Minimum moves required to change position with the given operation

Given two integers S and T and an array arr that contains elements from 1 to N in unsorted fashion. The task is to find the minimum number of moves to move Sth element to the Tth place in the array with the following operation:
A single move consists of the following

// Initially b[] = {1, 2, 3, ..., N}
// arr[] is input array
for (i = 1..n)
   temp[arr[i]] = b[i]
b = temp

If not possible then print -1 instead.

Examples:



Input: S = 2, T = 1, arr[] = {2, 3, 4, 1}
Output: 3
N is 4 (size of arr[])
Move 1: b[] = {4, 1, 2, 3}
Move 2: b[] = {3, 4, 1, 2}
Move 3: b[] = {2, 3, 4, 1}

Input: S = 3, T = 4, arr[] = {1, 2, 3, 4}
Output: -1
N is 4 (Size of arr[])
Regardless of how many moves are made, the permutation would remain the same.

Approach: The important observation here is that we are only concerned with the position of a single element, and not the entire array. So at each move we move the element at position S to the position arr[S], until we reach Tth position.
Since there are at most N distinct places that we can reach, if we don’t reach T within N moves, it would mean we can never reach it.

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 return the number of moves
int minimumMoves(int n, int a[], int s, int t)
{
    int i, x;
    x = s;
    for (i = 1; i <= n; i++) {
        if (x == t)
            break;
        x = a[x];
    }
  
    // Destination reached
    if (x == t)
        return i - 1;
    else
        return -1;
}
  
// Driver Code
int main()
{
    int s = 2, t = 1, i;
    int a[] = {-1, 2, 3, 4, 1};
    int n = sizeof(a) / sizeof(a[0]);
    cout << minimumMoves(n, a, s, t);
}

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Java

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// Java implementation of the approach 
public class GFG{
  
// Function to return the number of moves 
static int minimumMoves(int n, int a[], int s, int t) 
    int i, x; 
    x = s; 
    for (i = 1; i <= n; i++) { 
        if (x == t) 
            break
        x = a[x]; 
    
  
    // Destination reached 
    if (x == t) 
        return i - 1
    else
        return -1
  
    // Driver Code 
    public static void main(String []args){
    int s = 2, t = 1, i; 
    int a[] = {-1, 2, 3, 4, 1}; 
    int n = a.length ;
    System.out.println(minimumMoves(n, a, s, t));  
    }
    // This code is contributed by Ryuga
}

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Python3

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# Python3 implementation of the approach 
  
# Function to return the number of moves 
def minimumMoves(n, a, s, t): 
  
    x =
    for i in range(1, n+1):  
        # Destination reached
        if x == t:
            return i-1
        x = a[x] 
       
    return -1 
    
# Driver Code 
if __name__ == "__main__":
  
    s, t = 2, 1 
    a = [-1, 2, 3, 4, 1
    n = len(a) 
    print(minimumMoves(n, a, s, t)) 
   
# This code is contributed by Rituraj Jain

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C#

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// C# implementation of the approach 
using System;
public class GFG{
  
// Function to return the number of moves 
static int minimumMoves(int n, int []a, int s, int t) 
    int i, x; 
    x = s; 
    for (i = 1; i <= n; i++) { 
        if (x == t) 
            break
        x = a[x]; 
    
  
    // Destination reached 
    if (x == t) 
        return i - 1; 
    else
        return -1; 
  
    // Driver Code 
    public static void Main(){
    int s = 2, t = 1; 
    int []a = {-1, 2, 3, 4, 1}; 
    int n = a.Length ;
    Console.WriteLine(minimumMoves(n, a, s, t)); 
    }
    // This code is contributed by inder_verma.
}

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PHP

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<?php
// PHP implementation of the approach
  
  
// Function to return the number of moves
function minimumMoves($n, $a, $s, $t)
{
    $i; $x;
    $x = $s;
    for ($i = 1; $i <= $n; $i++) {
        if ($x == $t)
            break;
        $x = $a[$x];
    }
  
    // Destination reached
    if ($x == $t)
        return $i - 1;
    else
        return -1;
}
  
// Driver Code
  
    $s = 2; $t = 1; $i;
    $a = array(-1, 2, 3, 4, 1);
    $n = count($a);
    echo minimumMoves($n, $a, $s, $t);
     // This code is contributed by inder_verma.
?>

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Output:

3


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