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Time Complexity

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Space Complexity

What is Space Complexity and How to Calculate it?

Space complexity is a measure of how efficient your code is in terms of memory used.

Space complexity analysis happens almost in the same way time complexity analysis happens, i.e. it is measured by calculating the total space taken by an algorithm with respect to the input.

Eg: Let’s take the following example:

vector<int> V;
for (int i = 0; i < N; i++) V.push_back(i)

The code snippet ends up creating a vector of size N. So, space complexity of the code is O(n).

Eg: Let’s take another example. Let’s say we need to create a 2-D array of size n*n.

The space complexity in this case would be O(n2 ) .

Similar to Space complexity there is another concept called Auxiliary Space.

Auxiliary space is the extra space used by the algorithm apart from the input space.

Eg: The following is the code for calculating the sum of an input array.

Int sum( int arr[] , int n)
{
	int sum=0;
	for (int i=0 ; i< n ; i++)
	{
		sum+=arr[i];
      }
      return sum;
}

In the above algorithm apart from the input array we only declare one variable ‘sum’. 
Therefore for the above algorithm , 

  • Auxiliary Space = O(1)
  • Space complexity = O(n)

Difference between Time Complexity and Space Complexity:

Now that we know what time complexity and space complexity is, and how to calculate them, Let's discuss some key differences between them.

Time Complexity Space Complexity
Time Complexity is the time taken by an algorithm/program to run as a function of the length of the input. Space Complexity is the total amount of memory used by an algorithm to run.
Depends on the input size. Depends mostly on the auxillary size.(i.e the extra space used).
For modern hardware, it is more important to reduce your time complexity. For modern hardware, it is less important to reduce your space complexity as compared to the time complexity.

Space Complexity Cheat Sheet

Here’s a list of some famous algorithms and their space complexities.

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This topic has only Multiple Choice Questions

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Time Complexity Problems

Basic primer
Problem Score Companies Time Status
LOOP_CMPL 20
2:43
NESTED_CMPL 20
1:10
NESTED_CMPL2 30
1:25
CHOOSE4 50
0:57
Math
Problem Score Companies Time Status
WHILE_CMPL 50
1:31
NESTED_CMPL3 80 3:56
LOOP_CMPL2 80
2:43
GCD_CMPL 150
4:13
Compare functions
Problem Score Companies Time Status
CHOOSE3 50
1:39
CHOOSE1 50
1:43
CHOOSE2 80
2:23
Function calling itself
Problem Score Companies Time Status
REC_CMPL1 80
6:58
REC_CMPL2 80
6:25
REC_CMPL3 150
4:39
Amortized complexity
Problem Score Companies Time Status
AMORTIZED1 100
3:03

Additional Practice

Problem Score Companies Time Status
Collatz Conjecture 200 23:04
Palindromic Time 200 40:04
Pangram Check 100 27:13
Climbing Stairs 150 29:10
Integers in Strings 100 20:49
Word Count 150 23:09
Extracting Numbers 100
LTI
24:49
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