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

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  • Last Updated : 15 Nov, 2021
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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)


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