Check horizontal and vertical symmetry in binary matrix

Last Updated : 12 Sep, 2023

Given a 2D binary matrix of N rows and M columns. The task is to check whether the matrix is horizontal symmetric, vertical symmetric, or both. The matrix is said to be horizontal symmetric if the first row is the same as the last row, the second row is the same as the second last row, and so on. And the matrix is said to be vertical symmetric if the first column is the same as the last column, the second column is the same as the second last column, and so on.

Print "VERTICAL" if the matrix is vertically symmetric, "HORIZONTAL" if the matrix is vertically symmetric, "BOTH" if the matrix is vertical and horizontal symmetric, and "NO" if not symmetric.

Examples:

Input: N = 3 M = 3
0 1 0
0 0 0
0 1 0
Output: Both
Explanation: First and third row are same and also second row is in middle. So Horizontal Symmetric. Similarly, First and third column are same and also second column is in middle, so Vertical Symmetric.

Input: N = 3 M = 3
0 0 1
1 1 0
0 0 1
Output: Both

Approach: The idea is to use pointers indicating two rows (or columns) and compare each cell of both the pointed rows (or columns).

For Horizontal Symmetry, initialize one pointer i = 0 and another pointer j = N - 1.
Now, compare each element of i-th row and j-th row. Increase i by 1 and decrease j by 1 in each loop cycle.
- If at least one, not an identical element, is found, mark the matrix as not horizontal symmetric.
Similarly, for Vertical Symmetry, initialize one pointer i = 0 and another pointer j = M - 1.
Now, compare each element of i-th column and j-th column. Increase i by 1 and decrease j by 1 in each loop cycle.
- If at least one, not an identical element, is found, mark the matrix as not vertical symmetric.

Below is the implementation of the above idea:

C++

// C++ program to find if a matrix is symmetric.
#include <bits/stdc++.h>
#define MAX 1000
using namespace std;

void checkHV(int arr[][MAX], int N, int M)
{
    // Initializing as both horizontal and vertical
    // symmetric.
    bool horizontal = true, vertical = true;

    // Checking for Horizontal Symmetry.  We compare
    // first row with last row, second row with second
    // last row and so on.
    for (int i = 0, k = N - 1; i < N / 2; i++, k--) {
        // Checking each cell of a column.
        for (int j = 0; j < M; j++) {
            // check if every cell is identical
            if (arr[i][j] != arr[k][j]) {
                horizontal = false;
                break;
            }
        }
    }

    // Checking for Vertical Symmetry.  We compare
    // first column with last column, second column
    // with second last column and so on.
    for (int j = 0, k = M - 1; j < M / 2; j++, k--) {
        // Checking each cell of a row.
        for (int i = 0; i < N; i++) {
            // check if every cell is identical
            if (arr[i][j] != arr[i][k]) {
                vertical = false;
                break;
            }
        }
    }

    if (!horizontal && !vertical)
        cout << "NO\n";
    else if (horizontal && !vertical)
        cout << "HORIZONTAL\n";
    else if (vertical && !horizontal)
        cout << "VERTICAL\n";
    else
        cout << "BOTH\n";
}

// Driven Program
int main()
{
    int mat[MAX][MAX]
        = { { 0, 1, 0 }, { 0, 0, 0 }, { 0, 1, 0 } };
    checkHV(mat, 3, 3);

    return 0;
}

Java

// Java program to find if
// a matrix is symmetric.
import java.io.*;

public class GFG {

    static void checkHV(int[][] arr, int N, int M)
    {

        // Initializing as both horizontal
        // and vertical symmetric.
        boolean horizontal = true;
        boolean vertical = true;

        // Checking for Horizontal Symmetry.
        // We compare first row with last
        // row, second row with second
        // last row and so on.
        for (int i = 0, k = N - 1; i < N / 2; i++, k--) {

            // Checking each cell of a column.
            for (int j = 0; j < M; j++) {
                // check if every cell is identical
                if (arr[i][j] != arr[k][j]) {
                    horizontal = false;
                    break;
                }
            }
        }

        // Checking for Vertical Symmetry. We compare
        // first column with last column, second column
        // with second last column and so on.
        for (int j = 0, k = M - 1; j < M / 2; j++, k--) {

            // Checking each cell of a row.
            for (int i = 0; i < N; i++) {
                // check if every cell is identical
                if (arr[i][j] != arr[i][k]) {
                    horizontal = false;
                    break;
                }
            }
        }

        if (!horizontal && !vertical)
            System.out.println("NO");

        else if (horizontal && !vertical)
            System.out.println("HORIZONTAL");

        else if (vertical && !horizontal)
            System.out.println("VERTICAL");

        else
            System.out.println("BOTH");
    }

    // Driver Code
    static public void main(String[] args)
    {
        int[][] mat
            = { { 1, 0, 1 }, { 0, 0, 0 }, { 1, 0, 1 } };

        checkHV(mat, 3, 3);
    }
}

// This code is contributed by vt_m.

Python3

# Python3 program to find if a matrix is symmetric.
MAX = 1000


def checkHV(arr, N, M):

    # Initializing as both horizontal and vertical
    # symmetric.
    horizontal = True
    vertical = True

    # Checking for Horizontal Symmetry. We compare
    # first row with last row, second row with second
    # last row and so on.
    i = 0
    k = N - 1
    while(i < N // 2):

        # Checking each cell of a column.
        for j in range(M):

            # check if every cell is identical
            if (arr[i][j] != arr[k][j]):
                horizontal = False
                break
        i += 1
        k -= 1

    # Checking for Vertical Symmetry. We compare
    # first column with last column, second column
    # with second last column and so on.
    i = 0
    k = M - 1
    while(j < M // 2):

        # Checking each cell of a row.
        for i in range(N):

            # check if every cell is identical
            if (arr[i][j] != arr[i][k]):
                vertical = False
                break
        j += 1
        k -= 1

    if (not horizontal and not vertical):
        print("NO")
    elif (horizontal and not vertical):
        print("HORIZONTAL")
    elif (vertical and not horizontal):
        print("VERTICAL")
    else:
        print("BOTH")


# Driver code
mat = [[1, 0, 1], [0, 0, 0], [1, 0, 1]]

checkHV(mat, 3, 3)

# This code is contributed by shubhamsingh10

// C# program to find if
// a matrix is symmetric.
using System;

public class GFG {

    static void checkHV(int[, ] arr, int N, int M)
    {
        // Initializing as both horizontal
        // and vertical symmetric.
        bool horizontal = true;
        bool vertical = true;

        // Checking for Horizontal Symmetry.
        // We compare first row with last
        // row, second row with second
        // last row and so on.
        for (int j = 0, k = N - 1; j < N / 2; j++, k--) {

            // Checking each cell of a column.
            for (int i = 0; i < M; i++) {
                // check if every cell is identical
                if (arr[i, j] != arr[i, k]) {
                    horizontal = false;
                    break;
                }
            }
        }

        // Checking for Vertical Symmetry. We compare
        // first column with last column, second column
        // with second last column and so on.
        for (int i = 0, k = M - 1; i < M / 2; i++, k--) {

            // Checking each cell of a row.
            for (int j = 0; j < N; j++) {
                // check if every cell is identical
                if (arr[i, j] != arr[k, j]) {
                    horizontal = false;
                    break;
                }
            }
        }

        if (!horizontal && !vertical)
            Console.WriteLine("NO");

        else if (horizontal && !vertical)
            Console.WriteLine("HORIZONTAL");

        else if (vertical && !horizontal)
            Console.WriteLine("VERTICAL");

        else
            Console.WriteLine("BOTH");
    }

    // Driver Code
    static public void Main()
    {
        int[, ] mat
            = { { 1, 0, 1 }, { 0, 0, 0 }, { 1, 0, 1 } };

        checkHV(mat, 3, 3);
    }
}

// This code is contributed by vt_m.

PHP

<?php
// PHP program to find if 
// a matrix is symmetric.

function checkHV($arr, $N, $M)
{
    // Initializing as both horizontal 
    // and vertical symmetric.
    $horizontal = true; $vertical = true;

    // Checking for Horizontal Symmetry. 
    // We compare first row with last row,
    // second row with second last row 
    // and so on.
    for ($i = 0, $k = $N - 1; 
         $i < $N / 2; $i++, 
         $k--)
    {
        // Checking each cell of a column.
        for ($j = 0; $j < $M; $j++)
        {
            // check if every cell is identical
            if ($arr[$i][$j] != $arr[$k][$j])
            {
                $horizontal = false;
                break;
            }
        }
    }

    // Checking for Vertical Symmetry. 
    // We compare first column with 
    // last column, second column with 
    // second last column and so on.
    for ($j = 0, $k = $M - 1; 
         $j < $M / 2; $j++, 
         $k--)
    {
        // Checking each cell of a row.
        for ($i = 0; $i < $N; $i++)
        {
            // check if every cell is identical
            if ($arr[$i][$j] != $arr[$i][$k])
            {
                $horizontal = false;
                break;
            }
        }
    }

    if (!$horizontal && !$vertical)
        echo "NO\n";
    else if ($horizontal && !$vertical)
        cout << "HORIZONTAL\n";
    else if ($vertical && !$horizontal)
        echo "VERTICAL\n";
    else echo "BOTH\n";
}

// Driver Code
$mat = array(array (1, 0, 1),
             array (0, 0, 0),
             array (1, 0, 1));
checkHV($mat, 3, 3);

// This code is contributed by nitin mittal. 
?>

JavaScript

<script>
    // Javascript program to find if
    // a matrix is symmetric.
    
    function checkHV(arr, N, M)
    {
  
        // Initializing as both horizontal
        // and vertical symmetric.
        let horizontal = true;
        let vertical = true;
  
        // Checking for Horizontal Symmetry.
        // We compare first row with last
        // row, second row with second
        // last row and so on.
        for (let i = 0, k = N - 1;
             i < parseInt(N / 2, 10); i++, k--) {
  
            // Checking each cell of a column.
            for (let j = 0; j < M; j++) {
                // check if every cell is identical
                if (arr[i][j] != arr[k][j]) {
                    horizontal = false;
                    break;
                }
            }
        }
  
        // Checking for Vertical Symmetry. We compare
        // first column with last column, second column
        // with second last column and so on.
        for (let j = 0, k = M - 1;
             j < parseInt(M / 2, 10); j++, k--) {
  
            // Checking each cell of a row.
            for (let i = 0; i < N; i++) {
                // check if every cell is identical
                if (arr[i][j] != arr[i][k]) {
                    horizontal = false;
                    break;
                }
            }
        }
  
        if (!horizontal && !vertical)
            document.write("NO");
  
        else if (horizontal && !vertical)
            document.write("HORIZONTAL");
  
        else if (vertical && !horizontal)
            document.write("VERTICAL");
  
        else
            document.write("BOTH");
    }
    
    let mat = [ [ 1, 0, 1 ],
               [ 0, 0, 0 ],
               [ 1, 0, 1 ] ];
  
      checkHV(mat, 3, 3);
    
</script>

Output

BOTH

Time Complexity: O(N*M).
Auxiliary Space: O(1)

Analysis of Algorithms

Anuj Chauhan

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Check horizontal and vertical symmetry in binary matrix

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