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Time Complexity

Hello people, in this blog we are going to read about the “Time Complexity”.

What is time complexity? What is the importance of time Complexity?

 In programming, every code is like a solution to some problem, and there can be number of solutions to such problems. So for picking the best of all solutions we work on finding the fastest solution, here the fastest solution is considered to be the best solution. So for having the best solution of our problems, we must have a good knowledge of time complexity.

According to Wikipedia, “Time complexity is the computational complexity that describes the amount of time it takes to run an algorithm.”

A good thing about time complexity is that it doesn’t bothers about the configuration of the machine we are using, it only depends on the time taken by the code with respect to the input we have provided.

Now the question arrives “How do we calculate the time taken by any code to run?”, So explaining about calculation of running time of a code, we start by letting an hypothetical set of rules

Rule 1 – It takes 1 unit of time for any logical or algorithmic operation.

 Rule 2 – It takes 2 unit of time for assignment and return

Now let us calculate the time taken by the following code on the basis of above mentioned rules;

So the total time taken by this code to run will be 3 units.

Now let’s take another example on the same set of rules;

So the total time taken by this code to run will be [ 2 + 4(n+1) + 3n + 2 ]units.

We can now say that

 T_Sum = 3

 T_{Sum_list} = (8+7n)

                        Similarly, T_{Sum_matrix} = an² + bn + c

Now before moving any further you need to study about the asymptotic functions. If you already knew about these asymptotic notations then you can proceed.

The time complexity is commonly expressed using big O notation.So, here T_Sum = O(1)

T_{Sum_list} = O(n)

T_{Sum_matrix} = O(n²)

 

You know what is big O notation, if not then read this first.

For getting the definable value for time complexity you need to know about Time Complexity Analysis. 

To have it all done regarding time complexity, you also need to know about the time complexity analysis too. 

If you still have any doubt on this topic then do come to us via email "sophomoretechs@gmail.com" or via instagram "@coding.winds".

We also have an article on space complexity, give it a read by clicking here.