Update BinarySearch.js (TheAlgorithms#209)

* Update BinarySearch.js

The old algorithm didn't work, I believe for two main reasons:
1 -  Number.MAX_VALUE is not a valid array index as it is used to represent the highest possible value in javascript (https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Number/MAX_VALUE);

2 - splice() is not a pure function, every time it is called it has the side effect of modifying the original array (https://www.w3schools.com/jsref/jsref_splice.asp) ;

So I rewrote the algorithm, it now returns an index ( -1 if not found ) and it works both on numbers and on strings.

* Update BinarySearch.js

Style change

* Update BinarySearch.js

Style change

* Update BinarySearch.js

Author: Askanders

Search/BinarySearch.js

@@ -1,26 +1,70 @@
-/* Binary Search-Search a sorted array by repeatedly dividing the search interval
+/* Binary Search: https://en.wikipedia.org/wiki/Binary_search_algorithm
+ *
+ * Search a sorted array by repeatedly dividing the search interval
  * in half. Begin with an interval covering the whole array. If the value of the
  * search key is less than the item in the middle of the interval, narrow the interval
  * to the lower half. Otherwise narrow it to the upper half. Repeatedly check until the
  * value is found or the interval is empty.
  */
 
-function binarySearch (arr, i) {
-  var mid = Math.floor(arr.length / 2)
-  if (arr[mid] === i) {
-    console.log('match', arr[mid], i)
-    return arr[mid]
-  } else if (arr[mid] < i && arr.length > 1) {
-    binarySearch(arr.splice(mid, Number.MAX_VALUE), i)
-  } else if (arr[mid] > i && arr.length > 1) {
-    binarySearch(arr.splice(0, mid), i)
+function binarySearch (arr, x, low = 0, high = arr.length - 1) {
+  const mid = Math.floor(low + (high - low) / 2)
+
+  if (high >= low) {
+    if (arr[mid] === x) {
+      // item found => return its index
+      return mid
+    }
+
+    if (x < arr[mid]) {
+      // arr[mid] is an upper bound for x, so if x is in arr => low <= x < mid
+      return binarySearch(arr, x, low, mid - 1)
+    } else {
+      // arr[mid] is a lower bound for x, so if x is in arr => mid < x <= high
+      return binarySearch(arr, x, mid + 1, high)
+    }
   } else {
-    console.log('not found', i)
+    // if low > high => we have searched the whole array without finding the item
     return -1
   }
 }
 
-var ar = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
-binarySearch(ar, 3)
-binarySearch(ar, 7)
-binarySearch(ar, 13)
+/* ---------------------------------- Test ---------------------------------- */
+
+const arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
+const stringArr = [
+  'Alpha',
+  'Bravo',
+  'Charlie',
+  'Delta',
+  'Echo',
+  'Foxtrot',
+  'Golf',
+  'Hotel',
+  'India',
+  'Juliet',
+  'Kilo',
+  'Lima',
+  'Mike',
+  'November',
+  'Oscar',
+  'Papa',
+  'Quebec',
+  'Romeo',
+  'Sierra',
+  'Tango',
+  'Uniform',
+  'Victor',
+  'Whiskey',
+  'X-Ray',
+  'Yankee',
+  'Zulu'
+]
+
+console.log(binarySearch(arr, 3))
+console.log(binarySearch(arr, 7))
+console.log(binarySearch(arr, 13))
+
+console.log(binarySearch(stringArr, 'Charlie'))
+console.log(binarySearch(stringArr, 'Zulu'))
+console.log(binarySearch(stringArr, 'Sierra'))