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c++for-loopspace-complexity

Calculating the space complexity of for loops

I have a piece of code of which space complexity is to be calculated in Big-O notation

 int a = 0, b = 0;    
    for (i = 0; i < N; i++) {
        a = a + rand();  
    }
    for (j = 0; j < M; j++) {
        b = b + rand();
    }

The rand() is an O(1) space.

I think the answer should be O(max(M,N)) but the answer in my textbook is O(1). Shouldn't the space depend on N and M?

Solution

  • Space complexity here does not depend on N and M. Space complexity depends on int so the Space Complexity is O(1).
    Time Complexity is O(max(M,N)) and O(n) is just enough, no need for too much details (i mean here on max(M,N))