ADD - binary-search-recursive (#46)

* ADD - binary-search-recursive

This file contains recursive version of the Binary Search .

* Updated README.md

searching/README.md

@@ -15,7 +15,8 @@
 ### JavaScript
 
 1. [Linear Search](js/linear-search.js)
-2. [Binary Search](js/binary-search.js)
+2. [Binary Search ( Iterative )](js/binary-search.js)
+3. [Binary Search ( Recursive )](js/binary-search-recursive.js)
 
 ### Java
 

searching/js/binary-search-recursive.js

@@ -0,0 +1,52 @@
+//Recursive Method
+
+/*Arguments to Function 
+
+arr - array ( Sorted Only )
+low - lower index of array (0)
+high - max index of array  (length of array - 1 )
+item = Element to be searched .
+
+*/
+
+function binary_recurrence(arr, low, high, item) {
+ // Base Case for the termination of Recursion
+ 
+ if(low > high) { 
+   return -1 ; //Item is not present in the Array 
+  } 
+ 
+ // Calculating Mid Index 
+ let mid = Math.floor((low+high)/2) ;
+
+ //Equation Middle Element with the item to be searched 
+
+ if(arr[mid] == item ){  
+
+ // Middle Element equal to the Item 
+ // We found Element at the mid Index
+ return mid ;
+
+ }
+ else if( arr[mid] > item ){
+ 
+ // Item is less than the middle Element 
+ // Ignore the Right Half , as right half contains elements greater than middle element and so item too .
+ // Make a recursive call to the left Half 
+ 
+ return binary_recurrence(arr,low,mid-1,item); 
+ }
+ else {
+ //Item is greater than the middle Element 
+ //Ignore the Left Half ,as left half contains element less than middle element and so item too .
+ //Make recursive call to the right Half 
+ 
+ return binary_recurrence(arr,mid+1,high,item);
+ 
+ }
+
+}
+
+console.log(binary_recurrence([1,3,5,7,8,9], 0, 5, 7)); //returns 3 , Found at Index 3 
+
+console.log(binary_recurrence([1,3,5,7,8,9], 0, 5, 10)); //returns -1 , 10 is not present in array