Algorithmic Design: How Algorithms Are Created and Analyzed

Key takeaways

Algorithmic design is a structured approach to creating algorithms that solve computational problems using logic and mathematical principles. Here are some important things to know:

• As of May 2024, the median annual wage was $98,670 for computer programmers, $112,590 for data scientists, and $133,080 for software developers [1, 2, 3]. 

• Most algorithms involve a combination of sequencing, selection, and repetition building blocks. 

• You can explore algorithmic design techniques, such as divide-and-conquer, the greedy method, and dynamic programming, to optimize problem-solving.

Explore algorithmic design principles and techniques to help you design efficient, accurate, and reproducible algorithms. If you’re ready to start learning, enroll in the IBM Data Science Professional Certificate. You’ll have the opportunity to clean data sets, analyze and visualize data, and build machine learning models and pipelines in as little as four months.

What is algorithmic design?

Algorithmic design is the process of creating a series of instructions to accomplish a task or solve a computational problem. In a basic sense, an algorithm is a step-by-step process to reach a certain end result or generate a specific output. For example, you could consider the steps you take to prepare a cup of coffee as a simple algorithm. 

Where algorithmic design comes into play is creating a methodology that can reach this end result in the face of different scenarios or obstacles. What happens if you are out of coffee beans? What if your kettle won’t turn on? What if all of your coffee mugs are in the dishwasher? Algorithmic design provides a set of instructions for how to handle different scenarios and make informed decisions to complete the task at hand. In practice, designing an effective algorithm involves selecting the right data structures, mathematical models, and algorithmic techniques to reach the desired end result. 

Theory vs. practice in algorithms

While understanding the theory behind algorithmic design may help you design a strong model and predict its performance, practical implementation involves iterating on this design so it effectively runs in a real-world setting. In theory, you can often create many algorithms to solve the same problem, making it difficult to know which one is “best” for your use case. By comparing theoretical models in light of real-world constraints, you can decide which design most efficiently solves your problem.

Taking an algorithm from a theoretical design to a functional program requires a process of testing and debugging across a range of scenarios. To fully optimize your algorithm, you may need to adapt your design to operate under practical constraints. For example, challenges related to changing run-time environments, memory inefficiencies, or computational complexity may alter the performance of your algorithm in practice. In some cases, you may have to make decisions related to your priorities, such as trade-offs between model accuracy, computational demands, and system performance.

What is an example of algorithm design?

An example of algorithm design would be creating a navigation application that determines the fastest route to a destination. If you were creating this application, your algorithm would need to process live traffic data, evaluate multiple possible routes, and continually update to the most efficient set of directions as conditions change. During the design process, you would consider how to input the correct data, process it efficiently, and communicate the results to users.

Algorithm design patterns

An algorithmic pattern is a strategy to solve a problem. Understanding different options may help you choose the best one for your use case or develop several options to compare and contrast. 

Common patterns to start by exploring include:

• Brute force: Tests all solutions until finding the correct one, offering simplicity at the cost of efficiency.

• Divide and conquer: Divides a complex problem into smaller independent subproblems, solving each problem independently, and combines the results into a single solution. 

• Decrease and conquer: Reduces the size of the problem at each step, solving a smaller instance at each stage until it builds the full solution. 

• The greedy method: Makes the best immediate choice at each step, hoping that local optimizations will lead to the best overall solution. 

• Dynamic programming: Creates overlapping subproblems and stores intermediate results to avoid redundancy, caching the results of the overlapping subproblems for a final solution. 

• Backtracking: Explores possible solutions incrementally, backtracking when a potential solution proves infeasible. 

Example algorithm design patterns to explore

Choosing the right pattern for your problem depends on your data type and computational goals, and for each pattern type, you can find multiple algorithm options. For example, you might use a binary search method to solve a search problem with sorted data. This algorithm operates as a “decrease and conquer” approach, reducing the problem size by half with each step until finding the target. Conversely, if you were working with a problem that requires splitting your data set into smaller parts, then recombining them for a final result, you might opt for a divide-and-conquer algorithm such as mergesort or quicksort.

If you decided the greedy method was the best fit, you could take time to explore algorithm options such as minimum spanning trees and Huffman coding to find which one best fits your use case. Otherwise, if you want to use dynamic programming, interval scheduling and coin changing are example algorithms to start with, while backtracking methods such as map coloring and eight queens can provide a launch point for your project.

How do you create an algorithm?

Creating an effective and efficient algorithm involves a comprehensive understanding of your problem, the steps needed to reach your solution, and how to design a repeatable process that can be replicated by other users. 

The first step in doing this is decomposing your problem. To do this, you can represent the steps from the input to the desired output by using pseudocode, flowcharts, or other visualizations that clearly communicate how information will flow and be processed to reach the desired result. This flow should be interpretable by people from all backgrounds, not only those who know how to write the algorithmic code itself. 

Once you have clearly defined your program steps, you can begin building your algorithm. The information you need here falls into three categories:

• Inputs: Consider the type of data you have available and how to best design your algorithm to effectively work with this type of information.

• Outputs: Consider what format or data type your algorithm should output. This can help you design the endpoint of your algorithm effectively.

• Process considerations: Consider the conditions and test scenarios your algorithm should meet, practical constraints, and your process of iteration.

Once you’ve designed your algorithm, you can perform a few steps to validate that you have actually solved the problem you intended to and ensure that your algorithm is the most effective overall solution. Some ways you can do this include assessing computational resource use, time to completion, and having a trace algorithm follow the steps involved to check for any logical inefficiencies. 

What are the three algorithm designs?

The three algorithm design building blocks are sequencing, selection, and repetition. Sequencing is the simplest and includes running algorithm steps in the order they’re written. Selection is slightly more complex and involves branching. This means that for every input, some sections of the code may run, while others may not, depending on whether it meets certain criteria. The third building block is repetition, which involves looping control flow and iteration. With repetition, certain chunks of your code run repeatedly until you reach a certain outcome. By combining these three algorithm designs, you can build increasingly complex and effective algorithms.

Applications of the design and analysis of algorithms

The design and analysis of algorithms underpin the vast majority of technologies you use today. Algorithms power search engines, social media, recommendation systems, and technical applications. In fields like cybersecurity and cryptography, they protect sensitive information and data transfers. In finance, algorithms help traders automatically track the market prices and execute trades at certain thresholds. 

As machine learning and artificial intelligence begin to take center stage in many industries, professionals are developing more complex algorithms that allow computers to iteratively learn from new information and improve their performance over time. In some cases, generative artificial intelligence algorithms, such as those used by ChatGPT, can respond to user queries and create new content, changing the way we interact with machines.

Careers using algorithmic design

Professionals working in algorithmic design often work as algorithm engineers, software developers, computer programmers, or data scientists. These jobs tend to require technical expertise in one or more programming languages and a strong grasp of programming logic, data manipulation, and algorithmic design. 

Because of the required technical expertise, these professions tend to earn attractive salaries. According to the Bureau of Labor Statistics, the median annual wage as of 2024 was $98,670 for computer programmers, $112,590 for data scientists, and $133,080 for software developers [1, 2, 3]. Depending on your role and industry, you may use algorithmic development for different applications. 

Learn more: How to Become a Computer Programmer 

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• Learn key terms: Data Science Terminology and Definitions 

• Watch on YouTube: 7 Essential Skills Every Data Scientist Should Have 

• Explore career paths: Machine Learning Career Paths: Explore Roles & Specializations 

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