Question

I am learning algorithms and stumbled upon this article in top coder.

This is an example from the article

int result=0;                           //  1
for (int i=0; i<N; i++)                 //  2
  for (int j=i; j<N; j++) {             //  3
    for (int k=0; k<M; k++) {           //  4
      int x=0;                          //  5
      while (x<N) { result++; x+=3; }   //  6
    }                                   //  7
    for (int k=0; k<2*M; k++)           //  8
      if (k%7 == 4) result++;           //  9
  }                                     // 10

The time complexity of the while-cycle in line 6 is clearly O(N) – it is executed no more than N/3 + 1 times.

I am confused here as author says time complexity is O(N). For me it seems O(N^4). Please explain, what am I overlooking. I am only starting algorithms.

Answer 1

The complexity of the while-cycle in line 6 is O(N).