Time and Space Complexity of Algorithm or Program Explained

If you are a computer science student or professional, you must have come across time and space complexity terminologies.

These are two very important fundamental concepts in computer science. These fundamental concepts are very useful to analyze the efficiency of algorithms and programs.

If you are appearing for a software developer interview, these are the very important concepts you should definitely know.

Let’s check them one by one.

What is Time Complexity?

Time complexity is associated with the time it takes to execute the algorithm.

It measures how the runtime of an algorithm grows as the input size increases. 

Big O notation is used to express the time complexity, which provides an upper bound on the growth rate of an algorithm’s runtime.

Let’s take an example: 

If one says, the order of time complexity of the algorithm is O(n) (or O(n^2)), what does it mean?

An algorithm with a time complexity of O(n) means that the runtime grows linearly with the input size. 

An algorithm with O(n^2) means that the runtime grows quadratically with the input size, and so on.

What is Space Complexity?

Time complexity is associated with the amount of memory space it takes to execute the algorithm.

Space complexity measures the amount of memory an algorithm or program uses as a function of the input size. 

Similar to time complexity, it’s also usually expressed using big O notation.

Let’s take an example:

• An algorithm with O(n) space complexity means that the amount of memory used grows linearly with the input data size.
• An algorithm with O(n^2) space complexity means that the amount of memory used grows quadratically with the input data size.

Important Points about Time and Space Complexity

• The similarity between time and space complexities is that they are measured against the input data size.
• Time and space complexity is not the property of programming language. It is associated with the algorithm.
• Usually, space and time complexities are expressed using big O notations.
• These two complexities are very beneficial to measure the efficiency of any algorithm. 

What does O(1) time and space complexity mean?

If time complexity O(1) means, the algorithm takes constant time irrespective of the input data size. That is, the algorithm is independent of input size.

Similarly, if the space complexity is O(1) means, the algorithm takes constant space irrespective of the input data time. That is, the algorithm is independent of input size.

The algorithm that takes constant space and time is the most efficient algorithm. 

How to choose an efficient algorithm?

Let’s take an example of sorting algorithms to bring the comparison to the table. There are many sorting algorithms but you have to choose the best one for your project.

If you have a constraint on time execution, you should always choose an algorithm that has low time complexity. 

Similarly, if you have a constraint over the memory space, choose an algorithm that has low space complexity.

In case, if you have an algorithm that has both time and space complexity lower than other algorithms, you got the best one.

Summary

Both time complexity and space complexity are crucial for understanding the efficiency of algorithms and programs.

Analyzing these complexities helps developers choose the most appropriate algorithm to solve a specific problem.

Picking the right algorithm for development ensures that software is both performance (time) and resource (memory space) efficient.

I tried to keep it simple. I hope you like this tutorial. If you have any doubts, write down in the comment section below.

Aniruddha Chaudhari

I am complete Python Nut, love Linux and vim as an editor. I hold a Master of Computer Science from NIT Trichy. I dabble in C/C++, Java too. I keep sharing my coding knowledge and my own experience on <b>CSEstack.org</b> portal.