Binary Search

Given a sorted array arr[] of n elements, write a function to search a given element x in arr[].

A simple approach is to do linear search.The time complexity of above algorithm is O(n). Another approach to perform the same task is using Binary Search.

Binary Search: 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.

 

// Java implementation of recursive Binary Search
class BinarySearch
{
    // Returns index of x if it is present in arr[l..r], else
    // return -1
    int binarySearch(int arr[], int l, int r, int x)
    {
        if (r>=l)
        {
            int mid = l + (r - l)/2;
            // If the element is present at the middle itself
            if (arr[mid] == x)
               return mid;
            // If element is smaller than mid, then it can only
            // be present in left subarray
            if (arr[mid] > x)
               return binarySearch(arr, l, mid-1, x);
            // Else the element can only be present in right
            // subarray
            return binarySearch(arr, mid+1, r, x);
        }
        // We reach here when element is not present in array
        return -1;
    }
    // Driver method to test above
    public static void main(String args[])
    {
        BinarySearch ob = new BinarySearch();
        int arr[] = {2,3,4,10,40};
        int n = arr.length;
        int x = 10;
        int result = ob.binarySearch(arr,0,n-1,x);
        if (result == -1)
            System.out.println("Element not present");
        else
            System.out.println("Element found at index "+result);
    }
}
/* This code is contributed by Rajat Mishra */
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