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Last updated on 2024年9月12日

How can you reduce the time and space complexity of your algorithm design?

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Time and space complexity are two important measures of how efficient your algorithm is. They indicate how much time and memory your algorithm needs to run on a given input size. Reducing the time and space complexity of your algorithm design can improve the performance, scalability, and reliability of your code. In this article, you will learn some common techniques to achieve this goal.

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Shreyansh Sinha

SWE at Microsoft | Ex Siemens Healthineers, JP Morgan Chase | Hackerrank Certified at Problem Solving | Open for…
Georgios Korpas, Ph.D., MSCS

Senior Research Scientist | Quantum Computing, AI, Optimization, Applied Mathematics

1 Choose the right data structure

The first step to reduce the time and space complexity of your algorithm design is to choose the right data structure for your problem. Different data structures have different advantages and disadvantages in terms of access, insertion, deletion, and search operations. For example, arrays are good for random access, but bad for insertion and deletion. Linked lists are good for insertion and deletion, but bad for random access. Hash tables are good for fast search, but may have collisions and use extra space. Trees are good for hierarchical and sorted data, but may have balancing issues. Therefore, you should analyze the requirements and constraints of your problem and select the data structure that best suits your needs.

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Shreyansh Sinha

SWE at Microsoft | Ex Siemens Healthineers, JP Morgan Chase | Hackerrank Certified at Problem Solving | Open for Mentor/Instructor Roles | DM for Collaborations.
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One of the examples that I can think of w.r.t my work is when I did a optimization for one of the APIs I was building. Instead of using multiple loops, which would increase the complexity of the code and make the API slow, I used dictionary (or Hashmap/unordered_map) to precompute and store some of the results I needed. This way I was able to reduce the time complexity from O(N^2) to O(N) (assuming dictionary has constant lookup on average).

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Rodrigo Venancio

DevOps Engineer | SRE | Multicloud | CI/CD
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Avoid unnecessary recalculations with memoization and caching, memoization stores the results of expensive function calls and reuses them when the same inputs occur, reducing time complexity.

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2 Use divide and conquer

Another technique to reduce the time and space complexity of your algorithm design is to use divide and conquer. This is a strategy that breaks down a large problem into smaller and simpler subproblems, solves them recursively or iteratively, and combines their solutions to obtain the final result. Divide and conquer can help you reduce the time complexity of your algorithm by exploiting the subproblem overlap, reducing the input size, and applying efficient sorting and merging methods. It can also help you reduce the space complexity of your algorithm by using in-place modifications, avoiding unnecessary copies, and freeing up memory when possible.

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Georgios Korpas, Ph.D., MSCS

Senior Research Scientist | Quantum Computing, AI, Optimization, Applied Mathematics
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One idea is to consider quantum inspired solutions such as coherent Ising machines. While it’s hard to perform a theoretical convergence analysis since these algorithms are sort of heuristic, for the two best solvers I know (Fujitsu’s Digital Annealer and Lightsolver’s CIM) the specialised underlying chip architecture allows for very fast and very high quality solutions. While not an answer along the lines asked by the question (eg an answer there is something like warm starting and then using some deterministic method such as simplex or IPMs) I can safely guarantee that some of the worlds top organisations are looking into the solutions I suggest in the previous paragraph.

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3 Apply dynamic programming

A third technique to reduce the time and space complexity of your algorithm design is to apply dynamic programming. This is a method that solves complex problems by breaking them down into overlapping subproblems, storing the results of the subproblems in a table or an array, and reusing them whenever needed. Dynamic programming can help you reduce the time complexity of your algorithm by avoiding repeated computations, optimizing the order of calculations, and using memoization or tabulation techniques. It can also help you reduce the space complexity of your algorithm by using only the necessary amount of memory, pruning the table or the array, and using compression or hashing techniques.

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Jayapraveen A.

Full Stack Software Engineer | Java | Spring | Play | Angular | Kafka | Docker | Kubernetes | I help Enterprises to bring their Vision to Life
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Dynamic programming with memoization effectively reduces time and space complexity in algorithms. Consider the Fibonacci sequence: calculating F(5) requires F(4) and F(3), leading to repetitive calculations like F(3). A naive approach repeatedly recalculates these values, causing inefficiency. By employing dynamic programming, we store previously calculated values. When needed again, they're simply retrieved, not recalculated. This strategy reduces time complexity from exponential (O(2^n) in a naive approach) to linear (O(n) with memoization), optimizing algorithm efficiency significantly. This method also conserves space, making it an ideal choice for reducing recomputation.

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4 Optimize loops and conditions

Optimizing loops and conditions is a fourth technique to reduce the time and space complexity of your algorithm design. Variable names should be descriptive and meaningful, and variables should be initialized outside the loop. Pre-increment or post-increment operators should be used appropriately, and nested loops should be avoided if possible. Break and continue statements can be used to exit or skip iterations, and logical operators can combine or simplify conditions. Instead of multiple if-else statements, switch statements can be used, and short-circuit evaluation should be employed to avoid unnecessary evaluations.

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5 Test and debug your code

Testing and debugging are essential steps to ensure the correctness, robustness, and quality of your code, as well as to reduce the time and space complexity of your algorithm design. To do this, you should use some tools and methods, such as a debugger to step through your code and inspect the values of variables, expressions, and data structures; a profiler to measure the time and space usage of your code; a unit testing framework to write and run automated tests for your code; a code analyzer to check the syntax, style, and quality of your code; and a code reviewer to get feedback from other programmers. By applying these techniques, you can reduce the time and space complexity of your algorithm design while also improving your coding skills and confidence.

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Nanami K.

Staff Software Engineer (OWP @ Amazon) | Supercomputing, Cloud Computing, and Infrastructure
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Always write your own tests for your algorithms! Be able to test for edge-cases and any specifics detailed. Run through your code several times and look for ways to optimize. Think about downstream issues, think about long term optimizations, and write your code clear and concise!

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6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?

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How can you reduce the time and space complexity of your algorithm design?

1

2

3

4

5

6

1 Choose the right data structure

2 Use divide and conquer

3 Apply dynamic programming

4 Optimize loops and conditions

5 Test and debug your code

6 Here’s what else to consider

Algorithms

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How can you reduce the time and space complexity of your algorithm design?

1

2

3

4

5

6

1 Choose the right data structure

2 Use divide and conquer

3 Apply dynamic programming

4 Optimize loops and conditions

5 Test and debug your code

6 Here’s what else to consider

Algorithms

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