Print sum of matrix and its mirror image

You are given a matrix of order N*N. The task is to find the resultant matrix by adding the mirror image of given matrix with the matrix itself.

Examples: 

Input : mat[][] = {{1, 2, 3},
                              {4, 5, 6},
                              {7, 8, 9}}
Output : 4 4 4
               10 10 10
               16 16 16
Explanation:  
Resultant Matrix = {{1, 2, 3},      {{3, 2, 1}, 
                                 {4, 5, 6},   +   {6, 5, 4},
                                 {7, 8, 9}}       {9, 8, 7}}

Input : mat[][] = {{1, 2},
                               {3, 4}}
Output : 3 3
               7 7

While finding the mirror image of matrix the row of each element will remain same but the value of its columns will reshuffle. For any element A_ij its new position in mirror image will be A_i(n-j). After getting the mirror image of matrix add it to original matrix and print the result.

Points to take care:

1. Indexing of matrix will start from 0, 0 and ends on n-1, n-1 hence position of any element A_ij will be A_i(n-1-j).
2. While printing the result take care of proper output format

Below is the implementation of the above approach: 

C++

// C++ program to find sum of matrix and
// its mirror image
#include <bits/stdc++.h>

#define N 4
using namespace std;

// Function to print the resultant matrix
void printSum(int mat[][N])
{
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < N; j++) {
            cout << setw(3) << mat[i][N - 1 - j] + mat[i][j] << " ";
        }

        cout << "\n";
    }
}

// Driver Code
int main()
{
    int mat[N][N] = { { 2, 4, 6, 8 },
                      { 1, 3, 5, 7 },
                      { 8, 6, 4, 2 },
                      { 7, 5, 3, 1 } };

    printSum(mat);

    return 0;
}

Java

// Java program to find sum of
// matrix and its mirror image
import java.io.*;

class GFG
{
static int N = 4;

// Function to print the
// resultant matrix
static void printSum(int mat[][])
{
    for (int i = 0; i < N; i++)
    {
        for (int j = 0; j < N; j++)
        {
            System.out.print((mat[i][N - 1 - j] +
                              mat[i][j]) + " ");
        }

        System.out.println();
    }
}

// Driver Code
public static void main (String[] args)
{
    int mat[][] = { { 2, 4, 6, 8 },
                    { 1, 3, 5, 7 },
                    { 8, 6, 4, 2 },
                    { 7, 5, 3, 1 } };

    printSum(mat);
}
}

// This code is contributed by anuj_67

Python3

# Python 3 program to find sum of matrix
# and its mirror image

N = 4

# Function to print the resultant matrix
def printSum(mat):
    for i in range(N):
        for j in range(N):
            print('{:>3}'.format(mat[i][N - 1 - j] +
                                 mat[i][j]), end =" ")

        print("\n", end = "")

# Driver Code
if __name__ == '__main__':
    mat = [[2, 4, 6, 8],
           [1, 3, 5, 7],
           [8, 6, 4, 2],
           [7, 5, 3, 1]]

    printSum(mat)

# This code is contributed by
# Surendra_Gangwar

C#

// C# program to find sum of
// matrix and its mirror image
using System;

class GFG
{
static int N = 4;

// Function to print the
// resultant matrix
static void printSum(int [,]mat)
{
    for (int i = 0; i < N; i++)
    {
        for (int j = 0; j < N; j++)
        {
            Console.Write((mat[i, N - 1 - j] +
                           mat[i, j]) + " ");
        }

        Console.WriteLine();
    }
}

// Driver Code
public static void Main ()
{
    int [,]mat = { { 2, 4, 6, 8 },
                   { 1, 3, 5, 7 },
                   { 8, 6, 4, 2 },
                   { 7, 5, 3, 1 } };

    printSum(mat);
}
}

// This code is contributed by shs..

PHP

<?php
// PHP program to find sum of
// matrix and its mirror image

// Function to print the
// resultant matrix
function printSum($mat)
{
    for ($i = 0; $i < 4; $i++)
    {
        for ($j = 0; $j < 4; $j++)
        {
            echo ($mat[$i][4 - 1 - $j] +
                  $mat[$i][$j]) . " " ;
        }

        echo "\n";
    }
}

// Driver Code
$mat = array(array(2, 4, 6, 8 ),
             array(1, 3, 5, 7),
             array(8, 6, 4, 2),
             array(7, 5, 3, 1));

printSum($mat);

// This code is contributed
// by Akanksha Rai
?>

Javascript

<script>

// Javascript program to find sum of matrix and
// its mirror image

var N = 4

// Function to print the resultant matrix
function printSum(mat)
{
    for (var i = 0; i < N; i++) {
        for (var j = 0; j < N; j++) {
            document.write( (mat[i][N - 1 - j] + mat[i][j]) + " ");
        }

        document.write("<br>");
    }
}

// Driver Code
var mat = [ [ 2, 4, 6, 8 ],
                  [ 1, 3, 5, 7 ],
                  [ 8, 6, 4, 2 ],
                  [ 7, 5, 3, 1 ] ];
printSum(mat);

</script>

Output

 10  10  10  10 
  8   8   8   8 
 10  10  10  10 
  8   8   8   8 

Complexity Analysis:

• Time complexity : O(N²) for given input matrix of size N*N
• Auxiliary Space: O(1)