Count of pass required to visit same index again by moving arr[i] to index arr[i]

Given an array(1-based indexing) arr[] of permutation of the first N natural numbers, the task for each element is to find the number of moves required to reach that index such that in each move, array element at index i moves to the array element at index arr[i].

Examples:

Input: arr[] = {2, 3, 1}
Output: 3 3 3  
Explanation:
For array element arr[1] = 2, the set of moves of indices are 1 -> 2 -> 3 -> 1. The total count of moves required is 3.
For array element arr[2] = 3, the set of moves of indices are 2 -> 3 -> 1 -> 2. The total count of moves required is 3.
For array element arr[3] = 1, the set of moves of indices are 3 -> 1 -> 2 -> 3. The total count of moves required is 3.

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

Approach: The given problem can be solved by finding the number of moves required for every array element for each index. Follow the steps below to solve the given problem:

• Traverse the given array arr[] using the variable i and perform the following steps:
  • Initialize a variable, say count that stores the total number of moves required.
  • Initialize a variable, say K as i and iterate a do-while loop and in that loop update the value of K to arr[K] and increment the value of count by 1 until K is not the same as the value of i.
  • After completing the above steps, print the value of count as the resultant count of move required for the current index.

Below is the implementation of the above approach:

C++

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;

// Function to find the number of moves
// required to visit the same index
// again for every array element
void numberOfPasses(vector<int> arr, int N)
{
    // Make given array 0 index based
    for (int i = 0; i < N; ++i) {
        --arr[i];
    }

    for (int i = 0; i < N; ++i) {

        // Stores the number of moves
        int cnt = 0;

        // Store index value
        int k = i;

        do {

            // Update the value of cnt
            ++cnt;

            // Make a pass
            k = arr[k];

        } while (k != i);

        // Print the value of cnt
        cout << cnt << " ";
    }
}

// Driver Code
int main()
{
    vector<int> arr{ 4, 6, 2, 1, 5, 3 };
    int N = arr.size();
    numberOfPasses(arr, N);

    return 0;
}

Java

// Java program for the above approach
import java.io.*;

class GFG
{

  // Function to find the number of moves
  // required to visit the same index
  // again for every array element
  static void numberOfPasses(int[] arr, int N)
  {

    // Make given array 0 index based
    for (int i = 0; i < N; ++i) {
      --arr[i];
    }

    for (int i = 0; i < N; ++i) {

      // Stores the number of moves
      int cnt = 0;

      // Store index value
      int k = i;

      do {

        // Update the value of cnt
        ++cnt;

        // Make a pass
        k = arr[k];

      } while (k != i);

      // Print the value of cnt
      System.out.print(cnt+" ");
    }
  }

  // Driver Code
  public static void main (String[] args)
  {
    int[] arr = { 4, 6, 2, 1, 5, 3 };
    int N = arr.length;
    numberOfPasses(arr, N);

  }
}

// This code is contributed by Potta Lokesh

Python3

# Python program for the above approach

# Function to find the number of moves
# required to visit the same index
# again for every array element
def numberOfPasses(arr, N):

    # Make given array 0 index based
    for i in range(0, N):
        arr[i] = arr[i] - 1


    for i in range(0, N):

        # Stores the number of moves
        cnt = 0;

        # Store index value
        k = i;

        while(True):

            # Update the value of cnt
            cnt = cnt + 1

            # Make a pass
            k = arr[k]

            if (k == i):
                break;

        # Print the value of cnt
        print(cnt, end=" ")

# Driver Code

arr = [4, 6, 2, 1, 5, 3]
N = len(arr)
numberOfPasses(arr, N)

# This code is contributed by ihritik

C#

// C# program for the above approach
using System;
using System.Collections.Generic;

class GFG{

// Function to find the number of moves
// required to visit the same index
// again for every array element
static void numberOfPasses(int []arr, int N)
{

    // Make given array 0 index based
    for (int i = 0; i < N; ++i) {
        --arr[i];
    }

    for (int i = 0; i < N; ++i) {

    // Stores the number of moves
    int cnt = 0;

    // Store index value
    int k = i;

    do {
        // Update the value of cnt
        ++cnt;

        // Make a pass
        k = arr[k];

    } while (k != i);

    // Print the value of cnt
    Console.Write(cnt + " ");
    }
}

// Driver Code
public static void Main()
{
    int []arr = { 4, 6, 2, 1, 5, 3 };
    int N = arr.Length;
    numberOfPasses(arr, N);
}
}

// This code is contributed by Samim Hossain Mondal

Javascript

<script>
    // JavaScript program for the above approach

    // Function to find the number of moves
    // required to visit the same index
    // again for every array element
    const numberOfPasses = (arr, N) => {
        // Make given array 0 index based
        for (let i = 0; i < N; ++i) {
            --arr[i];
        }

        for (let i = 0; i < N; ++i) {

            // Stores the number of moves
            let cnt = 0;

            // Store index value
            let k = i;

            do {

                // Update the value of cnt
                ++cnt;

                // Make a pass
                k = arr[k];

            } while (k != i);

            // Print the value of cnt
            document.write(`${cnt} `);
        }
    }

    // Driver Code
    let arr = [4, 6, 2, 1, 5, 3];
    let N = arr.length;
    numberOfPasses(arr, N);

    // This code is contributed by rakeshsahni

</script>

Output

2 3 3 2 1 3 

Time Complexity: O(N²)
Auxiliary Space: O(1)