Implementation of C lower_bound

Here are the equivalent implementations of upper_bound and lower_bound. This algorithm is O(log(n)) in the worst case, unlike the accepted answer which gets to O(n) in the worst case.

Note that here high index is set to n instead of n - 1. These functions can return an index which is one beyond the bounds of the array. I.e., it will return the size of the array if the search key is not found and it is greater than all the array elements.

int bs_upper_bound(int a[], int n, int x) {
    int l = 0;
    int h = n; // Not n - 1
    while (l < h) {
        int mid =  l + (h - l) / 2;
        if (x >= a[mid]) {
            l = mid + 1;
        } else {
            h = mid;
        }
    }
    return l;
}

int bs_lower_bound(int a[], int n, int x) {
    int l = 0;
    int h = n; // Not n - 1
    while (l < h) {
        int mid =  l + (h - l) / 2;
        if (x <= a[mid]) {
            h = mid;
        } else {
            l = mid + 1;
        }
    }
    return l;
}

The actual C++ implementation works for all containers. You can find it here.