[Algorithm] Count occurrences of a number in a sorted array with duplicates using Binary Search

Let's say we are going to find out number of occurrences of a number in a sorted array using binary search in O(log n) time.

For example the given array is:

[1,1,3,5,5,5,5,5,9,11],

the number 5 appears 5 times;

the number 3 appears 1 time;

2 appears 0 times.

The idea:

we can use binary search twice, first time is to find first index of target number in the array; second is to find last index of given number in the array.

function count_numbers(ary, target) {
  function helper(ary, target, isFirst) {
    let start = ;
    let end = ary.length - ;
    let result = -;
    while (start <= end) {
      let mid = Math.floor((start + end) / );
      if (ary[mid] === target) {
        result = mid;
        isFirst ? (end = mid - ) : (start = mid + );
      } else {
        ary[mid] > target ? (end = mid - ) : (start = mid + );
      }
    }

    return result;
  }

  const first = helper(ary, target, true);
  const last = helper(ary, target, false);

  if (first === - || last === -) {
    return ;
  }
  return last - first + ;
}

console.log(count_numbers([, , , , , , , , , , ], )); //