Binary Search is a searching technique which works on the Divide and Conquer approach. It is used to search for any element in a sorted array.
Compared with linear, binary search is much faster with a Time Complexity of O(logN), whereas linear search works in O(N) time complexity.
In this article, the implementation of Binary Search in Javascript is discussed using both iterative and recursive ways.
Given a sorted array of numbers. The task is to search for a given element 
in the array using Binary search.
Examples:
Input : arr[] = {1, 3, 5, 7, 8, 9}
x = 5
Output : Element found!
Input : arr[] = {1, 3, 5, 7, 8, 9}
x = 6
Output : Element not found!
Note: Assuming the array is sorted.
Recursive Approach :
- BASE CONDITION: If starting index is greater than ending index return false.
- Compute the middle index.
- Compare the middle element with number x. If equal return true.
- If greater, call the same function with ending index = middle-1 and repeat step 1.
- If smaller, call the same function with starting index = middle+1 and repeat step 1.
Below is the implementation of Binary Search (Recursive Approach) in JavaScript:
javascript
<script>let recursiveFunction = function (arr, x, start, end) { // Base Condition if (start > end) return false; // Find the middle index let mid=Math.floor((start + end)/2); // Compare mid with given key x if (arr[mid]===x) return true; // If element at mid is greater than x, // search in the left half of mid if(arr[mid] > x) return recursiveFunction(arr, x, start, mid-1); else // If element at mid is smaller than x, // search in the right half of mid return recursiveFunction(arr, x, mid+1, end);} // Driver codelet arr = [1, 3, 5, 7, 8, 9];let x = 5; if (recursiveFunction(arr, x, 0, arr.length-1)) document.write("Element found!<br>");else document.write("Element not found!<br>"); x = 6; if (recursiveFunction(arr, x, 0, arr.length-1)) document.write("Element found!<br>");else document.write("Element not found!<br>");</script> |
Output:
Element found! Element not found!
Time Complexity: O(logN)
Auxiliary Space: O(1)
Iterative Approach : In this iterative approach, instead of recursion, we use a while loop, and the loop runs until it hits the base condition, i.e. start becomes greater than end.
Below is the implementation of Binary Search (Iterative Approach) in JavaScript:
javascript
<script>// Iterative function to implement Binary Searchlet iterativeFunction = function (arr, x) { let start=0, end=arr.length-1; // Iterate while start not meets end while (start<=end){ // Find the mid index let mid=Math.floor((start + end)/2); // If element is present at mid, return True if (arr[mid]===x) return true; // Else look in left or right half accordingly else if (arr[mid] < x) start = mid + 1; else end = mid - 1; } return false;} // Driver codelet arr = [1, 3, 5, 7, 8, 9];let x = 5; if (iterativeFunction(arr, x, 0, arr.length-1)) document.write("Element found!<br>");else document.write("Element not found!<br>"); x = 6; if (iterativeFunction(arr, x, 0, arr.length-1)) document.write("Element found!<br>");else document.write("Element not found!<br>");</script> |
Output:
Element found! Element not found!
Time Complexity: O(logN).
Auxiliary Space: O(1)
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