specific operations. It is defined for an algorithm. It does not use any graphical representation.

In pseudo code , the program is represented in terms of words and phrases, but the syntax of program is not strictly followed.

Advantages of Pseudocode

• Before writing codes in a high level language, a pseudocode of a program helps in representing the basic functionality of the intended program.
• By writing the code first in a human readable language, the programmer safeguards against leaving out any important step. Besides, for non-programmers, actual programs are difficult to read and understand.
• But pseudocode helps them to review the steps to confirm that the proposed implementation is going to achieve the desire output.

Related posts:

• 10 Types of Computers | History of Computers, Advantages
• What is Microprocessor? Evolution of Microprocessor, Types, Features
• Types of Computer Memory, Characteristics, Primary Memory, Secondary Memory
• Data and Information: Definition, Characteristics, Types, Channels, Approaches
• What is Cloud Computing? Classification, Characteristics, Principles, Types of Cloud Providers
• What is Debugging? Types of Errors
• Types of Storage Devices, Advantages, Examples
• 10 Evolution of Computing Machine, History
• What are Functions of Operating System? 6 Functions
• Advantages and Disadvantages of Operating System
• Data Representation in Computer: Number Systems, Characters, Audio, Image and Video
• What are Data Types in C++? Types
• What are Operators in C? Different Types of Operators in C
• What are Expressions in C? Types
• What are Decision Making Statements in C? Types

• 1. Micro-Worlds
• 2. Light-Bot in Java
• 3. Jeroos of Santong Island
• 4. Problem Solving and Algorithms
• 5. Creating Jeroo Methods
• 6. Conditionally Executing Actions
• 7. Repeating Actions
• 8. Handling Touch Events
• 9. Adding Text to the Screen

Problem Solving and Algorithms

Learn a basic process for developing a solution to a problem. Nothing in this chapter is unique to using a computer to solve a problem. This process can be used to solve a wide variety of problems, including ones that have nothing to do with computers.

Problems, Solutions, and Tools

I have a problem! I need to thank Aunt Kay for the birthday present she sent me. I could send a thank you note through the mail. I could call her on the telephone. I could send her an email message. I could drive to her house and thank her in person. In fact, there are many ways I could thank her, but that's not the point. The point is that I must decide how I want to solve the problem, and use the appropriate tool to implement (carry out) my plan. The postal service, the telephone, the internet, and my automobile are tools that I can use, but none of these actually solves my problem. In a similar way, a computer does not solve problems, it's just a tool that I can use to implement my plan for solving the problem.

Knowing that Aunt Kay appreciates creative and unusual things, I have decided to hire a singing messenger to deliver my thanks. In this context, the messenger is a tool, but one that needs instructions from me. I have to tell the messenger where Aunt Kay lives, what time I would like the message to be delivered, and what lyrics I want sung. A computer program is similar to my instructions to the messenger.

The story of Aunt Kay uses a familiar context to set the stage for a useful point of view concerning computers and computer programs. The following list summarizes the key aspects of this point of view.

A computer is a tool that can be used to implement a plan for solving a problem.

A computer program is a set of instructions for a computer. These instructions describe the steps that the computer must follow to implement a plan.

An algorithm is a plan for solving a problem.

A person must design an algorithm.

A person must translate an algorithm into a computer program.

This point of view sets the stage for a process that we will use to develop solutions to Jeroo problems. The basic process is important because it can be used to solve a wide variety of problems, including ones where the solution will be written in some other programming language.

An Algorithm Development Process

Every problem solution starts with a plan. That plan is called an algorithm.

There are many ways to write an algorithm. Some are very informal, some are quite formal and mathematical in nature, and some are quite graphical. The instructions for connecting a DVD player to a television are an algorithm. A mathematical formula such as πR 2 is a special case of an algorithm. The form is not particularly important as long as it provides a good way to describe and check the logic of the plan.

The development of an algorithm (a plan) is a key step in solving a problem. Once we have an algorithm, we can translate it into a computer program in some programming language. Our algorithm development process consists of five major steps.

Step 1: Obtain a description of the problem.

Step 2: analyze the problem., step 3: develop a high-level algorithm., step 4: refine the algorithm by adding more detail., step 5: review the algorithm..

This step is much more difficult than it appears. In the following discussion, the word client refers to someone who wants to find a solution to a problem, and the word developer refers to someone who finds a way to solve the problem. The developer must create an algorithm that will solve the client's problem.

The client is responsible for creating a description of the problem, but this is often the weakest part of the process. It's quite common for a problem description to suffer from one or more of the following types of defects: (1) the description relies on unstated assumptions, (2) the description is ambiguous, (3) the description is incomplete, or (4) the description has internal contradictions. These defects are seldom due to carelessness by the client. Instead, they are due to the fact that natural languages (English, French, Korean, etc.) are rather imprecise. Part of the developer's responsibility is to identify defects in the description of a problem, and to work with the client to remedy those defects.

The purpose of this step is to determine both the starting and ending points for solving the problem. This process is analogous to a mathematician determining what is given and what must be proven. A good problem description makes it easier to perform this step.

When determining the starting point, we should start by seeking answers to the following questions:

What data are available?

Where is that data?

What formulas pertain to the problem?

What rules exist for working with the data?

What relationships exist among the data values?

When determining the ending point, we need to describe the characteristics of a solution. In other words, how will we know when we're done? Asking the following questions often helps to determine the ending point.

What new facts will we have?

What items will have changed?

What changes will have been made to those items?

What things will no longer exist?

An algorithm is a plan for solving a problem, but plans come in several levels of detail. It's usually better to start with a high-level algorithm that includes the major part of a solution, but leaves the details until later. We can use an everyday example to demonstrate a high-level algorithm.

Problem: I need a send a birthday card to my brother, Mark.

Analysis: I don't have a card. I prefer to buy a card rather than make one myself.

High-level algorithm:

Go to a store that sells greeting cards Select a card Purchase a card Mail the card

This algorithm is satisfactory for daily use, but it lacks details that would have to be added were a computer to carry out the solution. These details include answers to questions such as the following.

"Which store will I visit?"

"How will I get there: walk, drive, ride my bicycle, take the bus?"

"What kind of card does Mark like: humorous, sentimental, risqué?"

These kinds of details are considered in the next step of our process.

A high-level algorithm shows the major steps that need to be followed to solve a problem. Now we need to add details to these steps, but how much detail should we add? Unfortunately, the answer to this question depends on the situation. We have to consider who (or what) is going to implement the algorithm and how much that person (or thing) already knows how to do. If someone is going to purchase Mark's birthday card on my behalf, my instructions have to be adapted to whether or not that person is familiar with the stores in the community and how well the purchaser known my brother's taste in greeting cards.

When our goal is to develop algorithms that will lead to computer programs, we need to consider the capabilities of the computer and provide enough detail so that someone else could use our algorithm to write a computer program that follows the steps in our algorithm. As with the birthday card problem, we need to adjust the level of detail to match the ability of the programmer. When in doubt, or when you are learning, it is better to have too much detail than to have too little.

Most of our examples will move from a high-level to a detailed algorithm in a single step, but this is not always reasonable. For larger, more complex problems, it is common to go through this process several times, developing intermediate level algorithms as we go. Each time, we add more detail to the previous algorithm, stopping when we see no benefit to further refinement. This technique of gradually working from a high-level to a detailed algorithm is often called stepwise refinement .

The final step is to review the algorithm. What are we looking for? First, we need to work through the algorithm step by step to determine whether or not it will solve the original problem. Once we are satisfied that the algorithm does provide a solution to the problem, we start to look for other things. The following questions are typical of ones that should be asked whenever we review an algorithm. Asking these questions and seeking their answers is a good way to develop skills that can be applied to the next problem.

Does this algorithm solve a very specific problem or does it solve a more general problem ? If it solves a very specific problem, should it be generalized?

For example, an algorithm that computes the area of a circle having radius 5.2 meters (formula π*5.2 2 ) solves a very specific problem, but an algorithm that computes the area of any circle (formula π*R 2 ) solves a more general problem.

Can this algorithm be simplified ?

One formula for computing the perimeter of a rectangle is:

length + width + length + width

A simpler formula would be:

2.0 * ( length + width )

Is this solution similar to the solution to another problem? How are they alike? How are they different?

For example, consider the following two formulae:

Rectangle area = length * width Triangle area = 0.5 * base * height

Similarities: Each computes an area. Each multiplies two measurements.

Differences: Different measurements are used. The triangle formula contains 0.5.

Hypothesis: Perhaps every area formula involves multiplying two measurements.

Example 4.1: Pick and Plant

This section contains an extended example that demonstrates the algorithm development process. To complete the algorithm, we need to know that every Jeroo can hop forward, turn left and right, pick a flower from its current location, and plant a flower at its current location.

Problem Statement (Step 1)

A Jeroo starts at (0, 0) facing East with no flowers in its pouch. There is a flower at location (3, 0). Write a program that directs the Jeroo to pick the flower and plant it at location (3, 2). After planting the flower, the Jeroo should hop one space East and stop. There are no other nets, flowers, or Jeroos on the island.

Analysis of the Problem (Step 2)

The flower is exactly three spaces ahead of the jeroo.

The flower is to be planted exactly two spaces South of its current location.

The Jeroo is to finish facing East one space East of the planted flower.

There are no nets to worry about.

High-level Algorithm (Step 3)

Let's name the Jeroo Bobby. Bobby should do the following:

Get the flower Put the flower Hop East

Detailed Algorithm (Step 4)

Get the flower Hop 3 times Pick the flower Put the flower Turn right Hop 2 times Plant a flower Hop East Turn left Hop once

Review the Algorithm (Step 5)

The high-level algorithm partitioned the problem into three rather easy subproblems. This seems like a good technique.

This algorithm solves a very specific problem because the Jeroo and the flower are in very specific locations.

This algorithm is actually a solution to a slightly more general problem in which the Jeroo starts anywhere, and the flower is 3 spaces directly ahead of the Jeroo.

Java Code for "Pick and Plant"

A good programmer doesn't write a program all at once. Instead, the programmer will write and test the program in a series of builds. Each build adds to the previous one. The high-level algorithm will guide us in this process.

FIRST BUILD

To see this solution in action, create a new Greenfoot4Sofia scenario and use the Edit Palettes Jeroo menu command to make the Jeroo classes visible. Right-click on the Island class and create a new subclass with the name of your choice. This subclass will hold your new code.

The recommended first build contains three things:

The main method (here myProgram() in your island subclass).

Declaration and instantiation of every Jeroo that will be used.

The high-level algorithm in the form of comments.

The instantiation at the beginning of myProgram() places bobby at (0, 0), facing East, with no flowers.

Once the first build is working correctly, we can proceed to the others. In this case, each build will correspond to one step in the high-level algorithm. It may seem like a lot of work to use four builds for such a simple program, but doing so helps establish habits that will become invaluable as the programs become more complex.

SECOND BUILD

This build adds the logic to "get the flower", which in the detailed algorithm (step 4 above) consists of hopping 3 times and then picking the flower. The new code is indicated by comments that wouldn't appear in the original (they are just here to call attention to the additions). The blank lines help show the organization of the logic.

By taking a moment to run the work so far, you can confirm whether or not this step in the planned algorithm works as expected.

THIRD BUILD

This build adds the logic to "put the flower". New code is indicated by the comments that are provided here to mark the additions.

FOURTH BUILD (final)

Example 4.2: replace net with flower.

This section contains a second example that demonstrates the algorithm development process.

There are two Jeroos. One Jeroo starts at (0, 0) facing North with one flower in its pouch. The second starts at (0, 2) facing East with one flower in its pouch. There is a net at location (3, 2). Write a program that directs the first Jeroo to give its flower to the second one. After receiving the flower, the second Jeroo must disable the net, and plant a flower in its place. After planting the flower, the Jeroo must turn and face South. There are no other nets, flowers, or Jeroos on the island.

Jeroo_2 is exactly two spaces behind Jeroo_1.

The only net is exactly three spaces ahead of Jeroo_2.

Each Jeroo has exactly one flower.

Jeroo_2 will have two flowers after receiving one from Jeroo_1. One flower must be used to disable the net. The other flower must be planted at the location of the net, i.e. (3, 2).

Jeroo_1 will finish at (0, 1) facing South.

Jeroo_2 is to finish at (3, 2) facing South.

Each Jeroo will finish with 0 flowers in its pouch. One flower was used to disable the net, and the other was planted.

Let's name the first Jeroo Ann and the second one Andy.

Ann should do the following: Find Andy (but don't collide with him) Give a flower to Andy (he will be straight ahead) After receiving the flower, Andy should do the following: Find the net (but don't hop onto it) Disable the net Plant a flower at the location of the net Face South

Ann should do the following: Find Andy Turn around (either left or right twice) Hop (to location (0, 1)) Give a flower to Andy Give ahead Now Andy should do the following: Find the net Hop twice (to location (2, 2)) Disable the net Toss Plant a flower at the location of the net Hop (to location (3, 2)) Plant a flower Face South Turn right

The high-level algorithm helps manage the details.

This algorithm solves a very specific problem, but the specific locations are not important. The only thing that is important is the starting location of the Jeroos relative to one another and the location of the net relative to the second Jeroo's location and direction.

Java Code for "Replace Net with Flower"

As before, the code should be written incrementally as a series of builds. Four builds will be suitable for this problem. As usual, the first build will contain the main method, the declaration and instantiation of the Jeroo objects, and the high-level algorithm in the form of comments. The second build will have Ann give her flower to Andy. The third build will have Andy locate and disable the net. In the final build, Andy will place the flower and turn East.

This build creates the main method, instantiates the Jeroos, and outlines the high-level algorithm. In this example, the main method would be myProgram() contained within a subclass of Island .

This build adds the logic for Ann to locate Andy and give him a flower.

This build adds the logic for Andy to locate and disable the net.

This build adds the logic for Andy to place a flower at (3, 2) and turn South.

Reset password New user? Sign up

Existing user? Log in

Already have an account? Log in here.

• Pete Tomiello
• Debarghya Adhikari
• ANKIT JAVERI

An algorithm is a procedure that takes in input, follows a certain set of steps, and then produces an output. Oftentimes, the algorithm defines a desired relationship between the input and output. For example, if the problem that we are trying to solve is sorting a hand of cards, the problem might be defined as follows:

Problem : Sort the input. Input : A set of 5 cards. Output : The set of 5 input cards, sorted. Procedure : Up to the designer of the algorithm!

This last part is very important, it's the meat and substance of the algorithm. And, as an algorithm designer, you can do whatever you want to produce the desired output! Think about some ways you could sort 5 cards in your hand, and then click below to see some more ideas.

Algorithm Ideas

\(\hspace{0mm}\) We could simply toss them up in the air and pick them up again. Maybe they'll be sorted. If not, we can try it again and again until it works (spoiler: this is a bad algorithm). \(\hspace{0mm}\) We can sort them one at a time, left to right. Let's say our hand looks like {2, 4, 1, 9, 8}. Well, 2 and 4 are already sorted. But then we have a 1. That should go before 4, and it should go before 2. Now we have {1, 2, 4, 9, 8}. 9 is in the right spot because its higher than the card to its left, 4. But 8 is wrong because it's smaller than 9, so we'll just put it before 9. Now, we have {1, 2, 4, 8, 9}, and we're done. This is called insertion sort . \(\hspace{0mm}\) We can sort them two at a time, left to right. So, our hand is again {2, 4, 1, 9, 8}. 2 and 4 are good. 4 and 1 need to be swapped, so now we have {2, 1, 4, 9, 8}. 4 and 9 are good. 9 and 8 should be swapped, so now we have {2, 1, 4, 8, 9}. We have to start at the beginning again, but that's no problem. We look at the first pair and see that 2 and 1 need to switch, so now we have {1, 2, 4, 8, 9}, and we're done. This is called bubble sort . \(\hspace{0mm}\) There are a million ways to sort this hand of cards! Some are great, most are terrible. It's up to you as the algorithm designer to make a great one.

The study of algorithms involves finding the best ways to achieve the desired output given an input and a goal. Learning about algorithms is essential to being a successful computer programmer, and understanding them can help give you an idea of how computers work. So, if you'd like to learn to code, it's absolutely essential to learn about algorithms.

Algorithms and Computers

Properties of algorithms, types of algorithms, designing an algorithm, analyzing and evaluating an algorithm, hard algorithms.

Even though algorithms existed before the modern computer, they lie at the heart of computing and technology. Everything you've ever done on any piece of technology relies on algorithms because they tell technology what to do. Algorithms are responsible for your ability to surf the web at tolerable speeds. Imagine that you're visiting a website, and that website has a lot of unsorted content to show you. If it randomly picked a content order every time you visited it, and threw that order away and tried again if it wasn't correct, you'd be waiting for minutes, hours, or even days before your web page loaded!

Studying computer science and computer programming always involves algorithms because the study of algorithms teaches you to think like a machine so that you can program them in the best way possible. If you'd like to learn how to write applications, make websites, or do data analysis, you need to know about algorithms so that your code will run fast and run correctly.

On the theoretical side, many of the simpler algorithms have long since been discovered and heavily studied, but there are many areas left to research. For example, in theoretical computer science, a lingering question is whether P = NP , or in other words, "Are problems that can be quickly verified by a computer able to be quickly solved by a computer?" Currently, we don't think so. But if it turned out to be true, then computing and technology would experience an enormous speed increase that we would all benefit from. However, this would also mean that modern cryptography is not safe and any hacker could easily crack codes to any system in the world!

As computing grew, applications of computing grew along with it. In order to perform the algorithms that would enable those applications, computer scientists needed a way to represent and store that data. If we wanted to input a set of cards into a computer program, how would we store that data? How would we feed it into the algorithm? Early on, it was good enough to simply represent data as computer bits (zeroes and ones). However, that method could never last, it was too difficult and time-consuming.

Data structures were the answer. Their invention and research is paralleled by, and is often taught alongside, algorithms. The card sorting algorithm, for example, could take in an array of numbers to represent cards. More data structures were invented over time, and they allowed algorithm design to progress with them. With these in place, it became much easier to reason about, develop, and research algorithms.

Algorithms have 3 main properties that are important to remember during their design and analysis.

Algorithm Properties: Time complexity. This is the time an algorithm takes to complete, and it is often given using big O notation with its input as the independent variable. For example, if we want to search a card in the sorted \(n\) cards, we can do in logarithmic time, and the time complexity would be \(O\big(\log(n)\big)\). Space complexity. This is the space (in computer memory) the algorithm uses during its execution. Again, if we're sorting \(n\) cards, and we need to make an extra array of size \(n\) for each card to do so, the space complexity would be \(O\big(\log(n^2)\big)\). Correctness. An algorithm is correct if and only if, for every input, it halts and outputs the correct output. Contrary to what you might think, algorithms that are not correct are sometimes useful. For example, partially correct algorithms only guarantee that if the algorithm halts, the answer will be correct.

An algorithm can be expressed in a variety of ways, many of which you'll find in different wikis here on Brilliant.

A few examples of how an algorithm can be described are as follows: A high-level description . This might be in the form of text or prose that describes the algorithm: it's input, output, and goal. Generally, this does not involve implementation details of the algorithm. Formal definition . A formal definition will often give the input and output of the algorithm in formal mathematical terms. The procedure by which the output is achieved is also formally notated. This is a more mathematical way of representing an algorithm. Pseudo-code . This is a way of loosely formalizing an algorithm, and it is often used when learning algorithms. There are general implementation details; however, language-specific details are left out so as not to complicate things. Implementation . An implementation in a given language will be a piece of code that is understandable and runnable by a computer. It will fulfill the goals and procedure of the algorithm; however, it is harder to include high-level detail in an implementation because a computer will reject plain text.

There are many types of algorithms, and the language that describes them varies from textbook to textbook and from person to person. Some algorithm labels describe their function, and others describe the process by which they perform their function.

For example, there is a type of algorithm called string matching algorithms ; these algorithms find occurrences of an input string in larger strings or pieces of text. An example of a string matching algorithm is the Rabin-Karp algorithm , but there are many more. On the other hand, an example of a label that describes an algorithm's method for solving the problem is the divide and conquer algorithm . An example of this is binary search , which searches for a target in sorted input by cutting up the input into smaller pieces until the target is found.

A specific algorithm can span both classes. For example, a sorting algorithm that performs its sorting recursively could be described as either a sorting function or a recursive function.

Labels that describe function:

Labels that describe process:

When designing an algorithm, it is important to remember that computers are not infinitely fast and that computer memory is not infinitely large. That's why we make algorithms, after all. So, maybe you're designing an algorithm for a computer that is super fast but doesn't have much memory. Maybe you'll make some concessions on the computational requirements so that you can save memory.

But even if you never had to worry about speed or space, you still need to design a good algorithm. Why? You need to design a good algorithm because you need to know that the algorithm will do what you want it to do and that it will stop once it's done. You need to know that it will be correct.

The efficacy of the algorithm you're designing comes down to time complexity and space complexity . In an ideal world, the algorithm is efficient in both ways, but there is sometimes a tradeoff between them. It is up to the designer to weigh their needs appropriately in order to strike a balance.

It is also up to the designer to make a good algorithm. Doing so requires an understanding of algorithms as well as an understanding of existing algorithms to guide your design process. Otherwise, they might find themselves with a bad algorithm.

Two algorithms that do the same exact thing in different ways could have enormous differences in efficacy. In sorting, for example, bubble sort requires \(O(n)\) space during its execution. Quick sort , on the other hand, requires \(O\big(n\lg(n)\big)\) space. What does that mean for the programmer using those algorithms? Let's assume for simplicity that the input is just 1KB of data (or 8000 bits). Quicksort will require \(\lg(8000)\) times more space, or almost 13 times more space than bubble sort. Scale that up to inputs of 1GB or even 1TB, and this difference becomes very noticeable and very inefficient.

However, it's worth noting that quicksort runs faster than bubble sort by the same factor. Again, it's a tradeoff, and it's up to the designer to understand the tradeoffs and to optimize their design for their needs.

The analysis and evaluation of an algorithm is a two-step process. In the analysis portion, the algorithm is studied to learn about its properties: time/space complexity and correctness. Any method of describing the algorithm, as enumerated above , can be studied. However, that description must contain enough information about the inner workings of the algorithm to provide a clear picture of its procedure.

In general, there are a few ways to describe time complexity. There's the best-case , the average-case , and the worst-case for the algorithm. As a programmer, it's important to know each case so that you fully understand how your algorithm will operate. Which case you focus on is up to you, but the worst-case performance is often used as a benchmark for algorithms.

The evaluation portion is more qualitative and requires the observer to make decisions about the efficacy of the algorithm on its own, and as it relates to other similar algorithms. You might see the algorithm and notice that it is making some critical errors that increase its runtime. You might also discover that its runtime is drastically different than other algorithms that accomplish the same thing. In either case, the evaluation result is poor.

Let's take a look at the pseudo-code for an algorithm and try to analyze its time complexity. The following pseudo-code is that of insertion sort , a basic sorting algorithm. It takes as its input an array, \(A\), of the number and returns that same array, sorted. Note that this pseudo-code assumes 1-indexing (the first index in the array is 1, not 0).

1 2 3 4 5 6 7 8 Insertion_Sort(A) for j = 2 to j = A.length: current = A[j] i = j - 1 while i > 0 and A[i] > current: A[i+1] = A[i] i = i - 1 A[i + 1] = current Show Answer First, let's look at what this code is doing. We are given an input array of numbers, let's say [4, 2, 3, 7, 8] . The algorithm iterates through that array, starting with the second element, in this case, 2 . It calls this number current . It grabs the index right before current , which is 1 and whose value is 4 , and sets it equal to i . Now it wants to move 4 to the correct location. The while loop says "while the index i is more than 0, and while the number 2 is greater than its neighbor to the left, move 2 to the left and decrease i by 1". So, 2 is moved until it's in the correct spot with respect to the numbers seen so far by the algorithm. This pseudo-code can be analyzed by looking through this code line by line. In line 2, it has a for loop that iterates from the value 2 to the value A.length which is our input size, \(n.\) So, already we know for a fact that this algorithm is at least dependent linearly on our input size. In other words, the runtime of this algorithm is at least \(O(n)\) or \(\Omega(n)\). Everything inside the for loop must be executed \(n\) times, so we can ignore constant time operations such as lines 3, 4, and 8. Instead, line 5 is where the focus must shift because it is another iterable loop. The while loop on line 5 is similar to the for loop on line 2, but it has a variable number of times it can be repeated. That number can vary from 1 to \(n\) depending on how sorted our array is initially. If the input array is [2, 3, 4, 7, 8] , for example, the while loop will only run 1 time because each element is not greater than the element to its left. However, if the input is [8, 7, 4, 3, 2] , the while loop will need to run \(O(n)\) times. To see why, let's see what the array looks like after each iteration of the while loop: 1 2 3 4 5 0 (input). [8, 7, 4, 3, 2] 1: [7, 8, 4, 3, 2] 2: [4, 7, 8, 3, 2] 3: [3, 4, 7, 8, 2] 4: [2, 3, 4, 7, 8] See how between the \(3^\text{rd}\) and \(4^\text{th}\) iteration the 2 had to move all the way across the array? That's \(O(n)\) times. So, the for loop on line 2 iterates \(O(n)\) times. And the while loop on line 5 iterates anywhere from \(O(1)\) to \(O(n)\) times. So, the best-case runtime is \(O(n)\) when the input list is already sorted, and the worst-case is \(O(n^2)\) when it is sorted in reverse order. The average-case is a little trickier to understand. Basically, we'd expect any element in the input array to be less than half the elements to its left. Half of the elements is still \(\frac{n}{2},\) which is still \(O(n)\), so the average-case is also \(O(n^2)\).

The following pseudo-code represents an algorithm that takes as input an array of elements that can contain either positive integers or strings. In other words, the input could look like this [42, 'a', 1, 'hello', 3] .

The algorithm outputs an array with the following properties: elements in the output alternate between being a string and being an integer, and each element is less than or equal to the previous element of the same type (except for the elements at position 1 and 2, which are the largest of their respective types). In computer science, it is possible to sort strings ('b' > 'a', for example). This output will contain more elements than the input if the input does not have the same number of integers and strings.

What is the runtime of this algorithm?

For this example, assume that the sorting algorithm Reverse_Cheating_Sort(A) is a constant \(O(1)\) operation.

Typical algorithms are generally efficient. They run in polynomial time. In other words, their runtime can be defined as \(O(n^x)\) for some input \(n\) and some integer \(x\). However, there is a class of algorithms that do not currently have a polynomial-time solution. Some famous examples of this are the traveling salesperson problem or the set cover problem .

These problems are called NP-complete problems and are very interesting to study. Although no polynomial-time algorithm has ever been discovered for them, no one has proven that there can't be one out there, waiting to be discovered. Furthermore, if a solution was found for just one of them, a solution could be inferred for all of them!

There are currently various algorithms that make good approximations for solutions to these problems. They might use heuristics to cut down on runtime. However, the answer is not always exact, and the algorithm is therefore not correct.

The field of computer science contains many exciting areas to explore. In theory and algorithms, the question of NP-completeness and its relationship to other algorithms is one that has puzzled computer scientists for decades and that has many important implications for technology and for the world.

Problem Loading...

Note Loading...

Set Loading...

7.3 Problem-Solving

Learning objectives.

By the end of this section, you will be able to:

• Describe problem solving strategies
• Define algorithm and heuristic
• Explain some common roadblocks to effective problem solving

   People face problems every day—usually, multiple problems throughout the day. Sometimes these problems are straightforward: To double a recipe for pizza dough, for example, all that is required is that each ingredient in the recipe be doubled. Sometimes, however, the problems we encounter are more complex. For example, say you have a work deadline, and you must mail a printed copy of a report to your supervisor by the end of the business day. The report is time-sensitive and must be sent overnight. You finished the report last night, but your printer will not work today. What should you do? First, you need to identify the problem and then apply a strategy for solving the problem.

The study of human and animal problem solving processes has provided much insight toward the understanding of our conscious experience and led to advancements in computer science and artificial intelligence. Essentially much of cognitive science today represents studies of how we consciously and unconsciously make decisions and solve problems. For instance, when encountered with a large amount of information, how do we go about making decisions about the most efficient way of sorting and analyzing all the information in order to find what you are looking for as in visual search paradigms in cognitive psychology. Or in a situation where a piece of machinery is not working properly, how do we go about organizing how to address the issue and understand what the cause of the problem might be. How do we sort the procedures that will be needed and focus attention on what is important in order to solve problems efficiently. Within this section we will discuss some of these issues and examine processes related to human, animal and computer problem solving.

PROBLEM-SOLVING STRATEGIES

   When people are presented with a problem—whether it is a complex mathematical problem or a broken printer, how do you solve it? Before finding a solution to the problem, the problem must first be clearly identified. After that, one of many problem solving strategies can be applied, hopefully resulting in a solution.

Problems themselves can be classified into two different categories known as ill-defined and well-defined problems (Schacter, 2009). Ill-defined problems represent issues that do not have clear goals, solution paths, or expected solutions whereas well-defined problems have specific goals, clearly defined solutions, and clear expected solutions. Problem solving often incorporates pragmatics (logical reasoning) and semantics (interpretation of meanings behind the problem), and also in many cases require abstract thinking and creativity in order to find novel solutions. Within psychology, problem solving refers to a motivational drive for reading a definite “goal” from a present situation or condition that is either not moving toward that goal, is distant from it, or requires more complex logical analysis for finding a missing description of conditions or steps toward that goal. Processes relating to problem solving include problem finding also known as problem analysis, problem shaping where the organization of the problem occurs, generating alternative strategies, implementation of attempted solutions, and verification of the selected solution. Various methods of studying problem solving exist within the field of psychology including introspection, behavior analysis and behaviorism, simulation, computer modeling, and experimentation.

A problem-solving strategy is a plan of action used to find a solution. Different strategies have different action plans associated with them (table below). For example, a well-known strategy is trial and error. The old adage, “If at first you don’t succeed, try, try again” describes trial and error. In terms of your broken printer, you could try checking the ink levels, and if that doesn’t work, you could check to make sure the paper tray isn’t jammed. Or maybe the printer isn’t actually connected to your laptop. When using trial and error, you would continue to try different solutions until you solved your problem. Although trial and error is not typically one of the most time-efficient strategies, it is a commonly used one.

   Another type of strategy is an algorithm. An algorithm is a problem-solving formula that provides you with step-by-step instructions used to achieve a desired outcome (Kahneman, 2011). You can think of an algorithm as a recipe with highly detailed instructions that produce the same result every time they are performed. Algorithms are used frequently in our everyday lives, especially in computer science. When you run a search on the Internet, search engines like Google use algorithms to decide which entries will appear first in your list of results. Facebook also uses algorithms to decide which posts to display on your newsfeed. Can you identify other situations in which algorithms are used?

A heuristic is another type of problem solving strategy. While an algorithm must be followed exactly to produce a correct result, a heuristic is a general problem-solving framework (Tversky & Kahneman, 1974). You can think of these as mental shortcuts that are used to solve problems. A “rule of thumb” is an example of a heuristic. Such a rule saves the person time and energy when making a decision, but despite its time-saving characteristics, it is not always the best method for making a rational decision. Different types of heuristics are used in different types of situations, but the impulse to use a heuristic occurs when one of five conditions is met (Pratkanis, 1989):

• When one is faced with too much information
• When the time to make a decision is limited
• When the decision to be made is unimportant
• When there is access to very little information to use in making the decision
• When an appropriate heuristic happens to come to mind in the same moment

Working backwards is a useful heuristic in which you begin solving the problem by focusing on the end result. Consider this example: You live in Washington, D.C. and have been invited to a wedding at 4 PM on Saturday in Philadelphia. Knowing that Interstate 95 tends to back up any day of the week, you need to plan your route and time your departure accordingly. If you want to be at the wedding service by 3:30 PM, and it takes 2.5 hours to get to Philadelphia without traffic, what time should you leave your house? You use the working backwards heuristic to plan the events of your day on a regular basis, probably without even thinking about it.

Another useful heuristic is the practice of accomplishing a large goal or task by breaking it into a series of smaller steps. Students often use this common method to complete a large research project or long essay for school. For example, students typically brainstorm, develop a thesis or main topic, research the chosen topic, organize their information into an outline, write a rough draft, revise and edit the rough draft, develop a final draft, organize the references list, and proofread their work before turning in the project. The large task becomes less overwhelming when it is broken down into a series of small steps.

Further problem solving strategies have been identified (listed below) that incorporate flexible and creative thinking in order to reach solutions efficiently.

Additional Problem Solving Strategies :

• Abstraction – refers to solving the problem within a model of the situation before applying it to reality.
• Analogy – is using a solution that solves a similar problem.
• Brainstorming – refers to collecting an analyzing a large amount of solutions, especially within a group of people, to combine the solutions and developing them until an optimal solution is reached.
• Divide and conquer – breaking down large complex problems into smaller more manageable problems.
• Hypothesis testing – method used in experimentation where an assumption about what would happen in response to manipulating an independent variable is made, and analysis of the affects of the manipulation are made and compared to the original hypothesis.
• Lateral thinking – approaching problems indirectly and creatively by viewing the problem in a new and unusual light.
• Means-ends analysis – choosing and analyzing an action at a series of smaller steps to move closer to the goal.
• Method of focal objects – putting seemingly non-matching characteristics of different procedures together to make something new that will get you closer to the goal.
• Morphological analysis – analyzing the outputs of and interactions of many pieces that together make up a whole system.
• Proof – trying to prove that a problem cannot be solved. Where the proof fails becomes the starting point or solving the problem.
• Reduction – adapting the problem to be as similar problems where a solution exists.
• Research – using existing knowledge or solutions to similar problems to solve the problem.
• Root cause analysis – trying to identify the cause of the problem.

The strategies listed above outline a short summary of methods we use in working toward solutions and also demonstrate how the mind works when being faced with barriers preventing goals to be reached.

One example of means-end analysis can be found by using the Tower of Hanoi paradigm . This paradigm can be modeled as a word problems as demonstrated by the Missionary-Cannibal Problem :

Missionary-Cannibal Problem

Three missionaries and three cannibals are on one side of a river and need to cross to the other side. The only means of crossing is a boat, and the boat can only hold two people at a time. Your goal is to devise a set of moves that will transport all six of the people across the river, being in mind the following constraint: The number of cannibals can never exceed the number of missionaries in any location. Remember that someone will have to also row that boat back across each time.

Hint : At one point in your solution, you will have to send more people back to the original side than you just sent to the destination.

The actual Tower of Hanoi problem consists of three rods sitting vertically on a base with a number of disks of different sizes that can slide onto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top making a conical shape. The objective of the puzzle is to move the entire stack to another rod obeying the following rules:

• 1. Only one disk can be moved at a time.
• 2. Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod.
• 3. No disc may be placed on top of a smaller disk.

  Figure 7.02. Steps for solving the Tower of Hanoi in the minimum number of moves when there are 3 disks.

Figure 7.03. Graphical representation of nodes (circles) and moves (lines) of Tower of Hanoi.

The Tower of Hanoi is a frequently used psychological technique to study problem solving and procedure analysis. A variation of the Tower of Hanoi known as the Tower of London has been developed which has been an important tool in the neuropsychological diagnosis of executive function disorders and their treatment.

GESTALT PSYCHOLOGY AND PROBLEM SOLVING

As you may recall from the sensation and perception chapter, Gestalt psychology describes whole patterns, forms and configurations of perception and cognition such as closure, good continuation, and figure-ground. In addition to patterns of perception, Wolfgang Kohler, a German Gestalt psychologist traveled to the Spanish island of Tenerife in order to study animals behavior and problem solving in the anthropoid ape.

As an interesting side note to Kohler’s studies of chimp problem solving, Dr. Ronald Ley, professor of psychology at State University of New York provides evidence in his book A Whisper of Espionage  (1990) suggesting that while collecting data for what would later be his book  The Mentality of Apes (1925) on Tenerife in the Canary Islands between 1914 and 1920, Kohler was additionally an active spy for the German government alerting Germany to ships that were sailing around the Canary Islands. Ley suggests his investigations in England, Germany and elsewhere in Europe confirm that Kohler had served in the German military by building, maintaining and operating a concealed radio that contributed to Germany’s war effort acting as a strategic outpost in the Canary Islands that could monitor naval military activity approaching the north African coast.

While trapped on the island over the course of World War 1, Kohler applied Gestalt principles to animal perception in order to understand how they solve problems. He recognized that the apes on the islands also perceive relations between stimuli and the environment in Gestalt patterns and understand these patterns as wholes as opposed to pieces that make up a whole. Kohler based his theories of animal intelligence on the ability to understand relations between stimuli, and spent much of his time while trapped on the island investigation what he described as  insight , the sudden perception of useful or proper relations. In order to study insight in animals, Kohler would present problems to chimpanzee’s by hanging some banana’s or some kind of food so it was suspended higher than the apes could reach. Within the room, Kohler would arrange a variety of boxes, sticks or other tools the chimpanzees could use by combining in patterns or organizing in a way that would allow them to obtain the food (Kohler & Winter, 1925).

While viewing the chimpanzee’s, Kohler noticed one chimp that was more efficient at solving problems than some of the others. The chimp, named Sultan, was able to use long poles to reach through bars and organize objects in specific patterns to obtain food or other desirables that were originally out of reach. In order to study insight within these chimps, Kohler would remove objects from the room to systematically make the food more difficult to obtain. As the story goes, after removing many of the objects Sultan was used to using to obtain the food, he sat down ad sulked for a while, and then suddenly got up going over to two poles lying on the ground. Without hesitation Sultan put one pole inside the end of the other creating a longer pole that he could use to obtain the food demonstrating an ideal example of what Kohler described as insight. In another situation, Sultan discovered how to stand on a box to reach a banana that was suspended from the rafters illustrating Sultan’s perception of relations and the importance of insight in problem solving.

Grande (another chimp in the group studied by Kohler) builds a three-box structure to reach the bananas, while Sultan watches from the ground.  Insight , sometimes referred to as an “Ah-ha” experience, was the term Kohler used for the sudden perception of useful relations among objects during problem solving (Kohler, 1927; Radvansky & Ashcraft, 2013).

Solving puzzles.

   Problem-solving abilities can improve with practice. Many people challenge themselves every day with puzzles and other mental exercises to sharpen their problem-solving skills. Sudoku puzzles appear daily in most newspapers. Typically, a sudoku puzzle is a 9×9 grid. The simple sudoku below (see figure) is a 4×4 grid. To solve the puzzle, fill in the empty boxes with a single digit: 1, 2, 3, or 4. Here are the rules: The numbers must total 10 in each bolded box, each row, and each column; however, each digit can only appear once in a bolded box, row, and column. Time yourself as you solve this puzzle and compare your time with a classmate.

How long did it take you to solve this sudoku puzzle? (You can see the answer at the end of this section.)

   Here is another popular type of puzzle (figure below) that challenges your spatial reasoning skills. Connect all nine dots with four connecting straight lines without lifting your pencil from the paper:

Did you figure it out? (The answer is at the end of this section.) Once you understand how to crack this puzzle, you won’t forget.

   Take a look at the “Puzzling Scales” logic puzzle below (figure below). Sam Loyd, a well-known puzzle master, created and refined countless puzzles throughout his lifetime (Cyclopedia of Puzzles, n.d.).

What steps did you take to solve this puzzle? You can read the solution at the end of this section.

Pitfalls to problem solving.

   Not all problems are successfully solved, however. What challenges stop us from successfully solving a problem? Albert Einstein once said, “Insanity is doing the same thing over and over again and expecting a different result.” Imagine a person in a room that has four doorways. One doorway that has always been open in the past is now locked. The person, accustomed to exiting the room by that particular doorway, keeps trying to get out through the same doorway even though the other three doorways are open. The person is stuck—but she just needs to go to another doorway, instead of trying to get out through the locked doorway. A mental set is where you persist in approaching a problem in a way that has worked in the past but is clearly not working now.

Functional fixedness is a type of mental set where you cannot perceive an object being used for something other than what it was designed for. During the Apollo 13 mission to the moon, NASA engineers at Mission Control had to overcome functional fixedness to save the lives of the astronauts aboard the spacecraft. An explosion in a module of the spacecraft damaged multiple systems. The astronauts were in danger of being poisoned by rising levels of carbon dioxide because of problems with the carbon dioxide filters. The engineers found a way for the astronauts to use spare plastic bags, tape, and air hoses to create a makeshift air filter, which saved the lives of the astronauts.

   Researchers have investigated whether functional fixedness is affected by culture. In one experiment, individuals from the Shuar group in Ecuador were asked to use an object for a purpose other than that for which the object was originally intended. For example, the participants were told a story about a bear and a rabbit that were separated by a river and asked to select among various objects, including a spoon, a cup, erasers, and so on, to help the animals. The spoon was the only object long enough to span the imaginary river, but if the spoon was presented in a way that reflected its normal usage, it took participants longer to choose the spoon to solve the problem. (German & Barrett, 2005). The researchers wanted to know if exposure to highly specialized tools, as occurs with individuals in industrialized nations, affects their ability to transcend functional fixedness. It was determined that functional fixedness is experienced in both industrialized and nonindustrialized cultures (German & Barrett, 2005).

In order to make good decisions, we use our knowledge and our reasoning. Often, this knowledge and reasoning is sound and solid. Sometimes, however, we are swayed by biases or by others manipulating a situation. For example, let’s say you and three friends wanted to rent a house and had a combined target budget of $1,600. The realtor shows you only very run-down houses for $1,600 and then shows you a very nice house for $2,000. Might you ask each person to pay more in rent to get the $2,000 home? Why would the realtor show you the run-down houses and the nice house? The realtor may be challenging your anchoring bias. An anchoring bias occurs when you focus on one piece of information when making a decision or solving a problem. In this case, you’re so focused on the amount of money you are willing to spend that you may not recognize what kinds of houses are available at that price point.

The confirmation bias is the tendency to focus on information that confirms your existing beliefs. For example, if you think that your professor is not very nice, you notice all of the instances of rude behavior exhibited by the professor while ignoring the countless pleasant interactions he is involved in on a daily basis. Hindsight bias leads you to believe that the event you just experienced was predictable, even though it really wasn’t. In other words, you knew all along that things would turn out the way they did. Representative bias describes a faulty way of thinking, in which you unintentionally stereotype someone or something; for example, you may assume that your professors spend their free time reading books and engaging in intellectual conversation, because the idea of them spending their time playing volleyball or visiting an amusement park does not fit in with your stereotypes of professors.

Finally, the availability heuristic is a heuristic in which you make a decision based on an example, information, or recent experience that is that readily available to you, even though it may not be the best example to inform your decision . Biases tend to “preserve that which is already established—to maintain our preexisting knowledge, beliefs, attitudes, and hypotheses” (Aronson, 1995; Kahneman, 2011). These biases are summarized in the table below.

Were you able to determine how many marbles are needed to balance the scales in the figure below? You need nine. Were you able to solve the problems in the figures above? Here are the answers.

   Many different strategies exist for solving problems. Typical strategies include trial and error, applying algorithms, and using heuristics. To solve a large, complicated problem, it often helps to break the problem into smaller steps that can be accomplished individually, leading to an overall solution. Roadblocks to problem solving include a mental set, functional fixedness, and various biases that can cloud decision making skills.

References:

Openstax Psychology text by Kathryn Dumper, William Jenkins, Arlene Lacombe, Marilyn Lovett and Marion Perlmutter licensed under CC BY v4.0. https://openstax.org/details/books/psychology

Review Questions:

1. A specific formula for solving a problem is called ________.

a. an algorithm

b. a heuristic

c. a mental set

d. trial and error

2. Solving the Tower of Hanoi problem tends to utilize a  ________ strategy of problem solving.

a. divide and conquer

b. means-end analysis

d. experiment

3. A mental shortcut in the form of a general problem-solving framework is called ________.

4. Which type of bias involves becoming fixated on a single trait of a problem?

a. anchoring bias

b. confirmation bias

c. representative bias

d. availability bias

5. Which type of bias involves relying on a false stereotype to make a decision?

6. Wolfgang Kohler analyzed behavior of chimpanzees by applying Gestalt principles to describe ________.

a. social adjustment

b. student load payment options

c. emotional learning

d. insight learning

7. ________ is a type of mental set where you cannot perceive an object being used for something other than what it was designed for.

a. functional fixedness

c. working memory

Critical Thinking Questions:

1. What is functional fixedness and how can overcoming it help you solve problems?

2. How does an algorithm save you time and energy when solving a problem?

Personal Application Question:

1. Which type of bias do you recognize in your own decision making processes? How has this bias affected how you’ve made decisions in the past and how can you use your awareness of it to improve your decisions making skills in the future?

anchoring bias

availability heuristic

confirmation bias

functional fixedness

hindsight bias

problem-solving strategy

representative bias

trial and error

working backwards

Answers to Exercises

algorithm:  problem-solving strategy characterized by a specific set of instructions

anchoring bias:  faulty heuristic in which you fixate on a single aspect of a problem to find a solution

availability heuristic:  faulty heuristic in which you make a decision based on information readily available to you

confirmation bias:  faulty heuristic in which you focus on information that confirms your beliefs

functional fixedness:  inability to see an object as useful for any other use other than the one for which it was intended

heuristic:  mental shortcut that saves time when solving a problem

hindsight bias:  belief that the event just experienced was predictable, even though it really wasn’t

mental set:  continually using an old solution to a problem without results

problem-solving strategy:  method for solving problems

representative bias:  faulty heuristic in which you stereotype someone or something without a valid basis for your judgment

trial and error:  problem-solving strategy in which multiple solutions are attempted until the correct one is found

working backwards:  heuristic in which you begin to solve a problem by focusing on the end result

Share This Book

• Increase Font Size

• Bipolar Disorder
• Therapy Center
• When To See a Therapist
• Types of Therapy
• Best Online Therapy
• Best Couples Therapy
• Best Family Therapy
• Managing Stress
• Sleep and Dreaming
• Understanding Emotions
• Self-Improvement
• Healthy Relationships
• Student Resources
• Personality Types
• Guided Meditations
• Verywell Mind Insights
• 2024 Verywell Mind 25
• Mental Health in the Classroom
• Editorial Process
• Meet Our Review Board
• Crisis Support

Overview of the Problem-Solving Mental Process

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Rachel Goldman, PhD FTOS, is a licensed psychologist, clinical assistant professor, speaker, wellness expert specializing in eating behaviors, stress management, and health behavior change.

• Identify the Problem
• Define the Problem
• Form a Strategy
• Organize Information
• Allocate Resources
• Monitor Progress
• Evaluate the Results

Frequently Asked Questions

Problem-solving is a mental process that involves discovering, analyzing, and solving problems. The ultimate goal of problem-solving is to overcome obstacles and find a solution that best resolves the issue.

The best strategy for solving a problem depends largely on the unique situation. In some cases, people are better off learning everything they can about the issue and then using factual knowledge to come up with a solution. In other instances, creativity and insight are the best options.

It is not necessary to follow problem-solving steps sequentially, It is common to skip steps or even go back through steps multiple times until the desired solution is reached.

In order to correctly solve a problem, it is often important to follow a series of steps. Researchers sometimes refer to this as the problem-solving cycle. While this cycle is portrayed sequentially, people rarely follow a rigid series of steps to find a solution.

The following steps include developing strategies and organizing knowledge.

1. Identifying the Problem

While it may seem like an obvious step, identifying the problem is not always as simple as it sounds. In some cases, people might mistakenly identify the wrong source of a problem, which will make attempts to solve it inefficient or even useless.

Some strategies that you might use to figure out the source of a problem include :

• Asking questions about the problem
• Breaking the problem down into smaller pieces
• Looking at the problem from different perspectives
• Conducting research to figure out what relationships exist between different variables

2. Defining the Problem

After the problem has been identified, it is important to fully define the problem so that it can be solved. You can define a problem by operationally defining each aspect of the problem and setting goals for what aspects of the problem you will address

At this point, you should focus on figuring out which aspects of the problems are facts and which are opinions. State the problem clearly and identify the scope of the solution.

3. Forming a Strategy

After the problem has been identified, it is time to start brainstorming potential solutions. This step usually involves generating as many ideas as possible without judging their quality. Once several possibilities have been generated, they can be evaluated and narrowed down.

The next step is to develop a strategy to solve the problem. The approach used will vary depending upon the situation and the individual's unique preferences. Common problem-solving strategies include heuristics and algorithms.

• Heuristics are mental shortcuts that are often based on solutions that have worked in the past. They can work well if the problem is similar to something you have encountered before and are often the best choice if you need a fast solution.
• Algorithms are step-by-step strategies that are guaranteed to produce a correct result. While this approach is great for accuracy, it can also consume time and resources.

Heuristics are often best used when time is of the essence, while algorithms are a better choice when a decision needs to be as accurate as possible.

4. Organizing Information

Before coming up with a solution, you need to first organize the available information. What do you know about the problem? What do you not know? The more information that is available the better prepared you will be to come up with an accurate solution.

When approaching a problem, it is important to make sure that you have all the data you need. Making a decision without adequate information can lead to biased or inaccurate results.

5. Allocating Resources

Of course, we don't always have unlimited money, time, and other resources to solve a problem. Before you begin to solve a problem, you need to determine how high priority it is.

If it is an important problem, it is probably worth allocating more resources to solving it. If, however, it is a fairly unimportant problem, then you do not want to spend too much of your available resources on coming up with a solution.

At this stage, it is important to consider all of the factors that might affect the problem at hand. This includes looking at the available resources, deadlines that need to be met, and any possible risks involved in each solution. After careful evaluation, a decision can be made about which solution to pursue.

6. Monitoring Progress

After selecting a problem-solving strategy, it is time to put the plan into action and see if it works. This step might involve trying out different solutions to see which one is the most effective.

It is also important to monitor the situation after implementing a solution to ensure that the problem has been solved and that no new problems have arisen as a result of the proposed solution.

Effective problem-solvers tend to monitor their progress as they work towards a solution. If they are not making good progress toward reaching their goal, they will reevaluate their approach or look for new strategies .

7. Evaluating the Results

After a solution has been reached, it is important to evaluate the results to determine if it is the best possible solution to the problem. This evaluation might be immediate, such as checking the results of a math problem to ensure the answer is correct, or it can be delayed, such as evaluating the success of a therapy program after several months of treatment.

Once a problem has been solved, it is important to take some time to reflect on the process that was used and evaluate the results. This will help you to improve your problem-solving skills and become more efficient at solving future problems.

A Word From Verywell​

It is important to remember that there are many different problem-solving processes with different steps, and this is just one example. Problem-solving in real-world situations requires a great deal of resourcefulness, flexibility, resilience, and continuous interaction with the environment.

Get Advice From The Verywell Mind Podcast

Hosted by therapist Amy Morin, LCSW, this episode of The Verywell Mind Podcast shares how you can stop dwelling in a negative mindset.

Follow Now : Apple Podcasts / Spotify / Google Podcasts

You can become a better problem solving by:

• Practicing brainstorming and coming up with multiple potential solutions to problems
• Being open-minded and considering all possible options before making a decision
• Breaking down problems into smaller, more manageable pieces
• Asking for help when needed
• Researching different problem-solving techniques and trying out new ones
• Learning from mistakes and using them as opportunities to grow

It's important to communicate openly and honestly with your partner about what's going on. Try to see things from their perspective as well as your own. Work together to find a resolution that works for both of you. Be willing to compromise and accept that there may not be a perfect solution.

Take breaks if things are getting too heated, and come back to the problem when you feel calm and collected. Don't try to fix every problem on your own—consider asking a therapist or counselor for help and insight.

If you've tried everything and there doesn't seem to be a way to fix the problem, you may have to learn to accept it. This can be difficult, but try to focus on the positive aspects of your life and remember that every situation is temporary. Don't dwell on what's going wrong—instead, think about what's going right. Find support by talking to friends or family. Seek professional help if you're having trouble coping.

Davidson JE, Sternberg RJ, editors.  The Psychology of Problem Solving .  Cambridge University Press; 2003. doi:10.1017/CBO9780511615771

Sarathy V. Real world problem-solving .  Front Hum Neurosci . 2018;12:261. Published 2018 Jun 26. doi:10.3389/fnhum.2018.00261

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Learn Creative Problem Solving Techniques to Stimulate Innovation in Your Organization

By Kate Eby | October 20, 2017 (updated August 27, 2021)

• Share on Facebook
• Share on LinkedIn

Link copied

In today’s competitive business landscape, organizations need processes in place to make strong, well-informed, and innovative decisions. Problem solving - in particular creative problem solving (CPS) - is a key skill in learning how to accurately identify problems and their causes, generate potential solutions, and evaluate all the possibilities to arrive at a strong corrective course of action. Every team in any organization, regardless of department or industry, needs to be effective, creative, and quick when solving problems. 

In this article, we’ll discuss traditional and creative problem solving, and define the steps, best practices, and common barriers associated. After that, we’ll provide helpful methods and tools to identify the cause(s) of problematic situations, so you can get to the root of the issue and start to generate solutions. Then, we offer nearly 20 creative problem solving techniques to implement at your organization, or even in your personal life. Along the way, experts weigh in on the importance of problem solving, and offer tips and tricks. 

What Is Problem Solving and Decision Making?

Problem solving is the process of working through every aspect of an issue or challenge to reach a solution. Decision making is choosing one of multiple proposed solutions  — therefore, this process also includes defining and evaluating all potential options. Decision making is often one step of the problem solving process, but the two concepts are distinct. 

Collective problem solving is problem solving that includes many different parties and bridges the knowledge of different groups. Collective problem solving is common in business problem solving because workplace decisions typically affect more than one person. 

Problem solving, especially in business, is a complicated science. Not only are business conflicts multifaceted, but they often involve different personalities, levels of authority, and group dynamics. In recent years, however, there has been a rise in psychology-driven problem solving techniques, especially for the workplace. In fact, the psychology of how people solve problems is now studied formally in academic disciplines such as psychology and cognitive science.

Joe Carella is the Assistant Dean for Executive Education at the University of Arizona . Joe has over 20 years of experience in helping executives and corporations in managing change and developing successful business strategies. His doctoral research and executive education engagements have seen him focus on corporate strategy, decision making and business performance with a variety of corporate clients including Hershey’s, Chevron, Fender Musical Instruments Corporation, Intel, DP World, Essilor, BBVA Compass Bank.

He explains some of the basic psychology behind problem solving: “When our brain is engaged in the process of solving problems, it is engaged in a series of steps where it processes and organizes the information it receives while developing new knowledge it uses in future steps. Creativity is embedded in this process by incorporating diverse inputs and/or new ways of organizing the information received.”

Laura MacLeod is a Professor of Social Group Work at City University of New York, and the creator of From The Inside Out Project® , a program that coaches managers in team leadership for a variety of workplaces. She has a background in social work and over two decades of experience as a union worker, and currently leads talks on conflict resolution, problem solving, and listening skills at conferences across the country. 

MacLeod thinks of problem solving as an integral practice of successful organizations. “Problem solving is a collaborative process — all voices are heard and connected, and resolution is reached by the group,” she says. “Problems and conflicts occur in all groups and teams in the workplace, but if leaders involve everyone in working through, they will foster cohesion, engagement, and buy in. Everybody wins.”

10 tips that will make you more productive.

Uncover the top three factors that are killing your productivity and 10 tips to help you overcome them.

Download the free e-book to overcome my productivity killers

Project Management Guide

Your one-stop shop for everything project management

Ready to get more out of your project management efforts? Visit our comprehensive project management guide for tips, best practices, and free resources to manage your work more effectively.

View the guide

What Is the First Step in Solving a Problem?

Although problem solving techniques vary procedurally, experts agree that the first step in solving a problem is defining the problem. Without a clear articulation of the problem at stake, it is impossible to analyze all the key factors and actors, generate possible solutions, and then evaluate them to pick the best option. 

Dr. Elliott Jaffa is a behavioral and management psychologist with over 25 years of problem solving training and management experience. “Start with defining the problem you want to solve,” he says, “And then define where you want to be, what you want to come away with.” He emphasizes these are the first steps in creating an actionable, clear solution. 

Bryan Mattimore is Co-Founder of Growth Engine, an 18-year old innovation agency based in Norwalk, CT. Bryan has facilitated over 1,000 ideation sessions and managed over 200 successful innovation projects leading to over $3 billion in new sales. His newest book is 21 Days to a Big Idea . When asked about the first critical component to successful problem solving, Mattimore says, “Defining the challenge correctly, or ‘solving the right problem’ … The three creative techniques we use to help our clients ‘identify the right problem to be solved’ are questioning assumptions, 20 questions, and problem redefinition. A good example of this was a new product challenge from a client to help them ‘invent a new iron. We got them to redefine the challenge as first: a) inventing new anti-wrinkle devices, and then b) inventing new garment care devices.”

What Are Problem Solving Skills?

To understand the necessary skills in problem solving, you should first understand the types of thinking often associated with strong decision making. Most problem solving techniques look for a balance between the following binaries:

• Convergent vs. Divergent Thinking: Convergent thinking is bringing together disparate information or ideas to determine a single best answer or solution. This thinking style values logic, speed, and accuracy, and leaves no chance for ambiguity. Divergent thinking is focused on generating new ideas to identify and evaluate multiple possible solutions, often uniting ideas in unexpected combinations. Divergent thinking is characterized by creativity, complexity, curiosity, flexibility, originality, and risk-taking.
• Pragmatics vs. Semantics: Pragmatics refer to the logic of the problem at hand, and semantics is how you interpret the problem to solve it. Both are important to yield the best possible solution.
• Mathematical vs. Personal Problem Solving: Mathematical problem solving involves logic (usually leading to a single correct answer), and is useful for problems that involve numbers or require an objective, clear-cut solution. However, many workplace problems also require personal problem solving, which includes interpersonal, collaborative, and emotional intuition and skills. 

The following basic methods are fundamental problem solving concepts. Implement them to help balance the above thinking models.

• Reproductive Thinking: Reproductive thinking uses past experience to solve a problem. However, be careful not to rely too heavily on past solutions, and to evaluate current problems individually, with their own factors and parameters. 
• Idea Generation: The process of generating many possible courses of action to identify a solution. This is most commonly a team exercise because putting everyone’s ideas on the table will yield the greatest number of potential solutions. 

However, many of the most critical problem solving skills are “soft” skills: personal and interpersonal understanding, intuitiveness, and strong listening. 

Mattimore expands on this idea: “The seven key skills to be an effective creative problem solver that I detail in my book Idea Stormers: How to Lead and Inspire Creative Breakthroughs are: 1) curiosity 2) openness 3) a willingness to embrace ambiguity 4) the ability to identify and transfer principles across categories and disciplines 5) the desire to search for integrity in ideas, 6) the ability to trust and exercise “knowingness” and 7) the ability to envision new worlds (think Dr. Seuss, Star Wars, Hunger Games, Harry Potter, etc.).”

“As an individual contributor to problem solving it is important to exercise our curiosity, questioning, and visioning abilities,” advises Carella. “As a facilitator it is essential to allow for diverse ideas to emerge, be able to synthesize and ‘translate’ other people’s thinking, and build an extensive network of available resources.”

MacLeod says the following interpersonal skills are necessary to effectively facilitate group problem solving: “The abilities to invite participation (hear all voices, encourage silent members), not take sides, manage dynamics between the monopolizer, the scapegoat, and the bully, and deal with conflict (not avoiding it or shutting down).” 

Furthermore, Jaffa explains that the skills of a strong problem solver aren’t measurable. The best way to become a creative problem solver, he says, is to do regular creative exercises that keep you sharp and force you to think outside the box. Carella echoes this sentiment: “Neuroscience tells us that creativity comes from creating novel neural paths. Allow a few minutes each day to exercise your brain with novel techniques and brain ‘tricks’ – read something new, drive to work via a different route, count backwards, smell a new fragrance, etc.”

What Is Creative Problem Solving? History, Evolution, and Core Principles

Creative problem solving (CPS) is a method of problem solving in which you approach a problem or challenge in an imaginative, innovative way. The goal of CPS is to come up with innovative solutions, make a decision, and take action quickly. Sidney Parnes and Alex Osborn are credited with developing the creative problem solving process in the 1950s. The concept was further studied and developed at SUNY Buffalo State and the Creative Education Foundation. 

The core principles of CPS include the following:

• Balance divergent and convergent thinking
• Ask problems as questions
• Defer or suspend judgement
• Focus on “Yes, and…” rather than “No, but…”

According to Carella, “Creative problem solving is the mental process used for generating innovative and imaginative ideas as a solution to a problem or a challenge. Creative problem solving techniques can be pursued by individuals or groups.”

When asked to define CPS, Jaffa explains that it is, by nature, difficult to create boundaries for. “Creative problem solving is not cut and dry,” he says, “If you ask 100 different people the definition of creative problem solving, you’ll get 100 different responses - it’s a non-entity.”

Business presents a unique need for creative problem solving. Especially in today’s competitive landscape, organizations need to iterate quickly, innovate with intention, and constantly be at the cutting-edge of creativity and new ideas to succeed. Developing CPS skills among your workforce not only enables you to make faster, stronger in-the-moment decisions, but also inspires a culture of collaborative work and knowledge sharing. When people work together to generate multiple novel ideas and evaluate solutions, they are also more likely to arrive at an effective decision, which will improve business processes and reduce waste over time. In fact, CPS is so important that some companies now list creative problem solving skills as a job criteria.

MacLeod reiterates the vitality of creative problem solving in the workplace. “Problem solving is crucial for all groups and teams,” she says. “Leaders need to know how to guide the process, hear all voices and involve all members - it’s not easy.”

“This mental process [of CPS] is especially helpful in work environments where individuals and teams continuously struggle with new problems and challenges posed by their continuously changing environment,” adds Carella. 

Problem Solving Best Practices

By nature, creative problem solving does not have a clear-cut set of do’s and don’ts. Rather, creating a culture of strong creative problem solvers requires flexibility, adaptation, and interpersonal skills. However, there are a several best practices that you should incorporate:

• Use a Systematic Approach: Regardless of the technique you use, choose a systematic method that satisfies your workplace conditions and constraints (time, resources, budget, etc.). Although you want to preserve creativity and openness to new ideas, maintaining a structured approach to the process will help you stay organized and focused. 
• View Problems as Opportunities: Rather than focusing on the negatives or giving up when you encounter barriers, treat problems as opportunities to enact positive change on the situation. In fact, some experts even recommend defining problems as opportunities, to remain proactive and positive.
• Change Perspective: Remember that there are multiple ways to solve any problem. If you feel stuck, changing perspective can help generate fresh ideas. A perspective change might entail seeking advice of a mentor or expert, understanding the context of a situation, or taking a break and returning to the problem later. “A sterile or familiar environment can stifle new thinking and new perspectives,” says Carella. “Make sure you get out to draw inspiration from spaces and people out of your usual reach.”
• Break Down Silos: To invite the greatest possible number of perspectives to any problem, encourage teams to work cross-departmentally. This not only combines diverse expertise, but also creates a more trusting and collaborative environment, which is essential to effective CPS. According to Carella, “Big challenges are always best tackled by a group of people rather than left to a single individual. Make sure you create a space where the team can concentrate and convene.”
• Employ Strong Leadership or a Facilitator: Some companies choose to hire an external facilitator that teaches problem solving techniques, best practices, and practicums to stimulate creative problem solving. But, internal managers and staff can also oversee these activities. Regardless of whether the facilitator is internal or external, choose a strong leader who will value others’ ideas and make space for creative solutions.  Mattimore has specific advice regarding the role of a facilitator: “When facilitating, get the group to name a promising idea (it will crystalize the idea and make it more memorable), and facilitate deeper rather than broader. Push for not only ideas, but how an idea might specifically work, some of its possible benefits, who and when would be interested in an idea, etc. This fleshing-out process with a group will generate fewer ideas, but at the end of the day will yield more useful concepts that might be profitably pursued.” Additionally, Carella says that “Executives and managers don’t necessarily have to be creative problem solvers, but need to make sure that their teams are equipped with the right tools and resources to make this happen. Also they need to be able to foster an environment where failing fast is accepted and celebrated.”
• Evaluate Your Current Processes: This practice can help you unlock bottlenecks, and also identify gaps in your data and information management, both of which are common roots of business problems.

MacLeod offers the following additional advice, “Always get the facts. Don’t jump too quickly to a solution – working through [problems] takes time and patience.”

Mattimore also stresses that how you introduce creative problem solving is important. “Do not start by introducing a new company-wide innovation process,” he says. “Instead, encourage smaller teams to pursue specific creative projects, and then build a process from the ground up by emulating these smaller teams’ successful approaches. We say: ‘You don’t innovate by changing the culture, you change the culture by innovating.’”

Barriers to Effective Problem Solving

Learning how to effectively solve problems is difficult and takes time and continual adaptation. There are several common barriers to successful CPS, including:

• Confirmation Bias: The tendency to only search for or interpret information that confirms a person’s existing ideas. People misinterpret or disregard data that doesn’t align with their beliefs.
• Mental Set: People’s inclination to solve problems using the same tactics they have used to solve problems in the past. While this can sometimes be a useful strategy (see Analogical Thinking in a later section), it often limits inventiveness and creativity.
• Functional Fixedness: This is another form of narrow thinking, where people become “stuck” thinking in a certain way and are unable to be flexible or change perspective.
• Unnecessary Constraints: When people are overwhelmed with a problem, they can invent and impose additional limits on solution avenues. To avoid doing this, maintain a structured, level-headed approach to evaluating causes, effects, and potential solutions.
• Groupthink: Be wary of the tendency for group members to agree with each other — this might be out of conflict avoidance, path of least resistance, or fear of speaking up. While this agreeableness might make meetings run smoothly, it can actually stunt creativity and idea generation, therefore limiting the success of your chosen solution.
• Irrelevant Information: The tendency to pile on multiple problems and factors that may not even be related to the challenge at hand. This can cloud the team’s ability to find direct, targeted solutions.
• Paradigm Blindness: This is found in people who are unwilling to adapt or change their worldview, outlook on a particular problem, or typical way of processing information. This can erode the effectiveness of problem solving techniques because they are not aware of the narrowness of their thinking, and therefore cannot think or act outside of their comfort zone.

According to Jaffa, the primary barrier of effective problem solving is rigidity. “The most common things people say are, ‘We’ve never done it before,’ or ‘We’ve always done it this way.’” While these feelings are natural, Jaffa explains that this rigid thinking actually precludes teams from identifying creative, inventive solutions that result in the greatest benefit.

“The biggest barrier to creative problem solving is a lack of awareness – and commitment to – training employees in state-of-the-art creative problem-solving techniques,” Mattimore explains. “We teach our clients how to use ideation techniques (as many as two-dozen different creative thinking techniques) to help them generate more and better ideas. Ideation techniques use specific and customized stimuli, or ‘thought triggers’ to inspire new thinking and new ideas.” 

MacLeod adds that ineffective or rushed leadership is another common culprit. “We're always in a rush to fix quickly,” she says. “Sometimes leaders just solve problems themselves, making unilateral decisions to save time. But the investment is well worth it — leaders will have less on their plates if they can teach and eventually trust the team to resolve. Teams feel empowered and engagement and investment increases.”

Strategies for Problem Cause Identification

As discussed, most experts agree that the first and most crucial step in problem solving is defining the problem. Once you’ve done this, however, it may not be appropriate to move straight to the solution phase. Rather, it is often helpful to identify the cause(s) of the problem: This will better inform your solution planning and execution, and help ensure that you don’t fall victim to the same challenges in the future. 

Below are some of the most common strategies for identifying the cause of a problem:

• Root Cause Analysis: This method helps identify the most critical cause of a problem. A factor is considered a root cause if removing it prevents the problem from recurring. Performing a root cause analysis is a 12 step process that includes: define the problem, gather data on the factors contributing to the problem, group the factors based on shared characteristics, and create a cause-and-effect timeline to determine the root cause. After that, you identify and evaluate corrective actions to eliminate the root cause.

‌ Download Fishbone Diagram Template - Excel

Download 5 Whys Template   Excel  |  Word  |  PDF   

Problem Solving Techniques and Strategies

In this section, we’ll explain several traditional and creative problem solving methods that you can use to identify challenges, create actionable goals, and resolve problems as they arise. Although there is often procedural and objective crossover among techniques, they are grouped by theme so you can identify which method works best for your organization.

Divergent Creative Problem Solving Techniques

Brainstorming: One of the most common methods of divergent thinking, brainstorming works best in an open group setting where everyone is encouraged to share their creative ideas. The goal is to generate as many ideas as possible – you analyze, critique, and evaluate the ideas only after the brainstorming session is complete. To learn more specific brainstorming techniques, read this article . 

Mind Mapping: This is a visual thinking tool where you graphically depict concepts and their relation to one another. You can use mind mapping to structure the information you have, analyze and synthesize it, and generate solutions and new ideas from there. The goal of a mind map is to simplify complicated problems so you can more clearly identify solutions.

Appreciative Inquiry (AI): The basic assumption of AI is that “an organization is a mystery to be embraced.” Using this principle, AI takes a positive, inquisitive approach to identifying the problem, analyzing the causes, and presenting possible solutions. The five principles of AI emphasize dialogue, deliberate language and outlook, and social bonding. 

Lateral Thinking: This is an indirect problem solving approach centered on the momentum of idea generation. As opposed to critical thinking, where people value ideas based on their truth and the absence of errors, lateral thinking values the “movement value” of new ideas: This means that you reward team members for producing a large volume of new ideas rapidly. With this approach, you’ll generate many new ideas before approving or rejecting any.

Problem Solving Techniques to Change Perspective

Constructive Controversy: This is a structured approach to group decision making to preserve critical thinking and disagreement while maintaining order. After defining the problem and presenting multiple courses of action, the group divides into small advocacy teams who research, analyze, and refute a particular option. Once each advocacy team has presented its best-case scenario, the group has a discussion (advocacy teams still defend their presented idea). Arguing and playing devil’s advocate is encouraged to reach an understanding of the pros and cons of each option. Next, advocacy teams abandon their cause and evaluate the options openly until they reach a consensus. All team members formally commit to the decision, regardless of whether they advocated for it at the beginning. You can learn more about the goals and steps in constructive controversy here . 

Carella is a fan of this approach. “Create constructive controversy by having two teams argue the pros and cons of a certain idea,” he says. “It forces unconscious biases to surface and gives space for new ideas to formulate.”

Abstraction: In this method, you apply the problem to a fictional model of the current situation. Mapping an issue to an abstract situation can shed extraneous or irrelevant factors, and reveal places where you are overlooking obvious solutions or becoming bogged down by circumstances. 

Analogical Thinking: Also called analogical reasoning , this method relies on an analogy: using information from one problem to solve another problem (these separate problems are called domains). It can be difficult for teams to create analogies among unrelated problems, but it is a strong technique to help you identify repeated issues, zoom out and change perspective, and prevent the problems from occurring in the future. .

CATWOE: This framework ensures that you evaluate the perspectives of those whom your decision will impact. The factors and questions to consider include (which combine to make the acronym CATWOE):

• Customers: Who is on the receiving end of your decisions? What problem do they currently have, and how will they react to your proposed solution?
• Actors: Who is acting to bring your solution to fruition? How will they respond and be affected by your decision?
• Transformation Process: What processes will you employ to transform your current situation and meet your goals? What are the inputs and outputs?
• World View: What is the larger context of your proposed solution? What is the larger, big-picture problem you are addressing?
• Owner: Who actually owns the process? How might they influence your proposed solution (positively or negatively), and how can you influence them to help you?
• Environmental Constraints: What are the limits (environmental, resource- and budget-wise, ethical, legal, etc.) on your ideas? How will you revise or work around these constraints?

Complex Problem Solving

Soft Systems Methodology (SSM): For extremely complex problems, SSM can help you identify how factors interact, and determine the best course of action. SSM was borne out of organizational process modeling and general systems theory, which hold that everything is part of a greater, interconnected system: This idea works well for “hard” problems (where logic and a single correct answer are prioritized), and less so for “soft” problems (i.e., human problems where factors such as personality, emotions, and hierarchy come into play). Therefore, SSM defines a seven step process for problem solving: 

• Begin with the problem or problematic situation 
• Express the problem or situation and build a rich picture of the themes of the problem 
• Identify the root causes of the problem (most commonly with CATWOE)
• Build conceptual models of human activity surrounding the problem or situation
• Compare models with real-world happenings
• Identify changes to the situation that are both feasible and desirable
• Take action to implement changes and improve the problematic situation

SSM can be used for any complex soft problem, and is also a useful tool in change management . 

Failure Mode and Effects Analysis (FMEA): This method helps teams anticipate potential problems and take steps to mitigate them. Use FMEA when you are designing (redesigning) a complex function, process, product, or service. First, identify the failure modes, which are the possible ways that a project could fail. Then, perform an effects analysis to understand the consequences of each of the potential downfalls. This exercise is useful for internalizing the severity of each potential failure and its effects so you can make adjustments or safeties in your plan. 

‌ Download FMEA Template  

Problem Solving Based on Data or Logic (Heuristic Methods)

TRIZ: A Russian-developed problem solving technique that values logic, analysis, and forecasting over intuition or soft reasoning. TRIZ (translated to “theory of inventive problem solving” or TIPS in English) is a systematic approach to defining and identifying an inventive solution to difficult problems. The method offers several strategies for arriving at an inventive solution, including a contradictions matrix to assess trade-offs among solutions, a Su-Field analysis which uses formulas to describe a system by its structure, and ARIZ (algorithm of inventive problem solving) which uses algorithms to find inventive solutions. 

Inductive Reasoning: A logical method that uses evidence to conclude that a certain answer is probable (this is opposed to deductive reasoning, where the answer is assumed to be true). Inductive reasoning uses a limited number of observations to make useful, logical conclusions (for example, the Scientific Method is an extreme example of inductive reasoning). However, this method doesn’t always map well to human problems in the workplace — in these instances, managers should employ intuitive inductive reasoning , which allows for more automatic, implicit conclusions so that work can progress. This, of course, retains the principle that these intuitive conclusions are not necessarily the one and only correct answer. 

Process-Oriented Problem Solving Methods

Plan Do Check Act (PDCA): This is an iterative management technique used to ensure continual improvement of products or processes. First, teams plan (establish objectives to meet desired end results), then do (implement the plan, new processes, or produce the output), then check (compare expected with actual results), and finally act (define how the organization will act in the future, based on the performance and knowledge gained in the previous three steps). 

Means-End Analysis (MEA): The MEA strategy is to reduce the difference between the current (problematic) state and the goal state. To do so, teams compile information on the multiple factors that contribute to the disparity between the current and goal states. Then they try to change or eliminate the factors one by one, beginning with the factor responsible for the greatest difference in current and goal state. By systematically tackling the multiple factors that cause disparity between the problem and desired outcome, teams can better focus energy and control each step of the process. 

Hurson’s Productive Thinking Model: This technique was developed by Tim Hurson, and is detailed in his 2007 book Think Better: An Innovator’s Guide to Productive Thinking . The model outlines six steps that are meant to give structure while maintaining creativity and critical thinking: 1) Ask “What is going on?” 2) Ask “What is success?” 3) Ask “What is the question?” 4) Generate answers 5) Forge the solution 6) Align resources. 

Control Influence Accept (CIA): The basic premise of CIA is that how you respond to problems determines how successful you will be in overcoming them. Therefore, this model is both a problem solving technique and stress-management tool that ensures you aren’t responding to problems in a reactive and unproductive way. The steps in CIA include:

• Control: Identify the aspects of the problem that are within your control.
• Influence: Identify the aspects of the problem that you cannot control, but that you can influence.
• Accept: Identify the aspects of the problem that you can neither control nor influence, and react based on this composite information. 

GROW Model: This is a straightforward problem solving method for goal setting that clearly defines your goals and current situation, and then asks you to define the potential solutions and be realistic about your chosen course of action. The steps break down as follows:

• Goal: What do you want?
• Reality: Where are you now?
• Options: What could you do?
• Will: What will you do?

OODA Loop: This acronym stands for observe, orient, decide, and act. This approach is a decision-making cycle that values agility and flexibility over raw human force. It is framed as a loop because of the understanding that any team will continually encounter problems or opponents to success and have to overcome them.

There are also many un-named creative problem solving techniques that follow a sequenced series of steps. While the exact steps vary slightly, they all follow a similar trajectory and aim to accomplish similar goals of problem, cause, and goal identification, idea generation, and active solution implementation.

MacLeod offers her own problem solving procedure, which echoes the above steps:

“1. Recognize the Problem: State what you see. Sometimes the problem is covert. 2. Identify: Get the facts — What exactly happened? What is the issue? 3. and 4. Explore and Connect: Dig deeper and encourage group members to relate their similar experiences. Now you're getting more into the feelings and background [of the situation], not just the facts.  5. Possible Solutions: Consider and brainstorm ideas for resolution. 6. Implement: Choose a solution and try it out — this could be role play and/or a discussion of how the solution would be put in place.  7. Evaluate: Revisit to see if the solution was successful or not.”

Many of these problem solving techniques can be used in concert with one another, or multiple can be appropriate for any given problem. It’s less about facilitating a perfect CPS session, and more about encouraging team members to continually think outside the box and push beyond personal boundaries that inhibit their innovative thinking. So, try out several methods, find those that resonate best with your team, and continue adopting new techniques and adapting your processes along the way. 

Improve Problem Solving with Work Management in Smartsheet

Empower your people to go above and beyond with a flexible platform designed to match the needs of your team — and adapt as those needs change. 

The Smartsheet platform makes it easy to plan, capture, manage, and report on work from anywhere, helping your team be more effective and get more done. Report on key metrics and get real-time visibility into work as it happens with roll-up reports, dashboards, and automated workflows built to keep your team connected and informed. 

When teams have clarity into the work getting done, there’s no telling how much more they can accomplish in the same amount of time.  Try Smartsheet for free, today.

Discover why over 90% of Fortune 100 companies trust Smartsheet to get work done.

35 problem-solving techniques and methods for solving complex problems

Design your next session with SessionLab

Join the 150,000+ facilitators 
using SessionLab.

Recommended Articles

A step-by-step guide to planning a workshop, how to create an unforgettable training session in 8 simple steps, 18 free facilitation resources we think you’ll love.

• 47 useful online tools for workshop planning and meeting facilitation

All teams and organizations encounter challenges as they grow. There are problems that might occur for teams when it comes to miscommunication or resolving business-critical issues . You may face challenges around growth , design , user engagement, and even team culture and happiness. In short, problem-solving techniques should be part of every team’s skillset.

Problem-solving methods are primarily designed to help a group or team through a process of first identifying problems and challenges , ideating possible solutions , and then evaluating the most suitable .

Finding effective solutions to complex problems isn’t easy, but by using the right process and techniques, you can help your team be more efficient in the process.

So how do you develop strategies that are engaging, and empower your team to solve problems effectively?

In this blog post, we share a series of problem-solving tools you can use in your next workshop or team meeting. You’ll also find some tips for facilitating the process and how to enable others to solve complex problems.

Let’s get started! 

How do you identify problems?

How do you identify the right solution.

• Tips for more effective problem-solving

Complete problem-solving methods

• Problem-solving techniques to identify and analyze problems
• Problem-solving techniques for developing solutions

Problem-solving warm-up activities

Closing activities for a problem-solving process.

Before you can move towards finding the right solution for a given problem, you first need to identify and define the problem you wish to solve. 

Here, you want to clearly articulate what the problem is and allow your group to do the same. Remember that everyone in a group is likely to have differing perspectives and alignment is necessary in order to help the group move forward. 

Identifying a problem accurately also requires that all members of a group are able to contribute their views in an open and safe manner. It can be scary for people to stand up and contribute, especially if the problems or challenges are emotive or personal in nature. Be sure to try and create a psychologically safe space for these kinds of discussions.

Remember that problem analysis and further discussion are also important. Not taking the time to fully analyze and discuss a challenge can result in the development of solutions that are not fit for purpose or do not address the underlying issue.

Successfully identifying and then analyzing a problem means facilitating a group through activities designed to help them clearly and honestly articulate their thoughts and produce usable insight.

With this data, you might then produce a problem statement that clearly describes the problem you wish to be addressed and also state the goal of any process you undertake to tackle this issue.  

Finding solutions is the end goal of any process. Complex organizational challenges can only be solved with an appropriate solution but discovering them requires using the right problem-solving tool.

After you’ve explored a problem and discussed ideas, you need to help a team discuss and choose the right solution. Consensus tools and methods such as those below help a group explore possible solutions before then voting for the best. They’re a great way to tap into the collective intelligence of the group for great results!

Remember that the process is often iterative. Great problem solvers often roadtest a viable solution in a measured way to see what works too. While you might not get the right solution on your first try, the methods below help teams land on the most likely to succeed solution while also holding space for improvement.

Every effective problem solving process begins with an agenda . A well-structured workshop is one of the best methods for successfully guiding a group from exploring a problem to implementing a solution.

In SessionLab, it’s easy to go from an idea to a complete agenda . Start by dragging and dropping your core problem solving activities into place . Add timings, breaks and necessary materials before sharing your agenda with your colleagues.

The resulting agenda will be your guide to an effective and productive problem solving session that will also help you stay organized on the day!

Tips for more effective problem solving

Problem-solving activities are only one part of the puzzle. While a great method can help unlock your team’s ability to solve problems, without a thoughtful approach and strong facilitation the solutions may not be fit for purpose.

Let’s take a look at some problem-solving tips you can apply to any process to help it be a success!

Clearly define the problem

Jumping straight to solutions can be tempting, though without first clearly articulating a problem, the solution might not be the right one. Many of the problem-solving activities below include sections where the problem is explored and clearly defined before moving on.

This is a vital part of the problem-solving process and taking the time to fully define an issue can save time and effort later. A clear definition helps identify irrelevant information and it also ensures that your team sets off on the right track.

Don’t jump to conclusions

It’s easy for groups to exhibit cognitive bias or have preconceived ideas about both problems and potential solutions. Be sure to back up any problem statements or potential solutions with facts, research, and adequate forethought.

The best techniques ask participants to be methodical and challenge preconceived notions. Make sure you give the group enough time and space to collect relevant information and consider the problem in a new way. By approaching the process with a clear, rational mindset, you’ll often find that better solutions are more forthcoming.  

Try different approaches  

Problems come in all shapes and sizes and so too should the methods you use to solve them. If you find that one approach isn’t yielding results and your team isn’t finding different solutions, try mixing it up. You’ll be surprised at how using a new creative activity can unblock your team and generate great solutions.

Don’t take it personally 

Depending on the nature of your team or organizational problems, it’s easy for conversations to get heated. While it’s good for participants to be engaged in the discussions, ensure that emotions don’t run too high and that blame isn’t thrown around while finding solutions.

You’re all in it together, and even if your team or area is seeing problems, that isn’t necessarily a disparagement of you personally. Using facilitation skills to manage group dynamics is one effective method of helping conversations be more constructive.

Get the right people in the room

Your problem-solving method is often only as effective as the group using it. Getting the right people on the job and managing the number of people present is important too!

If the group is too small, you may not get enough different perspectives to effectively solve a problem. If the group is too large, you can go round and round during the ideation stages.

Creating the right group makeup is also important in ensuring you have the necessary expertise and skillset to both identify and follow up on potential solutions. Carefully consider who to include at each stage to help ensure your problem-solving method is followed and positioned for success.

Document everything

The best solutions can take refinement, iteration, and reflection to come out. Get into a habit of documenting your process in order to keep all the learnings from the session and to allow ideas to mature and develop. Many of the methods below involve the creation of documents or shared resources. Be sure to keep and share these so everyone can benefit from the work done!

Bring a facilitator 

Facilitation is all about making group processes easier. With a subject as potentially emotive and important as problem-solving, having an impartial third party in the form of a facilitator can make all the difference in finding great solutions and keeping the process moving. Consider bringing a facilitator to your problem-solving session to get better results and generate meaningful solutions!

Develop your problem-solving skills

It takes time and practice to be an effective problem solver. While some roles or participants might more naturally gravitate towards problem-solving, it can take development and planning to help everyone create better solutions.

You might develop a training program, run a problem-solving workshop or simply ask your team to practice using the techniques below. Check out our post on problem-solving skills to see how you and your group can develop the right mental process and be more resilient to issues too!

Design a great agenda

Workshops are a great format for solving problems. With the right approach, you can focus a group and help them find the solutions to their own problems. But designing a process can be time-consuming and finding the right activities can be difficult.

Check out our workshop planning guide to level-up your agenda design and start running more effective workshops. Need inspiration? Check out templates designed by expert facilitators to help you kickstart your process!

In this section, we’ll look at in-depth problem-solving methods that provide a complete end-to-end process for developing effective solutions. These will help guide your team from the discovery and definition of a problem through to delivering the right solution.

If you’re looking for an all-encompassing method or problem-solving model, these processes are a great place to start. They’ll ask your team to challenge preconceived ideas and adopt a mindset for solving problems more effectively.

• Six Thinking Hats
• Lightning Decision Jam
• Problem Definition Process
• Discovery & Action Dialogue

Design Sprint 2.0

• Open Space Technology

1. Six Thinking Hats

Individual approaches to solving a problem can be very different based on what team or role an individual holds. It can be easy for existing biases or perspectives to find their way into the mix, or for internal politics to direct a conversation.

Six Thinking Hats is a classic method for identifying the problems that need to be solved and enables your team to consider them from different angles, whether that is by focusing on facts and data, creative solutions, or by considering why a particular solution might not work.

Like all problem-solving frameworks, Six Thinking Hats is effective at helping teams remove roadblocks from a conversation or discussion and come to terms with all the aspects necessary to solve complex problems.

2. Lightning Decision Jam

Featured courtesy of Jonathan Courtney of AJ&Smart Berlin, Lightning Decision Jam is one of those strategies that should be in every facilitation toolbox. Exploring problems and finding solutions is often creative in nature, though as with any creative process, there is the potential to lose focus and get lost.

Unstructured discussions might get you there in the end, but it’s much more effective to use a method that creates a clear process and team focus.

In Lightning Decision Jam, participants are invited to begin by writing challenges, concerns, or mistakes on post-its without discussing them before then being invited by the moderator to present them to the group.

From there, the team vote on which problems to solve and are guided through steps that will allow them to reframe those problems, create solutions and then decide what to execute on. 

By deciding the problems that need to be solved as a team before moving on, this group process is great for ensuring the whole team is aligned and can take ownership over the next stages. 

Lightning Decision Jam (LDJ)   #action   #decision making   #problem solving   #issue analysis   #innovation   #design   #remote-friendly   The problem with anything that requires creative thinking is that it’s easy to get lost—lose focus and fall into the trap of having useless, open-ended, unstructured discussions. Here’s the most effective solution I’ve found: Replace all open, unstructured discussion with a clear process. What to use this exercise for: Anything which requires a group of people to make decisions, solve problems or discuss challenges. It’s always good to frame an LDJ session with a broad topic, here are some examples: The conversion flow of our checkout Our internal design process How we organise events Keeping up with our competition Improving sales flow

3. Problem Definition Process

While problems can be complex, the problem-solving methods you use to identify and solve those problems can often be simple in design. 

By taking the time to truly identify and define a problem before asking the group to reframe the challenge as an opportunity, this method is a great way to enable change.

Begin by identifying a focus question and exploring the ways in which it manifests before splitting into five teams who will each consider the problem using a different method: escape, reversal, exaggeration, distortion or wishful. Teams develop a problem objective and create ideas in line with their method before then feeding them back to the group.

This method is great for enabling in-depth discussions while also creating space for finding creative solutions too!

Problem Definition   #problem solving   #idea generation   #creativity   #online   #remote-friendly   A problem solving technique to define a problem, challenge or opportunity and to generate ideas.

4. The 5 Whys 

Sometimes, a group needs to go further with their strategies and analyze the root cause at the heart of organizational issues. An RCA or root cause analysis is the process of identifying what is at the heart of business problems or recurring challenges. 

The 5 Whys is a simple and effective method of helping a group go find the root cause of any problem or challenge and conduct analysis that will deliver results. 

By beginning with the creation of a problem statement and going through five stages to refine it, The 5 Whys provides everything you need to truly discover the cause of an issue.

The 5 Whys   #hyperisland   #innovation   This simple and powerful method is useful for getting to the core of a problem or challenge. As the title suggests, the group defines a problems, then asks the question “why” five times, often using the resulting explanation as a starting point for creative problem solving.

5. World Cafe

World Cafe is a simple but powerful facilitation technique to help bigger groups to focus their energy and attention on solving complex problems.

World Cafe enables this approach by creating a relaxed atmosphere where participants are able to self-organize and explore topics relevant and important to them which are themed around a central problem-solving purpose. Create the right atmosphere by modeling your space after a cafe and after guiding the group through the method, let them take the lead!

Making problem-solving a part of your organization’s culture in the long term can be a difficult undertaking. More approachable formats like World Cafe can be especially effective in bringing people unfamiliar with workshops into the fold. 

World Cafe   #hyperisland   #innovation   #issue analysis   World Café is a simple yet powerful method, originated by Juanita Brown, for enabling meaningful conversations driven completely by participants and the topics that are relevant and important to them. Facilitators create a cafe-style space and provide simple guidelines. Participants then self-organize and explore a set of relevant topics or questions for conversation.

6. Discovery & Action Dialogue (DAD)

One of the best approaches is to create a safe space for a group to share and discover practices and behaviors that can help them find their own solutions.

With DAD, you can help a group choose which problems they wish to solve and which approaches they will take to do so. It’s great at helping remove resistance to change and can help get buy-in at every level too!

This process of enabling frontline ownership is great in ensuring follow-through and is one of the methods you will want in your toolbox as a facilitator.

Discovery & Action Dialogue (DAD)   #idea generation   #liberating structures   #action   #issue analysis   #remote-friendly   DADs make it easy for a group or community to discover practices and behaviors that enable some individuals (without access to special resources and facing the same constraints) to find better solutions than their peers to common problems. These are called positive deviant (PD) behaviors and practices. DADs make it possible for people in the group, unit, or community to discover by themselves these PD practices. DADs also create favorable conditions for stimulating participants’ creativity in spaces where they can feel safe to invent new and more effective practices. Resistance to change evaporates as participants are unleashed to choose freely which practices they will adopt or try and which problems they will tackle. DADs make it possible to achieve frontline ownership of solutions.

7. Design Sprint 2.0

Want to see how a team can solve big problems and move forward with prototyping and testing solutions in a few days? The Design Sprint 2.0 template from Jake Knapp, author of Sprint, is a complete agenda for a with proven results.

Developing the right agenda can involve difficult but necessary planning. Ensuring all the correct steps are followed can also be stressful or time-consuming depending on your level of experience.

Use this complete 4-day workshop template if you are finding there is no obvious solution to your challenge and want to focus your team around a specific problem that might require a shortcut to launching a minimum viable product or waiting for the organization-wide implementation of a solution.

8. Open space technology

Open space technology- developed by Harrison Owen – creates a space where large groups are invited to take ownership of their problem solving and lead individual sessions. Open space technology is a great format when you have a great deal of expertise and insight in the room and want to allow for different takes and approaches on a particular theme or problem you need to be solved.

Start by bringing your participants together to align around a central theme and focus their efforts. Explain the ground rules to help guide the problem-solving process and then invite members to identify any issue connecting to the central theme that they are interested in and are prepared to take responsibility for.

Once participants have decided on their approach to the core theme, they write their issue on a piece of paper, announce it to the group, pick a session time and place, and post the paper on the wall. As the wall fills up with sessions, the group is then invited to join the sessions that interest them the most and which they can contribute to, then you’re ready to begin!

Everyone joins the problem-solving group they’ve signed up to, record the discussion and if appropriate, findings can then be shared with the rest of the group afterward.

Open Space Technology   #action plan   #idea generation   #problem solving   #issue analysis   #large group   #online   #remote-friendly   Open Space is a methodology for large groups to create their agenda discerning important topics for discussion, suitable for conferences, community gatherings and whole system facilitation

Techniques to identify and analyze problems

Using a problem-solving method to help a team identify and analyze a problem can be a quick and effective addition to any workshop or meeting.

While further actions are always necessary, you can generate momentum and alignment easily, and these activities are a great place to get started.

We’ve put together this list of techniques to help you and your team with problem identification, analysis, and discussion that sets the foundation for developing effective solutions.

Let’s take a look!

• The Creativity Dice
• Fishbone Analysis
• Problem Tree
• SWOT Analysis
• Agreement-Certainty Matrix
• The Journalistic Six
• LEGO Challenge
• What, So What, Now What?
• Journalists

Individual and group perspectives are incredibly important, but what happens if people are set in their minds and need a change of perspective in order to approach a problem more effectively?

Flip It is a method we love because it is both simple to understand and run, and allows groups to understand how their perspectives and biases are formed. 

Participants in Flip It are first invited to consider concerns, issues, or problems from a perspective of fear and write them on a flip chart. Then, the group is asked to consider those same issues from a perspective of hope and flip their understanding.  

No problem and solution is free from existing bias and by changing perspectives with Flip It, you can then develop a problem solving model quickly and effectively.

Flip It!   #gamestorming   #problem solving   #action   Often, a change in a problem or situation comes simply from a change in our perspectives. Flip It! is a quick game designed to show players that perspectives are made, not born.

10. The Creativity Dice

One of the most useful problem solving skills you can teach your team is of approaching challenges with creativity, flexibility, and openness. Games like The Creativity Dice allow teams to overcome the potential hurdle of too much linear thinking and approach the process with a sense of fun and speed. 

In The Creativity Dice, participants are organized around a topic and roll a dice to determine what they will work on for a period of 3 minutes at a time. They might roll a 3 and work on investigating factual information on the chosen topic. They might roll a 1 and work on identifying the specific goals, standards, or criteria for the session.

Encouraging rapid work and iteration while asking participants to be flexible are great skills to cultivate. Having a stage for idea incubation in this game is also important. Moments of pause can help ensure the ideas that are put forward are the most suitable. 

The Creativity Dice   #creativity   #problem solving   #thiagi   #issue analysis   Too much linear thinking is hazardous to creative problem solving. To be creative, you should approach the problem (or the opportunity) from different points of view. You should leave a thought hanging in mid-air and move to another. This skipping around prevents premature closure and lets your brain incubate one line of thought while you consciously pursue another.

11. Fishbone Analysis

Organizational or team challenges are rarely simple, and it’s important to remember that one problem can be an indication of something that goes deeper and may require further consideration to be solved.

Fishbone Analysis helps groups to dig deeper and understand the origins of a problem. It’s a great example of a root cause analysis method that is simple for everyone on a team to get their head around. 

Participants in this activity are asked to annotate a diagram of a fish, first adding the problem or issue to be worked on at the head of a fish before then brainstorming the root causes of the problem and adding them as bones on the fish. 

Using abstractions such as a diagram of a fish can really help a team break out of their regular thinking and develop a creative approach.

Fishbone Analysis   #problem solving   ##root cause analysis   #decision making   #online facilitation   A process to help identify and understand the origins of problems, issues or observations.

12. Problem Tree 

Encouraging visual thinking can be an essential part of many strategies. By simply reframing and clarifying problems, a group can move towards developing a problem solving model that works for them. 

In Problem Tree, groups are asked to first brainstorm a list of problems – these can be design problems, team problems or larger business problems – and then organize them into a hierarchy. The hierarchy could be from most important to least important or abstract to practical, though the key thing with problem solving games that involve this aspect is that your group has some way of managing and sorting all the issues that are raised.

Once you have a list of problems that need to be solved and have organized them accordingly, you’re then well-positioned for the next problem solving steps.

Problem tree   #define intentions   #create   #design   #issue analysis   A problem tree is a tool to clarify the hierarchy of problems addressed by the team within a design project; it represents high level problems or related sublevel problems.

13. SWOT Analysis

Chances are you’ve heard of the SWOT Analysis before. This problem-solving method focuses on identifying strengths, weaknesses, opportunities, and threats is a tried and tested method for both individuals and teams.

Start by creating a desired end state or outcome and bare this in mind – any process solving model is made more effective by knowing what you are moving towards. Create a quadrant made up of the four categories of a SWOT analysis and ask participants to generate ideas based on each of those quadrants.

Once you have those ideas assembled in their quadrants, cluster them together based on their affinity with other ideas. These clusters are then used to facilitate group conversations and move things forward. 

SWOT analysis   #gamestorming   #problem solving   #action   #meeting facilitation   The SWOT Analysis is a long-standing technique of looking at what we have, with respect to the desired end state, as well as what we could improve on. It gives us an opportunity to gauge approaching opportunities and dangers, and assess the seriousness of the conditions that affect our future. When we understand those conditions, we can influence what comes next.

14. Agreement-Certainty Matrix

Not every problem-solving approach is right for every challenge, and deciding on the right method for the challenge at hand is a key part of being an effective team.

The Agreement Certainty matrix helps teams align on the nature of the challenges facing them. By sorting problems from simple to chaotic, your team can understand what methods are suitable for each problem and what they can do to ensure effective results. 

If you are already using Liberating Structures techniques as part of your problem-solving strategy, the Agreement-Certainty Matrix can be an invaluable addition to your process. We’ve found it particularly if you are having issues with recurring problems in your organization and want to go deeper in understanding the root cause. 

Agreement-Certainty Matrix   #issue analysis   #liberating structures   #problem solving   You can help individuals or groups avoid the frequent mistake of trying to solve a problem with methods that are not adapted to the nature of their challenge. The combination of two questions makes it possible to easily sort challenges into four categories: simple, complicated, complex , and chaotic .  A problem is simple when it can be solved reliably with practices that are easy to duplicate.  It is complicated when experts are required to devise a sophisticated solution that will yield the desired results predictably.  A problem is complex when there are several valid ways to proceed but outcomes are not predictable in detail.  Chaotic is when the context is too turbulent to identify a path forward.  A loose analogy may be used to describe these differences: simple is like following a recipe, complicated like sending a rocket to the moon, complex like raising a child, and chaotic is like the game “Pin the Tail on the Donkey.”  The Liberating Structures Matching Matrix in Chapter 5 can be used as the first step to clarify the nature of a challenge and avoid the mismatches between problems and solutions that are frequently at the root of chronic, recurring problems.

Organizing and charting a team’s progress can be important in ensuring its success. SQUID (Sequential Question and Insight Diagram) is a great model that allows a team to effectively switch between giving questions and answers and develop the skills they need to stay on track throughout the process. 

Begin with two different colored sticky notes – one for questions and one for answers – and with your central topic (the head of the squid) on the board. Ask the group to first come up with a series of questions connected to their best guess of how to approach the topic. Ask the group to come up with answers to those questions, fix them to the board and connect them with a line. After some discussion, go back to question mode by responding to the generated answers or other points on the board.

It’s rewarding to see a diagram grow throughout the exercise, and a completed SQUID can provide a visual resource for future effort and as an example for other teams.

SQUID   #gamestorming   #project planning   #issue analysis   #problem solving   When exploring an information space, it’s important for a group to know where they are at any given time. By using SQUID, a group charts out the territory as they go and can navigate accordingly. SQUID stands for Sequential Question and Insight Diagram.

16. Speed Boat

To continue with our nautical theme, Speed Boat is a short and sweet activity that can help a team quickly identify what employees, clients or service users might have a problem with and analyze what might be standing in the way of achieving a solution.

Methods that allow for a group to make observations, have insights and obtain those eureka moments quickly are invaluable when trying to solve complex problems.

In Speed Boat, the approach is to first consider what anchors and challenges might be holding an organization (or boat) back. Bonus points if you are able to identify any sharks in the water and develop ideas that can also deal with competitors!   

Speed Boat   #gamestorming   #problem solving   #action   Speedboat is a short and sweet way to identify what your employees or clients don’t like about your product/service or what’s standing in the way of a desired goal.

17. The Journalistic Six

Some of the most effective ways of solving problems is by encouraging teams to be more inclusive and diverse in their thinking.

Based on the six key questions journalism students are taught to answer in articles and news stories, The Journalistic Six helps create teams to see the whole picture. By using who, what, when, where, why, and how to facilitate the conversation and encourage creative thinking, your team can make sure that the problem identification and problem analysis stages of the are covered exhaustively and thoughtfully. Reporter’s notebook and dictaphone optional.

The Journalistic Six – Who What When Where Why How   #idea generation   #issue analysis   #problem solving   #online   #creative thinking   #remote-friendly   A questioning method for generating, explaining, investigating ideas.

18. LEGO Challenge

Now for an activity that is a little out of the (toy) box. LEGO Serious Play is a facilitation methodology that can be used to improve creative thinking and problem-solving skills. 

The LEGO Challenge includes giving each member of the team an assignment that is hidden from the rest of the group while they create a structure without speaking.

What the LEGO challenge brings to the table is a fun working example of working with stakeholders who might not be on the same page to solve problems. Also, it’s LEGO! Who doesn’t love LEGO! 

LEGO Challenge   #hyperisland   #team   A team-building activity in which groups must work together to build a structure out of LEGO, but each individual has a secret “assignment” which makes the collaborative process more challenging. It emphasizes group communication, leadership dynamics, conflict, cooperation, patience and problem solving strategy.

19. What, So What, Now What?

If not carefully managed, the problem identification and problem analysis stages of the problem-solving process can actually create more problems and misunderstandings.

The What, So What, Now What? problem-solving activity is designed to help collect insights and move forward while also eliminating the possibility of disagreement when it comes to identifying, clarifying, and analyzing organizational or work problems. 

Facilitation is all about bringing groups together so that might work on a shared goal and the best problem-solving strategies ensure that teams are aligned in purpose, if not initially in opinion or insight.

Throughout the three steps of this game, you give everyone on a team to reflect on a problem by asking what happened, why it is important, and what actions should then be taken. 

This can be a great activity for bringing our individual perceptions about a problem or challenge and contextualizing it in a larger group setting. This is one of the most important problem-solving skills you can bring to your organization.

W³ – What, So What, Now What?   #issue analysis   #innovation   #liberating structures   You can help groups reflect on a shared experience in a way that builds understanding and spurs coordinated action while avoiding unproductive conflict. It is possible for every voice to be heard while simultaneously sifting for insights and shaping new direction. Progressing in stages makes this practical—from collecting facts about What Happened to making sense of these facts with So What and finally to what actions logically follow with Now What . The shared progression eliminates most of the misunderstandings that otherwise fuel disagreements about what to do. Voila!

20. Journalists  

Problem analysis can be one of the most important and decisive stages of all problem-solving tools. Sometimes, a team can become bogged down in the details and are unable to move forward.

Journalists is an activity that can avoid a group from getting stuck in the problem identification or problem analysis stages of the process.

In Journalists, the group is invited to draft the front page of a fictional newspaper and figure out what stories deserve to be on the cover and what headlines those stories will have. By reframing how your problems and challenges are approached, you can help a team move productively through the process and be better prepared for the steps to follow.

Journalists   #vision   #big picture   #issue analysis   #remote-friendly   This is an exercise to use when the group gets stuck in details and struggles to see the big picture. Also good for defining a vision.

Problem-solving techniques for developing solutions 

The success of any problem-solving process can be measured by the solutions it produces. After you’ve defined the issue, explored existing ideas, and ideated, it’s time to narrow down to the correct solution.

Use these problem-solving techniques when you want to help your team find consensus, compare possible solutions, and move towards taking action on a particular problem.

• Improved Solutions
• Four-Step Sketch
• 15% Solutions
• How-Now-Wow matrix
• Impact Effort Matrix

21. Mindspin  

Brainstorming is part of the bread and butter of the problem-solving process and all problem-solving strategies benefit from getting ideas out and challenging a team to generate solutions quickly. 

With Mindspin, participants are encouraged not only to generate ideas but to do so under time constraints and by slamming down cards and passing them on. By doing multiple rounds, your team can begin with a free generation of possible solutions before moving on to developing those solutions and encouraging further ideation. 

This is one of our favorite problem-solving activities and can be great for keeping the energy up throughout the workshop. Remember the importance of helping people become engaged in the process – energizing problem-solving techniques like Mindspin can help ensure your team stays engaged and happy, even when the problems they’re coming together to solve are complex. 

MindSpin   #teampedia   #idea generation   #problem solving   #action   A fast and loud method to enhance brainstorming within a team. Since this activity has more than round ideas that are repetitive can be ruled out leaving more creative and innovative answers to the challenge.

22. Improved Solutions

After a team has successfully identified a problem and come up with a few solutions, it can be tempting to call the work of the problem-solving process complete. That said, the first solution is not necessarily the best, and by including a further review and reflection activity into your problem-solving model, you can ensure your group reaches the best possible result. 

One of a number of problem-solving games from Thiagi Group, Improved Solutions helps you go the extra mile and develop suggested solutions with close consideration and peer review. By supporting the discussion of several problems at once and by shifting team roles throughout, this problem-solving technique is a dynamic way of finding the best solution. 

Improved Solutions   #creativity   #thiagi   #problem solving   #action   #team   You can improve any solution by objectively reviewing its strengths and weaknesses and making suitable adjustments. In this creativity framegame, you improve the solutions to several problems. To maintain objective detachment, you deal with a different problem during each of six rounds and assume different roles (problem owner, consultant, basher, booster, enhancer, and evaluator) during each round. At the conclusion of the activity, each player ends up with two solutions to her problem.

23. Four Step Sketch

Creative thinking and visual ideation does not need to be confined to the opening stages of your problem-solving strategies. Exercises that include sketching and prototyping on paper can be effective at the solution finding and development stage of the process, and can be great for keeping a team engaged. 

By going from simple notes to a crazy 8s round that involves rapidly sketching 8 variations on their ideas before then producing a final solution sketch, the group is able to iterate quickly and visually. Problem-solving techniques like Four-Step Sketch are great if you have a group of different thinkers and want to change things up from a more textual or discussion-based approach.

Four-Step Sketch   #design sprint   #innovation   #idea generation   #remote-friendly   The four-step sketch is an exercise that helps people to create well-formed concepts through a structured process that includes: Review key information Start design work on paper,  Consider multiple variations , Create a detailed solution . This exercise is preceded by a set of other activities allowing the group to clarify the challenge they want to solve. See how the Four Step Sketch exercise fits into a Design Sprint

24. 15% Solutions

Some problems are simpler than others and with the right problem-solving activities, you can empower people to take immediate actions that can help create organizational change. 

Part of the liberating structures toolkit, 15% solutions is a problem-solving technique that focuses on finding and implementing solutions quickly. A process of iterating and making small changes quickly can help generate momentum and an appetite for solving complex problems.

Problem-solving strategies can live and die on whether people are onboard. Getting some quick wins is a great way of getting people behind the process.   

It can be extremely empowering for a team to realize that problem-solving techniques can be deployed quickly and easily and delineate between things they can positively impact and those things they cannot change. 

15% Solutions   #action   #liberating structures   #remote-friendly   You can reveal the actions, however small, that everyone can do immediately. At a minimum, these will create momentum, and that may make a BIG difference.  15% Solutions show that there is no reason to wait around, feel powerless, or fearful. They help people pick it up a level. They get individuals and the group to focus on what is within their discretion instead of what they cannot change.  With a very simple question, you can flip the conversation to what can be done and find solutions to big problems that are often distributed widely in places not known in advance. Shifting a few grains of sand may trigger a landslide and change the whole landscape.

25. How-Now-Wow Matrix

The problem-solving process is often creative, as complex problems usually require a change of thinking and creative response in order to find the best solutions. While it’s common for the first stages to encourage creative thinking, groups can often gravitate to familiar solutions when it comes to the end of the process. 

When selecting solutions, you don’t want to lose your creative energy! The How-Now-Wow Matrix from Gamestorming is a great problem-solving activity that enables a group to stay creative and think out of the box when it comes to selecting the right solution for a given problem.

Problem-solving techniques that encourage creative thinking and the ideation and selection of new solutions can be the most effective in organisational change. Give the How-Now-Wow Matrix a go, and not just for how pleasant it is to say out loud. 

How-Now-Wow Matrix   #gamestorming   #idea generation   #remote-friendly   When people want to develop new ideas, they most often think out of the box in the brainstorming or divergent phase. However, when it comes to convergence, people often end up picking ideas that are most familiar to them. This is called a ‘creative paradox’ or a ‘creadox’. The How-Now-Wow matrix is an idea selection tool that breaks the creadox by forcing people to weigh each idea on 2 parameters.

26. Impact and Effort Matrix

All problem-solving techniques hope to not only find solutions to a given problem or challenge but to find the best solution. When it comes to finding a solution, groups are invited to put on their decision-making hats and really think about how a proposed idea would work in practice. 

The Impact and Effort Matrix is one of the problem-solving techniques that fall into this camp, empowering participants to first generate ideas and then categorize them into a 2×2 matrix based on impact and effort.

Activities that invite critical thinking while remaining simple are invaluable. Use the Impact and Effort Matrix to move from ideation and towards evaluating potential solutions before then committing to them. 

Impact and Effort Matrix   #gamestorming   #decision making   #action   #remote-friendly   In this decision-making exercise, possible actions are mapped based on two factors: effort required to implement and potential impact. Categorizing ideas along these lines is a useful technique in decision making, as it obliges contributors to balance and evaluate suggested actions before committing to them.

27. Dotmocracy

If you’ve followed each of the problem-solving steps with your group successfully, you should move towards the end of your process with heaps of possible solutions developed with a specific problem in mind. But how do you help a group go from ideation to putting a solution into action? 

Dotmocracy – or Dot Voting -is a tried and tested method of helping a team in the problem-solving process make decisions and put actions in place with a degree of oversight and consensus. 

One of the problem-solving techniques that should be in every facilitator’s toolbox, Dot Voting is fast and effective and can help identify the most popular and best solutions and help bring a group to a decision effectively. 

Dotmocracy   #action   #decision making   #group prioritization   #hyperisland   #remote-friendly   Dotmocracy is a simple method for group prioritization or decision-making. It is not an activity on its own, but a method to use in processes where prioritization or decision-making is the aim. The method supports a group to quickly see which options are most popular or relevant. The options or ideas are written on post-its and stuck up on a wall for the whole group to see. Each person votes for the options they think are the strongest, and that information is used to inform a decision.

All facilitators know that warm-ups and icebreakers are useful for any workshop or group process. Problem-solving workshops are no different.

Use these problem-solving techniques to warm up a group and prepare them for the rest of the process. Activating your group by tapping into some of the top problem-solving skills can be one of the best ways to see great outcomes from your session.

• Check-in/Check-out
• Doodling Together
• Show and Tell
• Constellations
• Draw a Tree

28. Check-in / Check-out

Solid processes are planned from beginning to end, and the best facilitators know that setting the tone and establishing a safe, open environment can be integral to a successful problem-solving process.

Check-in / Check-out is a great way to begin and/or bookend a problem-solving workshop. Checking in to a session emphasizes that everyone will be seen, heard, and expected to contribute. 

If you are running a series of meetings, setting a consistent pattern of checking in and checking out can really help your team get into a groove. We recommend this opening-closing activity for small to medium-sized groups though it can work with large groups if they’re disciplined!

Check-in / Check-out   #team   #opening   #closing   #hyperisland   #remote-friendly   Either checking-in or checking-out is a simple way for a team to open or close a process, symbolically and in a collaborative way. Checking-in/out invites each member in a group to be present, seen and heard, and to express a reflection or a feeling. Checking-in emphasizes presence, focus and group commitment; checking-out emphasizes reflection and symbolic closure.

29. Doodling Together  

Thinking creatively and not being afraid to make suggestions are important problem-solving skills for any group or team, and warming up by encouraging these behaviors is a great way to start. 

Doodling Together is one of our favorite creative ice breaker games – it’s quick, effective, and fun and can make all following problem-solving steps easier by encouraging a group to collaborate visually. By passing cards and adding additional items as they go, the workshop group gets into a groove of co-creation and idea development that is crucial to finding solutions to problems. 

Doodling Together   #collaboration   #creativity   #teamwork   #fun   #team   #visual methods   #energiser   #icebreaker   #remote-friendly   Create wild, weird and often funny postcards together & establish a group’s creative confidence.

30. Show and Tell

You might remember some version of Show and Tell from being a kid in school and it’s a great problem-solving activity to kick off a session.

Asking participants to prepare a little something before a workshop by bringing an object for show and tell can help them warm up before the session has even begun! Games that include a physical object can also help encourage early engagement before moving onto more big-picture thinking.

By asking your participants to tell stories about why they chose to bring a particular item to the group, you can help teams see things from new perspectives and see both differences and similarities in the way they approach a topic. Great groundwork for approaching a problem-solving process as a team! 

Show and Tell   #gamestorming   #action   #opening   #meeting facilitation   Show and Tell taps into the power of metaphors to reveal players’ underlying assumptions and associations around a topic The aim of the game is to get a deeper understanding of stakeholders’ perspectives on anything—a new project, an organizational restructuring, a shift in the company’s vision or team dynamic.

31. Constellations

Who doesn’t love stars? Constellations is a great warm-up activity for any workshop as it gets people up off their feet, energized, and ready to engage in new ways with established topics. It’s also great for showing existing beliefs, biases, and patterns that can come into play as part of your session.

Using warm-up games that help build trust and connection while also allowing for non-verbal responses can be great for easing people into the problem-solving process and encouraging engagement from everyone in the group. Constellations is great in large spaces that allow for movement and is definitely a practical exercise to allow the group to see patterns that are otherwise invisible. 

Constellations   #trust   #connection   #opening   #coaching   #patterns   #system   Individuals express their response to a statement or idea by standing closer or further from a central object. Used with teams to reveal system, hidden patterns, perspectives.

32. Draw a Tree

Problem-solving games that help raise group awareness through a central, unifying metaphor can be effective ways to warm-up a group in any problem-solving model.

Draw a Tree is a simple warm-up activity you can use in any group and which can provide a quick jolt of energy. Start by asking your participants to draw a tree in just 45 seconds – they can choose whether it will be abstract or realistic. 

Once the timer is up, ask the group how many people included the roots of the tree and use this as a means to discuss how we can ignore important parts of any system simply because they are not visible.

All problem-solving strategies are made more effective by thinking of problems critically and by exposing things that may not normally come to light. Warm-up games like Draw a Tree are great in that they quickly demonstrate some key problem-solving skills in an accessible and effective way.

Draw a Tree   #thiagi   #opening   #perspectives   #remote-friendly   With this game you can raise awarness about being more mindful, and aware of the environment we live in.

Each step of the problem-solving workshop benefits from an intelligent deployment of activities, games, and techniques. Bringing your session to an effective close helps ensure that solutions are followed through on and that you also celebrate what has been achieved.

Here are some problem-solving activities you can use to effectively close a workshop or meeting and ensure the great work you’ve done can continue afterward.

• One Breath Feedback
• Who What When Matrix
• Response Cards

How do I conclude a problem-solving process?

All good things must come to an end. With the bulk of the work done, it can be tempting to conclude your workshop swiftly and without a moment to debrief and align. This can be problematic in that it doesn’t allow your team to fully process the results or reflect on the process.

At the end of an effective session, your team will have gone through a process that, while productive, can be exhausting. It’s important to give your group a moment to take a breath, ensure that they are clear on future actions, and provide short feedback before leaving the space. 

The primary purpose of any problem-solving method is to generate solutions and then implement them. Be sure to take the opportunity to ensure everyone is aligned and ready to effectively implement the solutions you produced in the workshop.

Remember that every process can be improved and by giving a short moment to collect feedback in the session, you can further refine your problem-solving methods and see further success in the future too.

33. One Breath Feedback

Maintaining attention and focus during the closing stages of a problem-solving workshop can be tricky and so being concise when giving feedback can be important. It’s easy to incur “death by feedback” should some team members go on for too long sharing their perspectives in a quick feedback round. 

One Breath Feedback is a great closing activity for workshops. You give everyone an opportunity to provide feedback on what they’ve done but only in the space of a single breath. This keeps feedback short and to the point and means that everyone is encouraged to provide the most important piece of feedback to them. 

One breath feedback   #closing   #feedback   #action   This is a feedback round in just one breath that excels in maintaining attention: each participants is able to speak during just one breath … for most people that’s around 20 to 25 seconds … unless of course you’ve been a deep sea diver in which case you’ll be able to do it for longer.

34. Who What When Matrix 

Matrices feature as part of many effective problem-solving strategies and with good reason. They are easily recognizable, simple to use, and generate results.

The Who What When Matrix is a great tool to use when closing your problem-solving session by attributing a who, what and when to the actions and solutions you have decided upon. The resulting matrix is a simple, easy-to-follow way of ensuring your team can move forward. 

Great solutions can’t be enacted without action and ownership. Your problem-solving process should include a stage for allocating tasks to individuals or teams and creating a realistic timeframe for those solutions to be implemented or checked out. Use this method to keep the solution implementation process clear and simple for all involved. 

Who/What/When Matrix   #gamestorming   #action   #project planning   With Who/What/When matrix, you can connect people with clear actions they have defined and have committed to.

35. Response cards

Group discussion can comprise the bulk of most problem-solving activities and by the end of the process, you might find that your team is talked out! 

Providing a means for your team to give feedback with short written notes can ensure everyone is head and can contribute without the need to stand up and talk. Depending on the needs of the group, giving an alternative can help ensure everyone can contribute to your problem-solving model in the way that makes the most sense for them.

Response Cards is a great way to close a workshop if you are looking for a gentle warm-down and want to get some swift discussion around some of the feedback that is raised. 

Response Cards   #debriefing   #closing   #structured sharing   #questions and answers   #thiagi   #action   It can be hard to involve everyone during a closing of a session. Some might stay in the background or get unheard because of louder participants. However, with the use of Response Cards, everyone will be involved in providing feedback or clarify questions at the end of a session.

Save time and effort discovering the right solutions

A structured problem solving process is a surefire way of solving tough problems, discovering creative solutions and driving organizational change. But how can you design for successful outcomes?

With SessionLab, it’s easy to design engaging workshops that deliver results. Drag, drop and reorder blocks  to build your agenda. When you make changes or update your agenda, your session  timing   adjusts automatically , saving you time on manual adjustments.

Collaborating with stakeholders or clients? Share your agenda with a single click and collaborate in real-time. No more sending documents back and forth over email.

Explore  how to use SessionLab  to design effective problem solving workshops or  watch this five minute video  to see the planner in action!

Over to you

The problem-solving process can often be as complicated and multifaceted as the problems they are set-up to solve. With the right problem-solving techniques and a mix of creative exercises designed to guide discussion and generate purposeful ideas, we hope we’ve given you the tools to find the best solutions as simply and easily as possible.

Is there a problem-solving technique that you are missing here? Do you have a favorite activity or method you use when facilitating? Let us know in the comments below, we’d love to hear from you! 

thank you very much for these excellent techniques

Certainly wonderful article, very detailed. Shared!

Your list of techniques for problem solving can be helpfully extended by adding TRIZ to the list of techniques. TRIZ has 40 problem solving techniques derived from methods inventros and patent holders used to get new patents. About 10-12 are general approaches. many organization sponsor classes in TRIZ that are used to solve business problems or general organiztational problems. You can take a look at TRIZ and dwonload a free internet booklet to see if you feel it shound be included per your selection process.

Leave a Comment Cancel reply

Your email address will not be published. Required fields are marked *

Going from a mere idea to a workshop that delivers results for your clients can feel like a daunting task. In this piece, we will shine a light on all the work behind the scenes and help you learn how to plan a workshop from start to finish. On a good day, facilitation can feel like effortless magic, but that is mostly the result of backstage work, foresight, and a lot of careful planning. Read on to learn a step-by-step approach to breaking the process of planning a workshop into small, manageable chunks.  The flow starts with the first meeting with a client to define the purposes of a workshop.…

How does learning work? A clever 9-year-old once told me: “I know I am learning something new when I am surprised.” The science of adult learning tells us that, in order to learn new skills (which, unsurprisingly, is harder for adults to do than kids) grown-ups need to first get into a specific headspace.  In a business, this approach is often employed in a training session where employees learn new skills or work on professional development. But how do you ensure your training is effective? In this guide, we'll explore how to create an effective training session plan and run engaging training sessions. As team leader, project manager, or consultant,…

Facilitation is more and more recognized as a key component of work, as employers and society are faced with bigger and more complex problems and ideas. From facilitating meetings to big, multi-stakeholder strategy development workshops, the facilitator's skillset is more and more in demand. In this article, we will go through a list of the best online facilitation resources, including newsletters, podcasts, communities, and 10 free toolkits you can bookmark and read to upskill and improve your facilitation practice. When designing activities and workshops, you'll probably start by using templates and methods you are familiar with. Soon enough, you'll need to expand your range and look for facilitation methods and…

Design your next workshop with SessionLab

Join the 150,000 facilitators using SessionLab

Sign up for free

What Is an Algorithm?

An algorithm is a set of instructions implemented by software engineers and data scientists to transform input data into output data through a computational series of arithmetic, decision making and repetition. Algorithms provide computers with a series of instructions that transform data into usable knowledge. Every algorithm is essentially trying to make a decision, often as part of a series of decisions, to ensure a computational input is processed and transmitted as usable data based on the task it’s trying to accomplish.

3 Examples of Algorithms

• Binary search algorithms take sorted arrays of data and return the index of the value for which you’ve searched. Essentially, this type of algorithm determines where a value exists within a specific set of data or if it exists within the data set at all.

Merge sort algorithms operate in a divide-and-conquer manner, similar to binary search. Where the two differ, however, is that merge sorting separates all elements into individual elements, continuing until every individual element exists in an index of its own, and then merges the elements and sorts them in an understandable order based on the input.

• Adding/removing items from a linked list means you can restructure linked lists so that nodes can be inserted or deleted from a specific location. Engineers and computer scientists can locate exactly where the node that needs to be inserted or removed is located as well as the pointers where the desired change should be rearranged.

How Does an Algorithm Work?

An algorithm consists of a series of three steps: the input, the computation and the output.

An input is the data that is fed into an algorithm to begin the computation process.

The computation process then applies arithmetic, decision making and repetition to create “if x, then y” equations to ensure only the proper data is fed through to the output. Many algorithms use  machine learning to use past knowledge in computational decision making .

The output process is the algorithm’s expression of its conclusion. This can be in the form of information displayed to a user, or much more commonly, as more data that becomes the input for another algorithm in a string of processes that enable a computer to make complex decisions in real time.

Related Reading on Built In Why Is Logistic Regression a Classification Algorithm?

What Are Some Examples of an Algorithm?

Three key algorithms commonly used include binary search, merge sort and adding/removing from a linked list.

Binary Search

Binary search algorithms take sorted arrays of data and return the index of the value for which you’ve searched. Essentially, this type of algorithm determines where a value exists within a specific set of data or if it exists within the data set at all. There are five steps this algorithm will perform in its search:

• It finds the midpoint of the sorted array.
• It compares the midpoint of the data to the value being searched.
• The algorithm then searches the right half of the array if the midpoint is larger than the value.
• If the midpoint is smaller than the value, it will search the left half of the array.
• Finally, the steps repeat until the algorithm finds the midpoint value or determines it doesn’t exist in the data set.

Merge sort algorithms manage both the dividing and merging processes simultaneously to provide faster results to the user.

Adding/Removing From a Linked List

Linked lists utilize nodes and pointers as opposed to arrays, which allows some processes to perform much more efficiently. Nodes house a piece of data and a pointer that directs it to the next node, allowing data to consistently feed in a specific direction.

Linked lists can be restructured so that nodes can be inserted or deleted from a specific location. Engineers and computer scientists can locate exactly where the node that needs to be inserted or removed is located as well as the pointers where the desired change should be rearranged, allowing items to be removed from the middle of a collection without having to shift the remainder of the data structure in memory. This makes for more efficient insertions and deletions.

More on Lists From Built In Experts How to Append Lists in Python

What Is the Best Way to Analyze an Algorithm?

In order to ensure an algorithm is as efficient as possible, there are several methods of analysis that check execution speed and memory usage across several use cases.

Algorithm analysis begins with counting the number of operations needed to determine an answer across different input variables. For example, a linear search algorithm, which searches for values in a list, will check every value on a given list to see if it matches the target value. Once the value is found, it immediately returns to the index. If no value is found, the equation returns -1 .  The number of checks necessary to find the target value will determine the execution speed of the algorithm. This execution speed will vary depending on the target value and the values present in the list, so several values should be checked to determine a relative average speed.

Other variables are necessary to determine the actual running speed of an algorithm, such as the speed of the computer, the programming language and the translation of that language into machine code. To get an accurate measurement of how an algorithm will run on a particular device, it must be made to run. This is possible by implementing the algorithm in an actual programming language, and in JavaScript , using the searchList function. This function will tell the amount of time it takes an algorithm to search a specific length of numbers in a list in milliseconds. By measuring the efficiency of different types of algorithms for a given set of values, programmers and data scientists can determine the best algorithm to use for specific use cases.

Built In’s expert contributor network publishes thoughtful, solutions-oriented stories written by innovative tech professionals. It is the tech industry’s definitive destination for sharing compelling, first-person accounts of problem-solving on the road to innovation.

Great Companies Need Great People. That's Where We Come In.

ETRS: efficient turn restrictions setting method for boundary routers in chiplet-based systems

• Published: 01 June 2024

Cite this article

• Zhipeng Cao 1 ,
• Wei Guo 1 ,
• Zhiquan Wan 2 ,
• Peijie Li 1 ,
• Qinrang Liu 1 ,
• Caining Wang 3 &
• Yangxue Shao 3  

The implementation of turn restrictions represents a critical research challenge in chiplet-based systems, with the objective of achieving deadlock-free communication. Nevertheless, existing methodologies encounter difficulties in terms of computational complexity, which impedes the design process. Moreover, as the scale of the problem increases, the cost of addressing it becomes increasingly untenable. In this paper, we introduce the efficient turn restrictions setting (ETRS) method to reduce the computational cost of implementing turn restrictions for boundary routers in chiplet-based systems. In stage 1, we present a symmetry-based preprocessing algorithm (SBPA). SBPA exploits the symmetry inherent in chiplet topologies by generating multiple sets of identical modes, ensuring that scenarios with the same objective function value are calculated only once per iteration. In stage 2, a heuristic selection algorithm (HSA) for turn restrictions based on NSGA-II is proposed as a means of searching for approximately optimal solutions and of solving the problem quickly. In stage 3, different filtering criteria are introduced to evaluate the Pareto fronts of HSA for making decisions on the placement of boundary routers and their turn restrictions. Evaluation results reveal that the proposed ETRS method surpasses existing solutions in terms of computation efficiency. Moreover, it delivers satisfactory optimal objective values.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price includes VAT (Russian Federation)

Instant access to the full article PDF.

Rent this article via DeepDyve

Institutional subscriptions

Kim J, Murali G, Park H, Qin E, Kwon H, Chekuri VCK, Rahman NM, Dasari N, Singh A, Lee M (2020) Architecture, chip, and package codesign flow for interposer-based 2.5-D chiplet integration enabling heterogeneous IP reuse. IEEE Trans Very Large Scale Integr VLSI Syst 28(11):2424–2437

Article   Google Scholar  

Coskun A, Eris F, Joshi A, Kahng AB, Ma Y, Narayan A, Srinivas V (2020) Cross-layer co-optimization of network design and chiplet placement in 2.5-D systems. IEEE Trans Comput Aided Des Integr Circuits Syst 39(12):5183–5196

Ma X, Wang Y, Wang Y, Cai X, Han Y (2022) Survey on chiplets: interface, interconnect and integration methodology. CCF Trans High Perform Comput 4(1):43–52

Sharma DD, Pasdast G, Qian Z, Aygun K (2022) Universal chiplet interconnect express (UCIe): an open industry standard for innovations with chiplets at package level. IEEE Trans Compon Packag Manuf Technol 12(9):1423–1431

Naffziger S, Beck N, Burd T, Lepak K, Loh GH, Subramony M, White S (2021) Pioneering chiplet technology and design for the amd epyc \(^{{\rm TM}}\) and ryzen \(^{{\rm TM}}\) processor families: industrial product. In: 2021 ACM/IEEE 48th Annual International Symposium on Computer Architecture (ISCA). IEEE, pp 57–70

Nassif N, Munch AO, Molnar CL, Pasdast G, Lyer SV, Yang Z, Mendoza O, Huddart M, Venkataraman S, Kandula S (2022) Sapphire rapids: the next-generation intel xeon scalable processor. In: 2022 IEEE International Solid-State Circuits Conference (ISSCC), vol 65. IEEE, pp 44–46

Dally WJ, Towles BP (2004) Principles and practices of interconnection networks. Elsevier, San Francisco

Google Scholar  

Jerger NDE, Krishna T, Peh L-S, Martonosi M (2017) On-chip networks, vol 12. Springer, Geneva

Book   Google Scholar  

Yin J, Lin Z, Kayiran O, Poremba M, Altaf MSB, Jerger NE, Loh GH (2018) Modular routing design for chiplet-based systems. In: 2018 ACM/IEEE 45th Annual International Symposium on Computer Architecture (ISCA). IEEE, pp 726–738

Cao W, Jiang S, Huang L (2022) Fast turn restriction algorithm to build deadlock-free modular chiplet integration systems. In: 2022 IEEE 4th International Conference on Circuits and Systems (ICCS). IEEE, pp 27–32

Chen C, Yin J, Peng Y, Palesi M, Cao W, Huang L, Singh AK, Zhi H, Wang X (2022) Design challenges of intra-and inter-chiplet interconnection. IEEE Des Test 39(6):99–109

Wu Y, Wang L, Wang X, Han J, Zhu J, Jiang H, Yin S, Wei S, Liu L (2022) Upward packet popup for deadlock freedom in modular chiplet-based systems. In: 2022 IEEE International Symposium on High-Performance Computer Architecture (HPCA). IEEE, pp 986–1000

Majumder P, Kim S, Huang J, Yum KH, Kim EJ (2020) Remote control: a simple deadlock avoidance scheme for modular systems-on-chip. IEEE Trans Comput 70(11):1928–1941

Article   MathSciNet   Google Scholar  

Woeginger GJ (2003) Exact algorithms for np-hard problems: a survey. In: Combinatorial Optimization-Eureka, You Shrink! Papers Dedicated to Jack Edmonds 5th International Workshop Aussois, France, 5–9 Mar, 2001 Revised Papers. Springer, pp 185–207

Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197

Li T, Hou J, Yan J, Liu R, Yang H, Sun Z (2020) Chiplet heterogeneous integration technology-status and challenges. Electronics 9(4):670–682

Shan G, Zheng Y, Xing C, Chen D, Li G, Yang Y (2022) Architecture of computing system based on chiplet. Micromachines 13(2):205–223

Pal S, Liu J, Alam I, Cebry N, Suhail H, Bu S, Iyer SS, Pamarti S, Kumar R, Gupta P (2021) Designing a 2048-chiplet, 14336-core waferscale processor. In: 2021 58th ACM/IEEE Design Automation Conference (DAC). IEEE, pp 1183–1188

Xia J, Cheng C, Zhou X, Hu Y, Chun P (2021) Kunpeng 920: the first 7-nm chiplet-based 64-core arm soc for cloud services. IEEE Micro 41(5):67–75

Naffziger S, Lepak K, Paraschou M, Subramony M (2020) 2.2 AMD chiplet architecture for high-performance server and desktop products. In: 2020 IEEE International Solid-State Circuits Conference-(ISSCC). IEEE, pp 44–45

Wade M, Anderson E, Ardalan S, Bhargava P, Buchbinder S, Davenport ML, Fini J, Lu H, Li C, Meade R (2020) Teraphy: a chiplet technology for low-power, high-bandwidth in-package optical I/O. IEEE Micro 40(2):63–71

Taheri E, Pasricha S, Nikdast M (2022) Deft: a deadlock-free and fault-tolerant routing algorithm for 2.5 D chiplet networks. In: 2022 Design, Automation & Test in Europe Conference & Exhibition (DATE). IEEE, pp 1047–1052

Stow D, Xie Y, Siddiqua T, Loh GH (2017) Cost-effective design of scalable high-performance systems using active and passive interposers. In: 2017 IEEE/ACM International Conference on Computer-Aided Design (ICCAD). IEEE, pp 728–735

Dally WJ, Seitz CL (1987) Deadlock-free message routing in multiprocessor interconnection networks. IEEE Trans Comput 100:547–553

Cao Z, Wan Z, Li P, Liu Q, Wang C, Shao Y (2024) Lbdr: A load-balanced deadlock-free routing strategy for chiplet systems. Integration 96:102149

Goldberg EI, Prasad MR, Brayton RK (2002) Using problem symmetry in search based satisfiability algorithms. In: Proceedings 2002 Design, Automation and Test in Europe Conference and Exhibition. IEEE, pp 134–141

Download references

Acknowledgements

This work was supported by National Key R &D Program: Design and Verification of System Level Development Environment for Wafer-Scale Chip (2022YFB4401401).

Author information

Authors and affiliations.

Information Engineering University, Zhengzhou, 450001, Henan, China

Zhipeng Cao, Wei Guo, Peijie Li & Qinrang Liu

Zhejiang Lab, Hangzhou, 311121, Zhejiang, China

Zhiquan Wan

Songshan Lab, Zhengzhou, 450000, Henan, China

Caining Wang & Yangxue Shao

You can also search for this author in PubMed   Google Scholar

Contributions

ZC completed the proposal of innovative points, experimental verification and paper writing. WG and ZW completed the proposal of innovative points, data analysis and collation. PL helped in investigation of chiplet, methodology of simulation and supervision. QL done project administration and resources. CW and YS done software and validation.

Corresponding author

Correspondence to Qinrang Liu .

Ethics declarations

Conflict of interest.

The authors declare no competing interests.

Additional information

Publisher's note.

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Cao, Z., Guo, W., Wan, Z. et al. ETRS: efficient turn restrictions setting method for boundary routers in chiplet-based systems. J Supercomput (2024). https://doi.org/10.1007/s11227-024-06261-z

Download citation

Accepted : 21 May 2024

Published : 01 June 2024

DOI : https://doi.org/10.1007/s11227-024-06261-z

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

• Chiplet-based systems
• Deadlock-free
• Low-complexity
• Multi-objective optimization heuristics
• Find a journal
• Publish with us
• Track your research

File(s) stored somewhere else

Please note: Linked content is NOT stored on Deakin University and we can ' t guarantee its availability, quality, security or accept any liability.

Solving timetabling problem using genetic and heuristic algorithms

Publisher doi.

• https://doi.org/10.1109/snpd.2007.464

Publication classification

Copyright notice, title of proceedings, place of publication, usage metrics.

• School Guide
• Class 8 Syllabus
• Maths Notes Class 8
• Science Notes Class 8
• History Notes Class 8
• Geography Notes Class 8
• Civics Notes Class 8
• NCERT Soln. Class 8 Maths
• RD Sharma Soln. Class 8
• Math Formulas Class 8

How to Use Algorithms to Solve Problems?

• How to use Chat-GPT to solve Coding Problems?
• Wicked Problems and How to Solve Them?
• How to implement Genetic Algorithm using PyTorch
• Best Data Structures and Algorithms Books
• How to improve your DSA skills?
• Tricks To Solve Age-Based Problems
• The Role of Algorithms in Computing
• Most important type of Algorithms
• How to Identify & Solve Binary Search Problems?
• Quiz on Algorithms | DSA MCQs
• Introduction to Beam Search Algorithm
• Algorithms Quiz | Sudo Placement [1.8] | Question 5
• Top 50 Problems on Recursion Algorithm asked in SDE Interviews
• What are Logical Puzzles And How to Solve them?
• What is Algorithm | Introduction to Algorithms
• Top 10 Algorithms in Interview Questions
• Data Structures & Algorithms Guide for Developers
• Top 50 Binary Search Tree Coding Problems for Interviews
• Top 20 Greedy Algorithms Interview Questions

An algorithm is a process or set of rules which must be followed to complete a particular task. This is basically the step-by-step procedure to complete any task. All the tasks are followed a particular algorithm, from making a cup of tea to make high scalable software. This is the way to divide a task into several parts. If we draw an algorithm to complete a task then the task will be easier to complete.

The algorithm is used for,

• To develop a framework for instructing computers.
• Introduced notation of basic functions to perform basic tasks.
• For defining and describing a big problem in small parts, so that it is very easy to execute.

Characteristics of Algorithm

• An algorithm should be defined clearly.
• An algorithm should produce at least one output.
• An algorithm should have zero or more inputs.
• An algorithm should be executed and finished in finite number of steps.
• An algorithm should be basic and easy to perform.
• Each step started with a specific indentation like, “Step-1”,
• There must be “Start” as the first step and “End” as the last step of the algorithm.

Let’s take an example to make a cup of tea,

Step 1: Start

Step 2: Take some water in a bowl.

Step 3: Put the water on a gas burner .

Step 4: Turn on the gas burner 

Step 5: Wait for some time until the water is boiled.  

Step 6: Add some tea leaves to the water according to the requirement.

Step 7: Then again wait for some time until the water is getting colorful as tea.

Step 8: Then add some sugar according to taste.

Step 9: Again wait for some time until the sugar is melted.

Step 10: Turn off the gas burner and serve the tea in cups with biscuits.

Step 11: End

Here is an algorithm for making a cup of tea. This is the same for computer science problems.

There are some basics steps to make an algorithm:

• Start – Start the algorithm
• Input – Take the input for values in which the algorithm will execute.
• Conditions – Perform some conditions on the inputs to get the desired output.
• Output – Printing the outputs.
• End – End the execution.

Let’s take some examples of algorithms for computer science problems.

Example 1. Swap two numbers with a third variable  

Step 1: Start Step 2: Take 2 numbers as input. Step 3: Declare another variable as “temp”. Step 4: Store the first variable to “temp”. Step 5: Store the second variable to the First variable. Step 6: Store the “temp” variable to the 2nd variable. Step 7: Print the First and second variables. Step 8: End

Example 2. Find the area of a rectangle

Step 1: Start Step 2: Take the Height and Width of the rectangle as input. Step 3: Declare a variable as “area” Step 4: Multiply Height and Width Step 5: Store the multiplication to “Area”, (its look like area = Height x Width) Step 6: Print “area”; Step 7: End

Example 3. Find the greatest between 3 numbers.

Step 1: Start Step 2: Take 3 numbers as input, say A, B, and C. Step 3: Check if(A>B and A>C) Step 4: Then A is greater Step 5: Print A Step 6 : Else Step 7: Check if(B>A and B>C) Step 8: Then B is greater Step 9: Print B Step 10: Else C is greater Step 11 : Print C Step 12: End

Advantages of Algorithm

• An algorithm uses a definite procedure.
• It is easy to understand because it is a step-by-step definition.
• The algorithm is easy to debug if there is any error happens.
• It is not dependent on any programming language
• It is easier for a programmer to convert it into an actual program because the algorithm divides a problem into smaller parts.

Disadvantages of Algorithms

• An algorithm is Time-consuming, there is specific time complexity for different algorithms.
• Large tasks are difficult to solve in Algorithms because the time complexity may be higher, so programmers have to find a good efficient way to solve that task.
• Looping and branching are difficult to define in algorithms.

Please Login to comment...

Similar reads.

• School Learning
• School Programming

Improve your Coding Skills with Practice

What kind of Experience do you want to share?