Binary search, binary search with recursion, rotation count, circular array search

binarySearch.js

// first = true - find first occurance
// first = false - find last occurance
// first = undefined - first found

function binarySearch(array, x, first) {
  var start = 0, end = array.length - 1, mid = 0, result = -1;
  while (start <= end) {
    mid = Math.floor((start + end) / 2);
    if (array[mid] == x) {
      result = mid;
      if (typeof first === 'undefined') {
        return result; 
      } else if (first === true) {
        end = mid - 1;
      } else if (first === false) {
        start = mid + 1;
      }
    } else if (x < array[mid]) {
      end = mid - 1;
    } else {
      start = mid + 1;
    }
  }
  return result;
}

binarySearchRecursion.js

// Binary search implemented with recursion

function binarySearchRecursion (array, x, low, high) {
  var _low = typeof low !== 'undefined' ? low : 0;
  var _high = typeof high !== 'undefined' ? high : array.length - 1;
  var mid = Math.floor((_high + _low) / 2);
  if (_low > _high) return -1;
  if (array[mid] === x) {
    return mid;
  } else if (x < array[mid]) {
    return binarySearchRecursion(array, x, _low, mid - 1);
  } else if (x > array[mid]) {
    return binarySearchRecursion(array, x, mid + 1, _high);
  }
}

circularArraySearch.js

// Searching for element x in circular (rotated) sorted array witout duplicates
// (looking for the sorted parts of the array, then searching for x in these sorted parts)

function circularArraySearch (array, x) {
  var start = 0, end = array.length - 1, mid;
  while (start <= end) {
    mid = Math.floor((start + end) / 2);
    if (array[mid] == x) {
      return mid;
    }
    if (array[mid] <= array[end]) {
      if (x > array[mid] && x <=array[end]) {
        start = mid + 1;
      } else {
        end = mid - 1;
      }
    }
    if (array[mid] >= array[start]) {
      if (x >= array[start] && x < array[mid]) {
        end = mid - 1;
      } else {
        start = mid + 1;
      }
    }
  }
  return -1;
}

findRotationCount.js

// Counting rotations in circular (rotated) sorted array
// (looking for the pivot point and returning its position)

function findRotationCount (array) {
  var low = 0;
  var high = array.length - 1;
  var mid, next, prev;
  while (low <= high) {
    if (array[low] <= array[high]) {
      return low;
    }
    mid = Math.floor((low + high) / 2);
    next = (mid + 1) % array.length;
    prev = (array.length + mid - 1) % array.length;
    if (array[mid] <= array[prev] && array[mid] <= array[next]) {
      return mid;
    }
    if (array[mid] <= array[high]) {
      high = mid - 1;
    }
    if (array[mid] >= array[low]){
      low = mid + 1;
    }
  }
}