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Big O notation of three for loops

The first loop is executed n times. The second loop executes n/2 times. The third loop is executed k/2 times, which equals to n/4 times.

This gives you a O(n^3) complexity.

Empirical test:

#include <iostream>

using namespace std;

int main () {
    int n = 1000;

    long first = 0, second = 0, third = 0;

    for (int m = 1; m <= n; m++)
       for (int k = m; k >= 1; k--)

          for (int i = 1; i <= k; i++)

    cout << first << " " <<
second << " " << third << endl;

    return 0;


1000 500500 167167000

Categories : Java

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