Check If the Given Array is Mirror Inverse in Java

It is a very interesting problem frequently asked in interviews of top IT companies like Google, Amazon, TCS, Accenture, etc. By solving the problem, one wants to check the logical ability, critical thinking, and problem-solving skill of the interviewee. So, in this section, we are going to check if the given array is mirror inverse or not in Java with different approaches and logic. Also, we will create Java programs for the same.

Problem Statement

We have given an array named a[], the task is to find whether the array is mirror inverse or not. If an array is mirror-inverse then print Yes else print No.

Reverse of Array

The reverse of an array can be found by writing the array right to left.

Example:

Check If the Given Array is Mirror Inverse in Java

Mirror Inverse of Array

If we swap array indices with corresponding array elements and rewrite the array values. If we get its inverse is equal to the given array, the array is called the mirror inverse. Let's understand it through examples.

Note: Reverse and mirror inverse array are not the same.

Example 1:

Input: arr[] = [3, 4, 2, 0, 1, 5, 6}

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)

index(5) -> value(5)

index(6) -> value(6)

In order to find the inverse of the array, swap the index and the value of the given array. Hence, we get:

index(3) -> value(0)

index(4) -> value(1)

index(2) -> value(2)

index(0) -> value(3)

index(1) -> value(4)

index(5) -> value(5)

index(6) -> value(6)

Inverse arr[] = {3, 4, 2, 0, 1, 5, 6}

We observe that the inverse array is equal to the given array. So, it is a mirror inverse of the given array.

Example 2:

Input: arr[] = {1, 3, 5, 7, 9}

index(0) -> value(1)

index(1) -> value(3)

index(2) -> value(5)

index(3) -> value(7)

index(4) -> value(9)

In order to find the inverse of the array, swap the index and the value of the given array. Hence, we get:

index(1) -> value(0)

index(3) -> value(1)

index(5) -> value(2)

index(7) -> value(3)

index(9) -> value(4)

Inverse arr[] = {0, 1, 2, 3, 4}

We observe that the inverse array is not equal to the given array. So, it is not a mirror inverse of the given array.

Java Program to Check if the Given Array is a Mirror Inverse or Not

create a new array by swapping the value of the array and indices of the given array.
Compare both arrays. If the new array is equal to the original one, the given array is a mirror inverse.

MirrorInverseArray1.java

public class MirrorInverseArray1
{
//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(Strin args[])
{
int arr[] = { 1, 2, 3, 0 };
//function calling
if (isMirrorInverse(arr))
System.out.println("Yes");
else
System.out.println("No");
}
}

Output:

No

Let's see another approach.

Another approach is that traverse over the given array and for all the indices if the condition array[array[index]] = index satisfies then the given array is mirror inverse. The approach is better than the above approach.

MirrorInverseArray2.java

public class MirrorInverseArray2
{
public static void main (String args[])
{
int count = 0;
//array to be inversed
int arr[ ] = { 3, 4, 5, 0, 1, 2 };
//loop iterates over the array 
for ( int i = 0 ; i < arr.length ; i ++ )
{
if ( arr [ arr [ i ] ] == 1 )
{
//increments the count variable by 1 if the above condition returns true
count ++;
}
}
if (count != 0)
{
System.out.println ( "The given array is mirror inverse.") ;
}
else
{
System.out.println ("The given array is not mirrored inverse.");
}
}
}

Output: