Convert an array into another by repeatedly removing the last element and placing it at any arbitrary index

Given two arrays A[] and B[], both consisting of a permutation of first N natural numbers, the task is to count the minimum number of times the last array element is required to be shifted to any arbitrary position in the array A[] to make both the arrays A[] and B[] equal.

Examples:

Input: A[] = {1, 2, 3, 4, 5}, B[] = {1, 5, 2, 3, 4}
Output:1
Explanation:
Initially, the array A[] is {1, 2, 3, 4, 5}. After moving the last array element, i.e. 5, and placing them between arr[0] (= 1) and arr[1](= 2) modifies the array to {1, 5, 2, 3, 4}, which is the same as the array B[].
Therefore, the minimum number of operations required to convert the array A[] to B[] is 1.

Input: A[] = {3, 2, 1}, B[] = {1, 2, 3}
Output: 2
Explanation:
Initially, the array A[] is {3, 2, 1}.
Operation 1: After moving the last array element, i.e. 1, to the beginning of the array, modifies the array to {1, 3, 2}.
Operation 2: After moving the last element of the array, i.e. 2 and placing them between the elements arr[0] (= 1) and arr[1] (= 3) modifies the array to {1, 2, 3}, which is the same as the array B[].
Therefore, the minimum number of operations required to convert the array A[] to B[] is 2.

Approach: The given problem can be solved by finding the first i consecutive elements of the first permutation which is the same as the subsequence of the second permutation, then the count of operations must be less at least (N - I), since the last (N - i) elements can be selected optimally and inserted at required indices. Therefore, (N - i) is the minimum number of steps required for the conversion of the array A[] to B[].

Below is the implementation of the above approach:

// C++ program for the above approach

#include <iostream>
using namespace std;

// Function to count the minimum number
// of operations required to convert
// the array A[] into array B[]
int minCount(int A[], int B[], int N)
{
    // Stores the index in the first
    // permutation A[] which is same
    // as the subsequence in B[]
    int i = 0;

    // Find the first i elements in A[]
    // which is a subsequence in B[]
    for (int j = 0; j < N; j++) {

        // If element A[i]
        // is same as B[j]
        if (A[i] == B[j]) {
            i++;
        }
    }

    // Return the count of
    // operations required
    return N - i;
}

// Driver Code
int main()
{
    int A[] = { 1, 2, 3, 4, 5 };
    int B[] = { 1, 5, 2, 3, 4 };

    int N = sizeof(A) / sizeof(A[0]);

    cout << minCount(A, B, N);

    return 0;
}

// Java program for the above approach
class GFG{
    
// Function to count the minimum number
// of operations required to convert
// the array A[] into array B[]
static int minCount(int A[], int B[], int N)
{
    
    // Stores the index in the first
    // permutation A[] which is same
    // as the subsequence in B[]
    int i = 0;

    // Find the first i elements in A[]
    // which is a subsequence in B[]
    for(int j = 0; j < N; j++)
    {
        
        // If element A[i]
        // is same as B[j]
        if (A[i] == B[j]) 
        {
            i++;
        }
    }

    // Return the count of
    // operations required
    return N - i;
}

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

    System.out.println(minCount(A, B, N));
}
}

// This code is contributed by AnkThon

# Python3 program for the above approach

# Function to count the minimum number
# of operations required to convert
# the array A[] into array B[]
def minCount(A, B, N):
    
    # Stores the index in the first
    # permutation A[] which is same
    # as the subsequence in B[]
    i = 0

    # Find the first i elements in A[]
    # which is a subsequence in B[]
    for j in range(N):
        
        # If element A[i]
        # is same as B[j]
        if (A[i] == B[j]):
            i += 1

    # Return the count of
    # operations required
    return N - i

# Driver Code
if __name__ == '__main__':
    
    A = [ 1, 2, 3, 4, 5 ]
    B = [ 1, 5, 2, 3, 4 ]

    N = len(A)

    print(minCount(A, B, N))
    
# This code is contributed by ipg2016107

// C# program for the above approach
using System;

class GFG{

// Function to count the minimum number
// of operations required to convert
// the array A[] into array B[]
static int minCount(int[] A, int[] B, int N)
{
    
    // Stores the index in the first
    // permutation A[] which is same
    // as the subsequence in B[]
    int i = 0;

    // Find the first i elements in A[]
    // which is a subsequence in B[]
    for(int j = 0; j < N; j++) 
    {
        
        // If element A[i]
        // is same as B[j]
        if (A[i] == B[j]) 
        {
            i++;
        }
    }

    // Return the count of
    // operations required
    return N - i;
}

// Driver Code
public static void Main(string[] args)
{
    int[] A = { 1, 2, 3, 4, 5 };
    int[] B = { 1, 5, 2, 3, 4 };
    int N = A.Length;

    Console.WriteLine(minCount(A, B, N));
}
}

// This code is contributed by ukasp

<script>

// JavaScript program for the above approach

// Function to count the minimum number
// of operations required to convert
// the array A[] into array B[]
function minCount(A, B, N){
    
    // Stores the index in the first
    // permutation A[] which is same
    // as the subsequence in B[]
    var i = 0

    // Find the first i elements in A[]
    // which is a subsequence in B[]
    for(let j = 0; j < N; j++){ 
        
        // If element A[i]
        // is same as B[j]
        if (A[i] == B[j])
            i += 1
      }
    // Return the count of
    // operations required
    return N - i
    
}

// Driver Code
    
var A = [ 1, 2, 3, 4, 5 ]
var B = [ 1, 5, 2, 3, 4 ]

N = A.length

document.write(minCount(A, B, N))
    
// This code is contributed by AnkThon

</script>

1

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