# Minimize operations to delete all elements of permutation A by removing a subsequence having order as array B

• Last Updated : 24 Oct, 2021

Given two permutation arrays A[] and B[] of the first N Natural Numbers, the task is to find the minimum number of operations required to remove all array elements A[] such that in each operation remove the subsequence of array elements A[] whose order is the same as in the array B[].

Example:

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Input: A[] = { 4, 2, 1, 3 }, B[] = { 1, 3, 2, 4 }
Output: 3
Explanation:
The given example can be solved by following the given steps:

1. During the 1st operation, integers at index 2 and 3 in the array A[] can be deleted. Hence, the array A[] = {4, 2}.
2. During the 2st operation, integer at index 1 in the array A[] can be deleted. Hence, the array A[] = {4}.
3. During the 3rd operation, integer at index 0 in the array A[] can be deleted. Hence, the array A[] = {}.

The order in which the elements are deleted is {1, 3, 2, 4} which is equal to B. Hence a minimum of 3 operations is required.

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

Approach: The given problem can be solved using the steps discussed below:

1. Create two variables i and j, where i keeps track of the index of the current element of B that is to be deleted next and j keeps track of the current element of A. Initially, both i=0 and j=0.
2. Traverse the permutation array A[] using j for all values of j in range [0, N-1]. If A[j] = B[i], increment the value of i by 1 and continue traversing the array A[].
3. After the array A[] has been traversed completely, increment the value of cnt variable which maintains the count of required operations.
4. Repeat steps 2 and 3 till i<N.
5. After completing the above steps, the value stored in cnt is the required answer.

Below is the implementation of the above approach:

## C++

 `// C++ program for the above approach``#include ``using` `namespace` `std;` `// Function to find the minimum number of``// operations to delete all elements of``// permutation A in order described by B``int` `minOperations(``int` `A[], ``int` `B[], ``int` `N)``{``    ``// Stores the count of operations``    ``int` `cnt = 0;` `    ``// Stores the index of current integer``    ``// in B to be deleted``    ``int` `i = 0;` `    ``// Loop to iterate over all values of B``    ``while` `(i < N) {` `        ``// Stores the current index in A``        ``int` `j = 0;` `        ``// Iterate over all values A``        ``while` `(j < N && i < N) {` `            ``// If current integer of B and A``            ``// equal, increment the index of``            ``// the current integer of B``            ``if` `(B[i] == A[j]) {``                ``i++;``            ``}``            ``j++;``        ``}` `        ``// As the permutation A has been``        ``// traversed completelly, increment``        ``// the count of operations by 1``        ``cnt++;``    ``}` `    ``// Return Answer``    ``return` `cnt;``}` `// Driver Code``int` `main()``{``    ``int` `A[] = { 2, 4, 6, 1, 5, 3 };``    ``int` `B[] = { 6, 5, 4, 2, 3, 1 };``    ``int` `N = ``sizeof``(A) / ``sizeof``(A);` `    ``cout << minOperations(A, B, N);` `    ``return` `0;``}`

## Java

 `// Java program for the above approach``import` `java.util.*;` `class` `GFG{` `// Function to find the minimum number of``// operations to delete all elements of``// permutation A in order described by B``static` `int` `minOperations(``int` `A[], ``int` `B[], ``int` `N)``{``  ` `    ``// Stores the count of operations``    ``int` `cnt = ``0``;` `    ``// Stores the index of current integer``    ``// in B to be deleted``    ``int` `i = ``0``;` `    ``// Loop to iterate over all values of B``    ``while` `(i < N) {` `        ``// Stores the current index in A``        ``int` `j = ``0``;` `        ``// Iterate over all values A``        ``while` `(j < N && i < N) {` `            ``// If current integer of B and A``            ``// equal, increment the index of``            ``// the current integer of B``            ``if` `(B[i] == A[j]) {``                ``i++;``            ``}``            ``j++;``        ``}` `        ``// As the permutation A has been``        ``// traversed completely, increment``        ``// the count of operations by 1``        ``cnt++;``    ``}` `    ``// Return Answer``    ``return` `cnt;``}` `// Driver Code``public` `static` `void` `main(String[] args)``{``    ``int` `A[] = { ``2``, ``4``, ``6``, ``1``, ``5``, ``3` `};``    ``int` `B[] = { ``6``, ``5``, ``4``, ``2``, ``3``, ``1` `};``    ``int` `N = A.length;` `    ``System.out.print(minOperations(A, B, N));` `}``}` `// This code is contributed by 29AjayKumar`

## Python3

 `# Python 3 program for the above approach` `# Function to find the minimum number of``# operations to delete all elements of``# permutation A in order described by B``def` `minOperations(A, B, N):``  ` `    ``# Stores the count of operations``    ``cnt ``=` `0` `    ``# Stores the index of current integer``    ``# in B to be deleted``    ``i ``=` `0` `    ``# Loop to iterate over all values of B``    ``while``(i < N):``      ` `        ``# Stores the current index in A``        ``j ``=` `0` `        ``# Iterate over all values A``        ``while` `(j < N ``and` `i < N):` `            ``# If current integer of B and A``            ``# equal, increment the index of``            ``# the current integer of B``            ``if` `(B[i] ``=``=` `A[j]):``                ``i ``+``=` `1``            ``j ``+``=` `1` `        ``# As the permutation A has been``        ``# traversed completely, increment``        ``# the count of operations by 1``        ``cnt ``+``=` `1` `    ``# Return Answer``    ``return` `cnt` `# Driver Code``if` `__name__ ``=``=` `'__main__'``:``    ``A ``=` `[``2``, ``4``, ``6``, ``1``, ``5``, ``3``]``    ``B ``=` `[``6``, ``5``, ``4``, ``2``, ``3``, ``1``]``    ``N ``=` `len``(A)` `    ``print``(minOperations(A, B, N))` `    ``# This code is contributed by SURENDRA_GANGWAR.`

## C#

 `// C# program for the above approach``using` `System;` `class` `GFG {` `    ``// Function to find the minimum number of``    ``// operations to delete all elements of``    ``// permutation A in order described by B``    ``static` `int` `minOperations(``int``[] A, ``int``[] B, ``int` `N)``    ``{` `        ``// Stores the count of operations``        ``int` `cnt = 0;` `        ``// Stores the index of current integer``        ``// in B to be deleted``        ``int` `i = 0;` `        ``// Loop to iterate over all values of B``        ``while` `(i < N) {` `            ``// Stores the current index in A``            ``int` `j = 0;` `            ``// Iterate over all values A``            ``while` `(j < N && i < N) {` `                ``// If current integer of B and A``                ``// equal, increment the index of``                ``// the current integer of B``                ``if` `(B[i] == A[j]) {``                    ``i++;``                ``}``                ``j++;``            ``}` `            ``// As the permutation A has been``            ``// traversed completely, increment``            ``// the count of operations by 1``            ``cnt++;``        ``}` `        ``// Return Answer``        ``return` `cnt;``    ``}` `    ``// Driver Code``    ``public` `static` `void` `Main(``string``[] args)``    ``{``        ``int``[] A = { 2, 4, 6, 1, 5, 3 };``        ``int``[] B = { 6, 5, 4, 2, 3, 1 };``        ``int` `N = A.Length;` `        ``Console.WriteLine(minOperations(A, B, N));``    ``}``}` `// This code is contributed by ukasp.`

## Javascript

 ``
Output:
`4`

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

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