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# Check if matrix A can be converted to B by changing parity of corner elements of any submatrix

• Last Updated : 25 Jun, 2021

Given two binary matrices, A[][] and B[][] of N×M. In a single operation, one can choose a sub-matrix (min of 2 rows and 2c columns) and change the parity of the corner elements i.e. 1 can be changed to a 0, and 0 can be changed to a 1. The task is to check if the matrix A can be converted to B using any number of operations.

Examples:

Input: A[][] = {{0, 1, 0}, {0, 1, 0}, {1, 0, 0}},
B[][] = {{1, 0, 0}, {1, 0, 0}, {1, 0, 0}}
Output: Yes
Choose the sub-matrix whose top-left corner is (0, 0)
and bottom-right corner is (1, 1).
Changing the parity of the corner elements
of this sub-matrix will convert A[][] to B[][]
Input: A[][] = {{0, 1, 0, 1}, {1, 0, 1, 0}, {0, 1, 0, 1}},
B[][] = {{1, 1, 1, 1}, {1, 1, 1, 1}, {1, 1, 1, 1}}
Output: No

Approach: The first thing to notice is that despite the conversions the total parity of both the matrix will remain the same. Hence, check if a[i][j] is not same as b[i][j] then change the parity of the corner elements of the sub-matrix whose left top corner is (0, 0) and right bottom corner is (i, j) for 1 ≤ i, j. After performing parity change for every a[i][j] which is not equal to b[i][j], check if both the matrix are the same or not. If they are the same, we can change A to B.
Below is the implementation of the above approach:

## C++

 `// C++ implementation of the``// above approach` `#include ``using` `namespace` `std;``#define N 3``#define M 3` `// Boolean function that returns``// true or false``bool` `check(``int` `a[N][M], ``int` `b[N][M])``{``    ``// Traverse for all elements``    ``for` `(``int` `i = 1; i < N; i++) {``        ``for` `(``int` `j = 1; j < M; j++) {` `            ``// If both are not equal``            ``if` `(a[i][j] != b[i][j]) {` `                ``// Change the parity of``                ``// all corner elements``                ``a[i][j] ^= 1;``                ``a[0][0] ^= 1;``                ``a[0][j] ^= 1;``                ``a[i][0] ^= 1;``            ``}``        ``}``    ``}` `    ``// Check if A is equal to B``    ``for` `(``int` `i = 0; i < N; i++) {``        ``for` `(``int` `j = 0; j < M; j++) {` `            ``// Not equal``            ``if` `(a[i][j] != b[i][j])``                ``return` `false``;``        ``}``    ``}``    ``return` `true``;``}` `// Driver Code``int` `main()``{``    ``// First binary matrix``    ``int` `a[N][N] = { { 0, 1, 0 },``                    ``{ 0, 1, 0 },``                    ``{ 1, 0, 0 } };` `    ``// Second binary matrix``    ``int` `b[N][N] = { { 1, 0, 0 },``                    ``{ 1, 0, 0 },``                    ``{ 1, 0, 0 } };` `    ``if` `(check(a, b))``        ``cout << ``"Yes"``;``    ``else``        ``cout << ``"No"``;``}`

## Java

 `// Java implementation of the``// above approach``class` `GFG``{``    ` `static` `final` `int` `N = ``3``,M =``3``;` `// Boolean function that returns``// true or false``static` `boolean` `check(``int` `a[][], ``int` `b[][])``{``    ``// Traverse for all elements``    ``for` `(``int` `i = ``1``; i < N; i++)``    ``{``        ``for` `(``int` `j = ``1``; j < M; j++)``        ``{` `            ``// If both are not equal``            ``if` `(a[i][j] != b[i][j])``            ``{` `                ``// Change the parity of``                ``// all corner elements``                ``a[i][j] ^= ``1``;``                ``a[``0``][``0``] ^= ``1``;``                ``a[``0``][j] ^= ``1``;``                ``a[i][``0``] ^= ``1``;``            ``}``        ``}``    ``}` `    ``// Check if A is equal to B``    ``for` `(``int` `i = ``0``; i < N; i++) {``        ``for` `(``int` `j = ``0``; j < M; j++) {` `            ``// Not equal``            ``if` `(a[i][j] != b[i][j])``                ``return` `false``;``        ``}``    ``}``    ``return` `true``;``}` `// Driver Code``public` `static` `void` `main(String args[])``{``    ``// First binary matrix``    ``int` `a[][] = { { ``0``, ``1``, ``0` `},``                    ``{ ``0``, ``1``, ``0` `},``                    ``{ ``1``, ``0``, ``0` `} };` `    ``// Second binary matrix``    ``int` `b[][] = { { ``1``, ``0``, ``0` `},``                    ``{ ``1``, ``0``, ``0` `},``                    ``{ ``1``, ``0``, ``0` `} };` `    ``if` `(check(a, b))``        ``System.out.print( ``"Yes"``);``    ``else``        ``System.out.print( ``"No"``);``}``}` `// This code is contributed by Arnab Kundu`

## Python3

 `# Python 3 implementation of the``# above approach``N ``=` `3``M ``=` `3` `# Boolean function that returns``# true or false``def` `check(a, b):``    ` `    ``# Traverse for all elements``    ``for` `i ``in` `range``(``1``, N, ``1``):``        ``for` `j ``in` `range``(``1``, M, ``1``):``            ` `            ``# If both are not equal``            ``if` `(a[i][j] !``=` `b[i][j]):``                ` `                ``# Change the parity of``                ``# all corner elements``                ``a[i][j] ^``=` `1``                ``a[``0``][``0``] ^``=` `1``                ``a[``0``][j] ^``=` `1``                ``a[i][``0``] ^``=` `1` `    ``# Check if A is equal to B``    ``for` `i ``in` `range``(N):``        ``for` `j ``in` `range``(M):``            ` `            ``# Not equal``            ``if` `(a[i][j] !``=` `b[i][j]):``                ``return` `False``    ` `    ``return` `True` `# Driver Code``if` `__name__ ``=``=` `'__main__'``:``    ` `    ``# First binary matrix``    ``a ``=` `[[``0``, ``1``, ``0``],``         ``[``0``, ``1``, ``0``],``         ``[``1``, ``0``, ``0``]]` `    ``# Second binary matrix``    ``b ``=` `[[``1``, ``0``, ``0``],``         ``[``1``, ``0``, ``0``],``         ``[``1``, ``0``, ``0``]]` `    ``if` `(check(a, b)):``        ``print``(``"Yes"``)``    ``else``:``        ``print``(``"No"``)` `# This code is contributed by``# Surendra_Gangwar`

## C#

 `// C# implementation of the``// above approach``using` `System;` `class` `GFG``{``    ` `static` `readonly` `int` `N = 3,M =3;` `// Boolean function that returns``// true or false``static` `bool` `check(``int` `[,]a, ``int` `[,]b)``{``    ``// Traverse for all elements``    ``for` `(``int` `i = 1; i < N; i++)``    ``{``        ``for` `(``int` `j = 1; j < M; j++)``        ``{` `            ``// If both are not equal``            ``if` `(a[i,j] != b[i,j])``            ``{` `                ``// Change the parity of``                ``// all corner elements``                ``a[i,j] ^= 1;``                ``a[0,0] ^= 1;``                ``a[0,j] ^= 1;``                ``a[i,0] ^= 1;``            ``}``        ``}``    ``}` `    ``// Check if A is equal to B``    ``for` `(``int` `i = 0; i < N; i++)``    ``{``        ``for` `(``int` `j = 0; j < M; j++)``        ``{` `            ``// Not equal``            ``if` `(a[i,j] != b[i,j])``                ``return` `false``;``        ``}``    ``}``    ``return` `true``;``}` `// Driver Code``public` `static` `void` `Main(String []args)``{``    ``// First binary matrix``    ``int` `[,]a = { { 0, 1, 0 },``                    ``{ 0, 1, 0 },``                    ``{ 1, 0, 0 } };` `    ``// Second binary matrix``    ``int` `[,]b = { { 1, 0, 0 },``                    ``{ 1, 0, 0 },``                    ``{ 1, 0, 0 } };` `    ``if` `(check(a, b))``        ``Console.Write( ``"Yes"``);``    ``else``        ``Console.Write( ``"No"``);``}``}` `// This code has been contributed by 29AjayKumar`

## PHP

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## Javascript

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Output:
`Yes`

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