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September 20, 2022

Our ability to understand and solve problems is fascinating. Whether we face a technical challenge or a simple everyday issue, we immediately start thinking about a solution. If we look closely, a solution to a problem is simply a series of steps, also called an algorithm. All modern technology, like AI, is fueled by robust algorithms that solve millions of complex problems. This is only possible because they have been developed using the right algorithm design strategy. This article discusses examples of algorithm design that can help improve your project's efficiency dramatically.

An algorithm is a particular set of instructions to solve a problem. The steps can involve logical or mathematical operations together. Each step can be an action performed just once or repetitively for several times. In addition, some steps will only perform actions if a certain condition is satisfied, e.g. a quantity has a specific value, the user has given an input or not, etc. We have used algorithms throughout our lives. Hence, we don't need to look at technical problems to understand how they work. Instead, we can use an activity from our daily lives as an example.

Let's look at a simple problem of adding two numbers and storing the answer. The algorithm will look like the following:

- Step. 1 – Declare variables 'A', 'B', and 'Answer'.
- Step. 2 – Take the value of 'A'
- Step. 3 – Take the value of 'B'
- Step. 4 – Sum the values of 'A' and 'B'
- Step. 5 – Assign their sum to the 'Answer' variable
- Step. 6 – Display 'Answer'
- Step. 7 – Stop

**Note: **Technologies like Google's search and Facebook involve much more complex problems. Hence, they typically use the best and proprietary algorithm design techniques. In this blog, we will explore 9 simple examples of algorithm design techniques.

An algorithm design technique means a unique approach or mathematical method for creating algorithms and solving problems. While multiple algorithms can solve a problem, not all algorithms can solve it efficiently. Therefore, we must create algorithms using a suitable algorithm design method based on the nature of the problem. An algorithm created with the right design technique can solve the problem much more efficiently with respect to the computational power required.

The nine most commonly used algorithm design techniques and the nature of algorithms they help create are:

- Sorting: Sorting input in an increasing or decreasing order
- Greedy: Selecting each part of a solution only because it is immediately beneficial
- Backtracking: Solving all possible combinations then backtracking if the current solution doesn't look desirable
- Divide and conquer: Solving the problem by dividing it into sub-problems
- Brute Force: Finding all the possible solutions and trying each one-by-one
- Recursive: Breaking the problem into small pieces, finding the answer, and using that solution to solve a larger problem
- Searching: Searching for an element in a collection
- Dynamic Programming: Solving problems with overlapping sub-problems
- Randomized Algorithms: Using randomness to help solve a problem more efficiently

Sorting algorithms accept a collection of elements as input and sort the collection according to a particular characteristic. For example, a collection of numbers can be sorted according to their value or their difference from some other number. Similarly, a collection of string values can be sorted based on their lengths or the number of specific letters in them.

The sorting can be in an increasing or decreasing arrangement. It can also be in a logical or lexicographical order. Ultimately, the sorting algorithm returns the sorted arrangement of the input collection.

Here are some of the most widely known sorting algorithms:

- Selection Sort
- Bubble Sort
- Insertion Sort
- Merge Sort
- Quick Sort
- Heap Sort
- Radix Sort
- Bucket Sort
- Comb Sort

Let's look at Merge Sort. The algorithm sorts input in the following way:

- Step 1 – Divides the input into halves
- Step 2 – Sorts each half
- Step 3 – Combines both halves in a sorted manner

In the second step, the algorithm calls itself to sort each half. It keeps doing this until it reaches a single element. Then, it starts returning smaller sorted collections and keeps combining them to return the sorted input.

Greedy algorithms craft a solution piece by piece, and their selection criteria when selecting the next piece is that it should be instantly fruitful. Hence, the algorithm evaluates all the options at each step and chooses the best one at the moment. However, they aren't beneficial in all situations.

A greedy algorithm solution isn't necessarily an overall optimal solution since it only goes from one best solution to the next. Additionally, there is no backtracking involved if it chooses the wrong option or step.

Greedy algorithms are the best option for certain problems. A popular example of greedy algorithm is sending some information to the closest node in a network. Some other graph-based greedy algorithm examples are: Dijkstra's Algorithm Prim and Kruskal's Algorithm Huffman Coding Tree.

A backtracking algorithm finds all the possible combinations of a solution and evaluates if it isn't optimal. If it isn't, the algorithm backtracks and starts evaluating other solutions. Backtracking algorithms share a common approach with the brute force algorithm design technique. However, they are much faster than brute-force algorithms.

There are different kinds of backtracking algorithms based on the kind of problems they solve:

- Decision Problem – Find a feasible solution
- Optimization Problem – Find the most optimal solution
- Enumeration Problem – Find all feasible solutions

Backtracking algorithms are the most optimal for problems where we may need to go back a few steps and make different decisions. For example, one of the most famous backtracking algorithm examples is the one for solving crossword puzzles. Similarly, the eight queens puzzle also requires going back if the current solution isn't the right one.

A divide and conquer algorithm breaks down the complexity of its problem so it can solve smaller and easier sub-problems. It involves three major steps:

- Divide – Divide the problem into multiple sub-problems of the same nature
- Solve – Solve each resulting sub-problem
- Combine – Combine the solutions to the sub-problems to get the solution to the starting problem

A divide and conquer algorithm handles each sub-problem separately. Such algorithms give the most optimal solution for problems like efficiently sorting a collection of elements.

Thanks to their simple approach, it isn't hard to understand divide and conquer algorithms. There are many divide and conquer algorithm examples in the real world. For example, take the common problem of looking for a lost item in a huge space. It is easier to divide the space into smaller sections and search in each separately.

A brute force algorithm uses the most straightforward way of achieving a problem's solution: keep trying until you find the right one. One example of a brute force algorithm is having multiple keys and trying to open a lock.

Such algorithms create all solutions from the input and try each to solve the problem. In principle, brute force and backtracking use the same approach. The only difference is that the latter backtracks if they find a solution unsuitable.

Cracking the password of an application is a popular brute force algorithm example. Given that there are unlimited retries, the only way is to try every possible password combination until we find the right one. Another example is visiting multiple locations and finding the shortest routes. Such examples show that brute force algorithms rely on having plenty of computational power.

Recursive algorithms solve a problem by first breaking it down into smaller parts. The algorithm solves that smaller problem and then the recursive algorithm starts solving the bigger problem it branched off from. It keeps happening until it reaches the main problem.

Recursive algorithms are easily understandable but have pitfalls such as infinite recursion calls and high computational power usage. Some types of recursion algorithms are:

- Direct Recursion
- Indirect Recursion
- Tailed Recursion
- Non-tail Recursion

One of the most famous recursive algorithm examples is for generating a Fibonacci sequence. The sequence starts from 0 and 1, and the next number is generated using the sum of the previous two. The recursive algorithm to generate the n-th Fibonacci number calls itself twice to find the n-1th and n-2th Fibonacci numbers and add them. Here, it solves the smaller problem (finding n-1th and n-2th Fibonacci numbers) and uses that to solve the main problem. The most common implementation of Merge Sort also uses recursion. It recursively sorts the two halves of the input and combines them.

A searching algorithm retrieves information about an element's existence in a collection. Here are different types of searching algorithms based on their approach:

- Linear Search: Checks each element in the collection
- Binary Search: Searches the first or latter half of a sorted collection depending on the element's value
- Hashing: Searches using the hash value obtained through a hashing algorithm

There are different search algorithms, each searching for the element in a certain data structure. For example, some popular searching algorithms for graphs are:

- Breadth-first Search
- Depth-first Search
- A* search

Similarly, hash-based searching uses unique values called hash values generated by a hashing algorithm. Linear and binary search are the common options for searching an element in a collection.

Dynamic programming is a class of algorithms that solve problems that have overlapping sub-problems. Therefore, they are well-suited for problems where certain sub-problems get solved repeatedly. Hence, a dynamic programming algorithm optimizes the solution by storing the answers to sub-problems in an optimal structure and retrieving them when needed.

The problem of generating a Fibonacci sequence is one of the popular dynamic programming algorithm examples. After all, we keep solving the sub-problems repeatedly. For example, if we found the 5th number, we must have found all the ones before. Therefore, they are handy for finding the 6th number.

Randomized algorithms use random numbers as part of their logic to decide what to do next. A randomized algorithm can help speed up an otherwise brute force approach and improve efficiency by getting us a momentarily, if not overall, optimal solution.

One of the most popular randomized algorithm examples is Quicksort. The algorithm divides the input into two halves on a randomly chosen pivot point. All elements on the left of the pivot are smaller, and all on the right are greater. The random pivot helps improve Quicksort's time complexity.

Now that we know different techniques for designing algorithms, here is the process of conceiving an algorithm:

- Collect the problem's requirements and details
- Analyze the collected details
- Choose the right algorithm design technique and create an algorithm
- Fine-tune the algorithm's workings
- Thoroughly test the algorithms for edge cases

In Collimator, you can easily design and test any algorithm using our easy to use GUI and high performance computing power. Here is the simple process to get started:

- Create your project in Collimator
- Design your algorithm using a variety of function blocks
- Run your simulation
- Visualize your results
- Share your results with your team

And that's it! Read more about how to use Collimator and what makes us the best MATLAB alternative for algorithm design. Our system design software features a comprehensive GUI for Python. There are numerous built-in function blocks to choose from to save time when designing algorithms and hybrid dynamical systems.