Question

Below is a binary search function.

int search(int a[], int v, int left, int right)
{
    while (right >= left)
    {
        int m = (left + right)/2;
        if (v == a[m]) 
            return m;
        if (v < a[m])
            right = m - 1;
        else left = m + 1;
    }
    return -1;
}

How do I determine the Big-O notation for this function?

Is this search function O(n) since the while loop is dependent on the value of left?

Answer 1

In each step, the range of values halves (roughly) – if you start with right - left == 100, then at the second step it will be 49, then 24, then 11 etc.

Assuming n = right - left, the complexity is O(log n). (It’s dependent on the values of both right and left.)