Permute the elements of an array following given order

A permutation is a rearrangement of members of a sequence into a new sequence. For example, there are 24 permutations of [a, b, c, d]. Some of them are [b, a, d, c], [d, a, b, c] and [a, d, b, c].
A permutation can be specified by an array P[] where P[i] represents the location of the element at index i in the permutation.

For example, the array [3, 2, 1, 0] represents the permutation that maps the element at index 0 to index 3, the element at index 1 to index 2, the element at index 2 to index 1 and the element at index 3 to index 0.

Given the array arr[] of N elements and a permutation array P[], the task is to permute the given array arr[] based on the permutation array P[].



Examples:

Input: arr[] = {1, 2, 3, 4}, P[] = {3, 2, 1, 0}
Output: 4 3 2 1

Input: arr[] = {11, 32, 3, 42}, P[] = {2, 3, 0, 1}
Output: 3 42 11 32

Approach: Every permutation can be represented by a collection of independent permutations, each of which is cyclic i.e. it moves all the elements by a fixed offset wrapping around. To find and apply the cycle that indicates entry i, just keep going forward (from i to P[i]) till we get back at i. After completing the current cycle, find another cycle that has not yet been applied. To check this, subtract n from P[i] after applying it. This means that if an entry in P[i] is negative, we have performed the corresponding move.

Below is the implementation of the above approach:

C++

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// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
  
// Function to permute the the given
// array based on the given conditions
int permute(int A[], int P[], int n)
{
    // For each element of P
    for (int i = 0; i < n; i++) {
        int next = i;
  
        // Check if it is already
        // considered in cycle
        while (P[next] >= 0) {
  
            // Swap the current element according
            // to the permutation in P
            swap(A[i], A[P[next]]);
            int temp = P[next];
  
            // Subtract n from an entry in P
            // to make it negative which indicates
            // the corresponding move
            // has been performed
            P[next] -= n;
            next = temp;
        }
    }
}
  
// Driver code
int main()
{
    int A[] = { 5, 6, 7, 8 };
    int P[] = { 3, 2, 1, 0 };
    int n = sizeof(A) / sizeof(int);
  
    permute(A, P, n);
  
    // Print the new array after
    // applying the permutation
    for (int i = 0; i < n; i++)
        cout << A[i] << " ";
  
    return 0;
}

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Java

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// Java implementation of the approach
class GFG
{
  
// Function to permute the the given
// array based on the given conditions
static void permute(int A[], int P[], int n)
{
    // For each element of P
    for (int i = 0; i < n; i++)
    {
        int next = i;
  
        // Check if it is already
        // considered in cycle
        while (P[next] >= 0)
        {
  
            // Swap the current element according
            // to the permutation in P
            swap(A, i, P[next]);
            int temp = P[next];
  
            // Subtract n from an entry in P
            // to make it negative which indicates
            // the corresponding move
            // has been performed
            P[next] -= n;
            next = temp;
        }
    }
}
  
static int[] swap(int []arr, int i, int j)
{
    int temp = arr[i];
    arr[i] = arr[j];
    arr[j] = temp;
    return arr;
  
// Driver code
public static void main(String[] args)
{
    int A[] = { 5, 6, 7, 8 };
    int P[] = { 3, 2, 1, 0 };
    int n = A.length;
  
    permute(A, P, n);
  
    // Print the new array after
    // applying the permutation
    for (int i = 0; i < n; i++)
        System.out.print(A[i]+ " ");
  
}
}
  
// This code is contributed by 29AjayKumar

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Python 3

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# Python 3 implementation of the approach
  
# Function to permute the the given
# array based on the given conditions
def permute(A, P, n):
      
    # For each element of P
    for i in range(n):
        next = i
  
        # Check if it is already
        # considered in cycle
        while (P[next] >= 0):
              
            # Swap the current element according
            # to the permutation in P
            t = A[i]
            A[i] = A[P[next]]
            A[P[next]] = t
              
            temp = P[next]
  
            # Subtract n from an entry in P
            # to make it negative which indicates
            # the corresponding move
            # has been performed
            P[next] -= n
            next = temp
  
# Driver code
if __name__ == '__main__':
    A = [5, 6, 7, 8]
    P = [3, 2, 1, 0]
    n = len(A)
  
    permute(A, P, n)
  
    # Print the new array after
    # applying the permutation
    for i in range(n):
        print(A[i], end = " ")
          
# This code is contributed by Surendra_Gangwar

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C#

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// C# implementation of the approach 
using System;
  
class GFG 
      
    // Function to permute the the given 
    // array based on the given conditions 
    static void permute(int []A, int []P, int n) 
    
        // For each element of P 
        for (int i = 0; i < n; i++) 
        
            int next = i; 
      
            // Check if it is already 
            // considered in cycle 
            while (P[next] >= 0) 
            
      
                // Swap the current element according 
                // to the permutation in P 
                swap(A, i, P[next]); 
                int temp = P[next]; 
      
                // Subtract n from an entry in P 
                // to make it negative which indicates 
                // the corresponding move 
                // has been performed 
                P[next] -= n; 
                next = temp; 
            
        
    
      
    static int[] swap(int []arr, int i, int j) 
    
        int temp = arr[i]; 
        arr[i] = arr[j]; 
        arr[j] = temp; 
        return arr; 
    
      
    // Driver code 
    public static void Main() 
    
        int []A = { 5, 6, 7, 8 }; 
        int []P = { 3, 2, 1, 0 }; 
        int n = A.Length; 
      
        permute(A, P, n); 
      
        // Print the new array after 
        // applying the permutation 
        for (int i = 0; i < n; i++) 
            Console.Write(A[i]+ " "); 
      
    
  
// This code is contributed by AnkitRai01

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Output:

8 7 6 5

Time Complexity: O(n)

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