Given an array arr[] consisting of integers in the range [1, N], the task is to determine whether the Inverse Permutation of the given array is same as the given array.
An inverse permutation is a permutation obtained by inserting the position of all elements at the position equal to the respective values of the element in the array.
Illustration:
arr[] = {2, 4, 1, 3, 5}
The inverse permutation of the array will be equal to {3, 1, 4, 2, 5}
Examples:
Input: N = 4, arr[] = {1, 4, 3, 2}
Output: Yes
Explanation:
The inverse permutation of the given array is {1, 4, 3, 2} which is same as the given array.
Input: N = 5, arr[] = {2, 3, 4, 5, 1}
Output: No
Explanation:
The inverse permutation of the given array is {5, 1, 2, 3, 4} which is not the same as the given array.
Method 1 :
In this method, we will generate the inverse permutation of the array, then check if it is same as the original array.
Follow the steps below to solve the problem:
- Find the inverse permutation of the given array.
- Check, if the generated array is same as the original array.
- If both are same, then print Yes. Otherwise, print No.
Below is the implementation of the above approach:
// C++ Program to implement // the above approach #include <iostream> using namespace std;
// Function to check if the inverse // permutation of the given array is // same as the original array void inverseEqual( int arr[], int n)
{ // Stores the inverse
// permutation
int brr[n];
// Generate the inverse permutation
for ( int i = 0; i < n; i++) {
int present_index = arr[i] - 1;
brr[present_index] = i + 1;
}
// Check if the inverse permutation
// is same as the given array
for ( int i = 0; i < n; i++) {
if (arr[i] != brr[i]) {
cout << "No" << endl;
return ;
}
}
cout << "Yes" << endl;
} // Driver Code int main()
{ int n = 4;
int arr[n] = { 1, 4, 3, 2 };
inverseEqual(arr, n);
return 0;
} |
// Java program to implement // the above approach import java.util.*;
class GFG{
// Function to check if the inverse // permutation of the given array is // same as the original array static void inverseEqual( int arr[], int n)
{ // Stores the inverse
// permutation
int [] brr = new int [n];
// Generate the inverse permutation
for ( int i = 0 ; i < n; i++)
{
int present_index = arr[i] - 1 ;
brr[present_index] = i + 1 ;
}
// Check if the inverse permutation
// is same as the given array
for ( int i = 0 ; i < n; i++)
{
if (arr[i] != brr[i])
{
System.out.println( "No" );
return ;
}
}
System.out.println( "Yes" );
} // Driver code public static void main(String[] args)
{ int n = 4 ;
int [] arr = { 1 , 4 , 3 , 2 };
inverseEqual(arr, n);
} } // This code is contributed by offbeat |
# Python3 program to implement # the above approach # Function to check if the inverse # permutation of the given array is # same as the original array def inverseEqual(arr, n):
# Stores the inverse
# permutation
brr = [ 0 ] * n
# Generate the inverse permutation
for i in range (n):
present_index = arr[i] - 1
brr[present_index] = i + 1
# Check if the inverse permutation
# is same as the given array
for i in range (n):
if arr[i] ! = brr[i]:
print ( "NO" )
return
print ( "YES" )
# Driver code n = 4
arr = [ 1 , 4 , 3 , 2 ]
inverseEqual(arr, n) # This code is contributed by Stuti Pathak |
// C# program to implement // the above approach using System;
class GFG{
// Function to check if the inverse // permutation of the given array is // same as the original array static void inverseEqual( int []arr, int n)
{ // Stores the inverse
// permutation
int [] brr = new int [n];
// Generate the inverse permutation
for ( int i = 0; i < n; i++)
{
int present_index = arr[i] - 1;
brr[present_index] = i + 1;
}
// Check if the inverse permutation
// is same as the given array
for ( int i = 0; i < n; i++)
{
if (arr[i] != brr[i])
{
Console.WriteLine( "No" );
return ;
}
}
Console.WriteLine( "Yes" );
} // Driver code public static void Main(String[] args)
{ int n = 4;
int [] arr = { 1, 4, 3, 2 };
inverseEqual(arr, n);
} } // This code is contributed by sapnasingh4991 |
<script> // Javascript Program to implement // the above approach // Function to check if the inverse // permutation of the given array is // same as the original array function inverseEqual(arr, n)
{ // Stores the inverse
// permutation
var brr = Array(n).fill(0);
// Generate the inverse permutation
for ( var i = 0; i < n; i++) {
var present_index = arr[i] - 1;
brr[present_index] = i + 1;
}
// Check if the inverse permutation
// is same as the given array
for ( var i = 0; i < n; i++) {
if (arr[i] != brr[i]) {
document.write( "No" );
return ;
}
}
document.write( "Yes" );
} // Driver Code var n = 4;
var arr = [ 1, 4, 3, 2 ];
inverseEqual(arr, n); // This code is contributed by noob2000. </script> |
Yes
Time Complexity: O(N)
Auxiliary Space: O(N)
Method 2 :
In this method, we take elements one by one and check for elements if at (arr[i] -1) index i+1 is present or not . If not then the inverse permutation of the given array is not the same as the array.
Below is the implementation of the above approach:
// C++ Program to implement // the above approach #include <bits/stdc++.h> using namespace std;
// Function to check if the inverse // permutation of the given array is // same as the original array bool inverseEqual( int arr[], int n)
{ // Check the if inverse permutation is not same
for ( int i = 0; i < n; i++)
if (arr[arr[i] - 1] != i + 1)
return false ;
return true ;
} // Driver Code int main()
{ int n = 4;
int arr[n] = { 1, 4, 3, 2 };
// Function Call
cout << (inverseEqual(arr, n) ? "Yes" : "No" );
return 0;
} |
/*package whatever //do not write package name here */ import java.io.*;
class GFG
{ // Java program to implement
// the above approach
// Function to check if the inverse
// permutation of the given array is
// same as the original array
static boolean inverseEqual( int [] arr, int n){
// Check the if inverse permutation
// is not same
for ( int i= 0 ;i<n;i++){
if (arr[arr[i] - 1 ] != i + 1 )
return false ;
}
return true ;
}
// Driver code
public static void main(String args[])
{
int n = 4 ;
int [] arr = { 1 , 4 , 3 , 2 };
// Function Call
System.out.println((inverseEqual(arr, n)== true )? "Yes" : "No" );
}
} // This Code is contributed by shinjanpatra |
# Python program to implement # the above approach # Function to check if the inverse # permutation of the given array is # same as the original array def inverseEqual(arr, n):
# Check the if inverse permutation
# is not same
for i in range (n):
if (arr[arr[i] - 1 ] ! = i + 1 ):
return False
return True
# Driver Code n = 4
arr = [ 1 , 4 , 3 , 2 ]
# Function Call print ( "Yes" if (inverseEqual(arr, n) = = True ) else "No" )
# This code is contributed by shinjanpatra |
// C# Program to implement // the above approach using System;
class GFG
{ // Function to check if the inverse // permutation of the given array is // same as the original array static bool inverseEqual( int [] arr, int n){
// Check the if inverse permutation is not same
for ( int i=0;i<n;i++){
if (arr[arr[i] - 1] != i + 1)
return false ;
}
return true ;
} // Driver code public static void Main(String[] args)
{ int n = 4;
int [] arr = { 1, 4, 3, 2 };
// Function Call
Console.WriteLine((inverseEqual(arr, n)== true )? "Yes" : "No" );
} } // This Code is contributed by Pushpesh Raj. |
<script> // Javascript program to implement // the above approach // Function to check if the inverse // permutation of the given array is // same as the original array function inverseEqual(arr, n)
{ // Check the if inverse permutation
// is not same
for (let i = 0; i < n; i++)
if (arr[arr[i] - 1] != i + 1)
return false ;
return true ;
} // Driver Code
let n = 4;
let arr = [ 1, 4, 3, 2 ];
// Function Call
document.write(inverseEqual(arr, n) ? "Yes" : "No" );
</script> |
Yes
Time Complexity: O(N)
Auxiliary Space: O(1)