Efficient way to count occurrences of a key in a sorted array

Question

This was asked in on-site Microsoft interview.

Count the number of occurrences of a given key in an array.

I answered linear search because the elements may be s

Answer 1

How about this for the sorted part, with O(logN) time complexity?

int count(int a[], int k, int l, int h) {
  if (l>h) {
    return 0;
  }
  int mid = (l+h)/2;
  if (k > a[mid]) {
     return count(a, k, mid+1, h);
  }
  else if (k < a[mid]) {
     return count(a, k, l, mid-1);
  }
  else {
     return count(a, k, mid+1, h) + count(a, k, l, mid-1) + 1;
  }
}