# Check if the given array is mirror-inverse

• Difficulty Level : Easy
• Last Updated : 01 Apr, 2021

Given an array arr[], the task is to find whether the array is mirror inverse. Inverse of an array means if the array elements are swapped with their corresponding indices and the array is called mirror-inverse if it’s inverse is equal to itself. If array is mirror-inverse then print Yes else print No.
Examples:

Input: arr[] = [3, 4, 2, 0, 1}
Output: Yes
In the given array:
index(0) -> value(3)
index(1) -> value(4)
index(2) -> value(2)
index(3) -> value(0)
index(4) -> value(1)
To find the inverse of the array, swap the index and the value of the array.
index(3) -> value(0)
index(4) -> value(1)
index(2) -> value(2)
index(0) -> value(3)
index(1) -> value(4)
Inverse arr[] = {3, 4, 2, 0, 1}
So, the inverse array is equal to the given array.
Input: arr[] = {1, 2, 3, 0}
Output: No

A simple approach is to create a new array by swapping the value and index of the given array and check whether the new array is equal to the original array or not.
A better approach is to traverse the array and for all the indices, if arr[arr[index]] = index is satisfied then the given array is mirror inverse.
Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach` `#include` `using` `namespace` `std;`   `// Function that returns true if` `// the array is mirror-inverse` `bool` `isMirrorInverse(``int` `arr[], ``int` `n)` `{` `    ``for` `(``int` `i = 0; i < n; i++) ` `    ``{`   `        ``// If condition fails for any element` `        ``if` `(arr[arr[i]] != i)` `            ``return` `false``;` `    ``}`   `    ``// Given array is mirror-inverse` `    ``return` `true``;` `}`   `// Driver code` `int` `main()` `{` `        ``int` `arr[] = { 1, 2, 3, 0 };` `        ``int` `n = ``sizeof``(arr)/``sizeof``(arr[0]);` `        ``if` `(isMirrorInverse(arr,n))` `            ``cout << ``"Yes"``;` `        ``else` `            ``cout << ``"No"``;` `        ``return` `0;` `}`   `// This code is contributed by Rajput-Ji`

## Java

 `// Java implementation of the approach` `public` `class` `GFG {`   `    ``// Function that returns true if` `    ``// the array is mirror-inverse` `    ``static` `boolean` `isMirrorInverse(``int` `arr[])` `    ``{` `        ``for` `(``int` `i = ``0``; i < arr.length; i++) {`   `            ``// If condition fails for any element` `            ``if` `(arr[arr[i]] != i)` `                ``return` `false``;` `        ``}`   `        ``// Given array is mirror-inverse` `        ``return` `true``;` `    ``}`   `    ``// Driver code` `    ``public` `static` `void` `main(String[] args)` `    ``{` `        ``int` `arr[] = { ``1``, ``2``, ``3``, ``0` `};` `        ``if` `(isMirrorInverse(arr))` `            ``System.out.println(``"Yes"``);` `        ``else` `            ``System.out.println(``"No"``);` `    ``}` `}`

## Python3

 `# Python 3 implementation of the approach `   `# Function that returns true if ` `# the array is mirror-inverse ` `def` `isMirrorInverse(arr, n) : `   `    ``for` `i ``in` `range``(n) :`   `        ``# If condition fails for any element ` `        ``if` `(arr[arr[i]] !``=` `i) :` `            ``return` `False``; ` `    `  `    ``# Given array is mirror-inverse ` `    ``return` `true; `   `# Driver code ` `if` `__name__ ``=``=` `"__main__"` `:` `    `  `    ``arr ``=` `[ ``1``, ``2``, ``3``, ``0` `]; ` `    `  `    ``n ``=` `len``(arr) ;` `    ``if` `(isMirrorInverse(arr,n)) :` `        ``print``(``"Yes"``); ` `    ``else` `:` `        ``print``(``"No"``); `   `# This code is contributed by Ryuga`

## C#

 `// C# implementation of the approach` `using` `System;`   `class` `GFG` `{` `    `  `    ``// Function that returns true if` `    ``// the array is mirror-inverse` `    ``static` `bool` `isMirrorInverse(``int` `[]arr)` `    ``{` `        ``for` `(``int` `i = 0; i < arr.Length; i++) ` `        ``{`   `            ``// If condition fails for any element` `            ``if` `(arr[arr[i]] != i)` `                ``return` `false``;` `        ``}`   `        ``// Given array is mirror-inverse` `        ``return` `true``;` `    ``}`   `    ``// Driver code` `    ``static` `public` `void` `Main ()` `    ``{` `        ``int` `[]arr = { 1, 2, 3, 0 };` `        ``if` `(isMirrorInverse(arr))` `            ``Console.WriteLine(``"Yes"``);` `        ``else` `            ``Console.WriteLine(``"No"``);` `    ``}` `}`   `// This code is contributed by ajit...`

## PHP

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## Javascript

 ``

Output:

`No`

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