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# Order-Agnostic Binary Search

• Difficulty Level : Easy
• Last Updated : 17 Jan, 2022

Order-Agnostic Binary Search is a modified version of Binary Search algorithm. Here in this modified binary search comes with one more condition checking. The intuition behind this algorithm is what if the order of the sorted array is not given. So here check that the value of the first element is greater or smaller than the last element.

• If the first element is smaller than the last element-then if the search key value X is less than the middle of the interval then the end pointer will be changed to middle -1 otherwise start will be changed to middle + 1.
• If the first element is greater than the last element-then if the search key value X is less than the middle of the interval then the start pointer will move to the next element of the middle element otherwise the end pointer will move previous to the middle element.

In the end, if the search key value matches with the middle element then the element which was given to the search is found.

Implementation of Order-Agnostic Binary Search:

Let us see the implementation of Order-Agnostic Binary Search with the help of an example.

Given an array, arr[ ] of size N and an element X and the array is sorted in any order(ascending or descending), the task is to find whether the element x is present in the array or not. If yes, then print its index, else print -1.

Examples:

Input: arr[] = {40, 10, 5, 2, 1}, N=5, X=10
Output: 1
Explanation:

The array is sorted in descending order and the element is present at index 1.

Input: arr[] = {1}, N=1, X=10
Output: -1

Approach: The brute force idea would be to linearly traverse the array and check whether the element is present in the array or not. Optimization to this algorithm would be to use binary search if the order of sorting of the array was known – ascending/descending. A variation of binary search can be used i.e, Order-Agnostic Binary search as stated below:

Follow the steps below to solve the problem using Order-Agnostic Binary Search:

• Initialize a boolean variable isAsc as true if arr[start] is less than arr[end] else set it as false.
• Traverse over a while loop till start is less than equal to end and perform the following steps:
• Initialize the variable middle as the average of start and end.
• If arr[middle] equals X, then return the value of middle as the answer,
• If the array is in ascending order then perform the following steps:
• If arr[middle] is less than X, then set the value of start as  middle+1 else set the value of end as middle-1.
• Else, if arr[middle] is less than X, then set the value of end as middle-1 else set the value of start as middle+1.
• After performing the above steps, return the value of -1 as the answer as the element is not found.

Iterative implementation of Order-Agnostic Binary Search.

## C++

 `// C++ program for the above approach``#include ``using` `namespace` `std;` `// An iterative binary search function.``int` `binarySearch(``int` `arr[], ``int` `start, ``int` `end, ``int` `x)``{` `    ``// Checking the sorted order of the given array``    ``bool` `isAsc = arr[start] < arr[end];``    ``while` `(start <= end) {``        ``int` `middle = start + (end - start) / 2;` `        ``// Check if x is present at mid``        ``if` `(arr[middle] == x)``            ``return` `middle;` `        ``// Ascending order``        ``if` `(isAsc == ``true``) {` `            ``// If x greater, ignore left half``            ``if` `(arr[middle] < x)``                ``start = middle + 1;` `            ``// If x smaller, ignore right half``            ``else``                ``end = middle - 1;``        ``}` `        ``// Descending order``        ``else` `{` `            ``// If x smaller, ignore left half``            ``if` `(arr[middle] > x)``                ``start = middle + 1;` `            ``// If x greater, ignore right half``            ``else``                ``end = middle - 1;``        ``}``    ``}` `    ``// Element is not present``    ``return` `-1;``}` `// Driver Code``int` `main()``{``    ``int` `arr[] = { 40, 10, 5, 2, 1 };``    ``int` `x = 10;``    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);``    ``cout << binarySearch(arr, 0, n - 1, x);` `    ``return` `0;``}`

## Java

 `// Java program for the above approach``import` `java.util.*;``class` `GFG {` `// An iterative binary search function.``static` `int` `binarySearch(``int` `arr[], ``int` `start, ``int` `end, ``int` `x)``{` `    ``// Checking the sorted order of the given array``    ``boolean` `isAsc = arr[start] < arr[end];``    ``while` `(start <= end) {``        ``int` `middle = start + (end - start) / ``2``;` `        ``// Check if x is present at mid``        ``if` `(arr[middle] == x)``            ``return` `middle;` `        ``// Ascending order``        ``if` `(isAsc == ``true``) {` `            ``// If x greater, ignore left half``            ``if` `(arr[middle] < x)``                ``start = middle + ``1``;` `            ``// If x smaller, ignore right half``            ``else``                ``end = middle - ``1``;``        ``}` `        ``// Descending order``        ``else` `{` `            ``// If x smaller, ignore left half``            ``if` `(arr[middle] > x)``                ``start = middle + ``1``;` `            ``// If x greater, ignore right half``            ``else``                ``end = middle - ``1``;``        ``}``    ``}` `    ``// Element is not present``    ``return` `-``1``;``}` `    ``// Driver Code``    ``public` `static` `void` `main(String[] args)``    ``{``    ``int` `arr[] = { ``40``, ``10``, ``5``, ``2``, ``1` `};``    ``int` `x = ``10``;``    ``int` `n = arr.length;``    ``System.out.println(binarySearch(arr, ``0``, n - ``1``, x));``    ``}``}` `// This code is contributed by sanjoy_62.`

## Python

 `# Python program for the above approach` `# An iterative binary search function.``def` `binarySearch(arr, start, end, x):` `    ``# Checking the sorted order of the given array``    ``isAsc ``=` `arr[start] < arr[end]``    ` `    ``while` `(start <``=` `end):``        ``middle ``=` `start ``+` `(end ``-` `start) ``/``/` `2` `        ``# Check if x is present at mid``        ``if` `(arr[middle] ``=``=` `x):``            ``return` `middle` `        ``# Ascending order``        ``if` `(isAsc ``=``=` `True``):` `            ``# If x greater, ignore left half``            ``if` `(arr[middle] < x):``                ``start ``=` `middle ``+` `1` `            ``# If x smaller, ignore right half``            ``else``:``                ``end ``=` `middle ``-` `1` `        ``# Descending order``        ``else``:` `            ``# If x smaller, ignore left half``            ``if` `(arr[middle] > x):``                ``start ``=` `middle ``+` `1` `            ``# If x greater, ignore right half``            ``else``:``                ``end ``=` `middle ``-` `1` `    ``# Element is not present``    ``return` `-``1` `# Driver Code``arr ``=` `[ ``40``, ``10``, ``5``, ``2``, ``1` `]``x ``=` `10``n ``=` `len``(arr)``print``(binarySearch(arr, ``0``, n ``-` `1``, x))` `# This code is ciontributed by Samim Hossain Mondal.`

## C#

 `// C# program for the above approach``using` `System;``using` `System.Collections.Generic;` `class` `GFG {` `// An iterative binary search function.``static` `int` `binarySearch(``int``[] arr, ``int` `start, ``int` `end, ``int` `x)``{`` ` `    ``// Checking the sorted order of the given array``    ``bool` `isAsc = arr[start] < arr[end];``    ``while` `(start <= end) {``        ``int` `middle = start + (end - start) / 2;`` ` `        ``// Check if x is present at mid``        ``if` `(arr[middle] == x)``            ``return` `middle;`` ` `        ``// Ascending order``        ``if` `(isAsc == ``true``) {`` ` `            ``// If x greater, ignore left half``            ``if` `(arr[middle] < x)``                ``start = middle + 1;`` ` `            ``// If x smaller, ignore right half``            ``else``                ``end = middle - 1;``        ``}`` ` `        ``// Descending order``        ``else` `{`` ` `            ``// If x smaller, ignore left half``            ``if` `(arr[middle] > x)``                ``start = middle + 1;`` ` `            ``// If x greater, ignore right half``            ``else``                ``end = middle - 1;``        ``}``    ``}`` ` `    ``// Element is not present``    ``return` `-1;``}` `    ``// Driver Code``    ``public` `static` `void` `Main(String[] args) {``        ` `    ``int``[] arr = { 40, 10, 5, 2, 1 };``    ``int` `x = 10;``    ``int` `n = arr.Length;``    ``Console.Write(binarySearch(arr, 0, n - 1, x));` `    ``}``}` `// This code is contributed by code_hunt.`

## Javascript

 ``

Output:
`1`

Time Complexity: O(log(N)).
Auxiliary Space: O(1)

Recursive implementation of Order-Agnostic Binary Search :

## C++

 `// C++ program for the above approach``#include ``using` `namespace` `std;` `// A recursive binary search function.``// It returns location of x in given``// array arr[l..r] is present,``// otherwise -1``int` `binarySearch(``int` `arr[], ``int` `start,``                 ``int` `end, ``int` `x)``{``    ``bool` `isAsc = arr[start] < arr[end];``    ``if` `(end >= start) {``        ``int` `middle = start + (end - start) / 2;` `        ``// If the element is present``        ``// at the middle itself``        ``if` `(arr[middle] == x)``            ``return` `middle;` `        ``if` `(isAsc == ``true``) {` `            ``// If element is smaller than mid,``            ``// then it can only be``            ``// present in left subarray``            ``if` `(arr[middle] > x)``                ``return` `binarySearch(``                    ``arr, start,``                    ``middle - 1, x);` `            ``// Else the element can only be present``            ``// in right subarray``            ``return` `binarySearch(arr, middle + 1,``                                ``end, x);``        ``}``        ``else` `{``            ``if` `(arr[middle] < x)``                ``return` `binarySearch(arr, start,``                                    ``middle - 1, x);` `            ``// Else the element can only be present``            ``// in left subarray``            ``return` `binarySearch(arr, middle + 1,``                                ``end, x);``        ``}``    ``}` `    ``// Element not found``    ``return` `-1;``}` `// Driver Code``int` `main(``void``)``{``    ``int` `arr[] = { 40, 10, 5, 2, 1 };``    ``int` `x = 10;``    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);``    ``cout << binarySearch(arr, 0, n - 1, x);` `    ``return` `0;``}`

Output:
`1`

Time Complexity: O(log(N)).
Auxiliary Space: O(1)

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