Check horizontal and vertical symmetry in binary matrix

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 same as the last row, the second row is same as the second last row and so on. And the matrix is said to be vertical symmetric if the first column is same as the last column, the second column is same as the second last column and so on. Print “VERTICAL” if the matrix is vertical symmetric, “HORIZONTAL” if the matrix is vertical 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
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 :
0 0 1
1 1 0
0 0 1.
Output : Horizontal

The idea is to use to 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 identical element is found, mark 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 identical element is found, mark matrix as not vertical symmetric.

Below is the implementation of above idea :

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// 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 xolumn
    // 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]) {
                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] = { { 1, 0, 1 },
                          { 0, 0, 0 },
                          { 1, 0, 1 } };
  
    checkHV(mat, 3, 3);
  
    return 0;
}

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// 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 xolumn
        // 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)
            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.

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// 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 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 xolumn
        // 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.

chevron_right


PHP

filter_none

edit
close

play_arrow

link
brightness_4
code

<?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 xolumn with 
    // second last column and so on.
    for ($i = 0, $k = $M - 1; 
         $i < $M / 2; $i++, 
         $k--)
    {
        // Checking each cell of a row.
        for ($j = 0; $j < $N; $j++)
        {
            // check if every cell is identical
            if ($arr[$i][$j] != $arr[$k][$j])
            {
                $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. 
?>

chevron_right


Output :

BOTH

Time Complexity: O(N*M).

This article is contributed by Anuj Chauhan. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.



My Personal Notes arrow_drop_up



Article Tags :
Practice Tags :


Be the First to upvote.


Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.