Check given matrix is magic square or not

Given a matrix, check whether it’s Magic Square or not. A Magic Square is a n x n matrix of the distinct elements from 1 to n² where the sum of any row, column, or diagonal is always equal to the same number.

Examples: 

Input : n = 3
  2   7   6
  9   5   1
  4   3   8
  
Output : Magic matrix
Explanation:In matrix sum of each
row and each column and diagonals sum is 
same = 15.

Input : n = 3
  1   2   2 
  2   2   1
  2   1   2
Output : Not a Magic Matrix
Explanation:In matrix sum of each
row and each column and diagonals sum is
not same.

1. Find the sum of prime diagonal and secondary diagonal. 
2. Calculate the sum of each row and column. 
3. If the prime diagonal and secondary diagonal sums are equal to every row’s sum and every column’s sum, then it is the magic matrix.

Implementation:

C++

// C++ program to check whether a given
// matrix is magic matrix or not
#include <bits/stdc++.h>

# define my_sizeof(type) ((char *)(&type+1)-(char*)(&type))
using namespace std;

// Returns true if mat[][] is magic
// square, else returns false.
bool isMagicSquare(int mat[][3])
{
    int n = my_sizeof(mat)/my_sizeof(mat[0]);
    // calculate the sum of
    // the prime diagonal
    int i=0,j=0;
    // sumd1 and sumd2 are the sum of the two diagonals
    int sumd1 = 0, sumd2=0;
    for (i = 0; i < n; i++)
    {
        // (i, i) is the diagonal from top-left -> bottom-right
        // (i, n - i - 1) is the diagonal from top-right -> bottom-left
        sumd1 += mat[i][i];
        sumd2 += mat[i][n-1-i];
    }
    // if the two diagonal sums are unequal then it is not a magic square
    if(sumd1!=sumd2)
        return false;

    // For sums of Rows
    for (i = 0; i < n; i++) {

        int rowSum = 0, colSum = 0;
        for (j = 0; j < n; j++)
        {
            rowSum += mat[i][j];
            colSum += mat[j][i];
        }
        if (rowSum != colSum || colSum != sumd1)
            return false;
    }
   return true;
}

// driver program to
// test above function
int main()
{
    int mat[3][3] = {{ 2, 7, 6 },
                    { 9, 5, 1 },
                    { 4, 3, 8 }};

    if (isMagicSquare(mat))
        cout << "Magic Square";
    else
        cout << "Not a magic Square";

    return 0;
}

C

// C program to check whether a given
// matrix is magic matrix or not
#include <stdio.h>
#include <stdbool.h>

# define my_sizeof(type) ((char *)(&type+1)-(char*)(&type))

// Returns true if mat[][] is magic
// square, else returns false.
bool isMagicSquare(int mat[][3])
{
    int n = my_sizeof(mat)/my_sizeof(mat[0]);

    // calculate the sum of
    // the prime diagonal
    int i = 0, j = 0;

    // sumd1 and sumd2 are the sum of the two diagonals
    int sumd1 = 0, sumd2=0;
    for (i = 0; i < n; i++)
    {
        // (i, i) is the diagonal from top-left -> bottom-right
        // (i, n - i - 1) is the diagonal from top-right -> bottom-left
        sumd1 += mat[i][i];
        sumd2 += mat[i][n-1-i];
    }

    // if the two diagonal sums are unequal then it is not a magic square
    if(sumd1!=sumd2)
        return false;

    // For sums of Rows
    for (i = 0; i < n; i++) {

        int rowSum = 0, colSum = 0;
        for (j = 0; j < n; j++)
        {
            rowSum += mat[i][j];
            colSum += mat[j][i];
        }
        if (rowSum != colSum || colSum != sumd1)
            return false;
    }
   return true;
}

// driver program to
// test above function
int main()
{
    int mat[3][3] = {{ 2, 7, 6 },
                    { 9, 5, 1 },
                    { 4, 3, 8 }};

    if (isMagicSquare(mat))
        printf("Magic Square");
    else
        printf("Not a magic Square");

    return 0;
}

// This code is contributed by kothavvsaakash.

Java

// JAVA program to check whether a given
// matrix is magic matrix or not

import java.io.*;

class GFG {

    static int N = 3;

    // Returns true if mat[][] is magic
    // square, else returns false.
    static boolean isMagicSquare(int mat[][])
    {

        // sumd1 and sumd2 are the sum of the two diagonals
        int sumd1 = 0,sumd2=0;
        for (int i = 0; i < N; i++)
        {
            // (i, i) is the diagonal from top-left -> bottom-right
               // (i, N - i - 1) is the diagonal from top-right -> bottom-left
            sumd1 += mat[i][i];
               sumd2 += mat[i][N-1-i];
        }
    // if the two diagonal sums are unequal then it is not a magic square
        if(sumd1!=sumd2)
            return false;

        // calculating sums of Rows and columns and checking if they are equal to each other,
        // as well as equal to diagonal sum or not
        for (int i = 0; i < N; i++) {

            int rowSum = 0, colSum = 0;
            for (int j = 0; j < N; j++)
            {
                rowSum += mat[i][j];
                colSum += mat[j][i];
            }
            if (rowSum != colSum || colSum != sumd1)
                return false;
        }


        return true;
    }

    // driver program to
    // test above function
    public static void main(String[] args)
    {
        int mat[][] = {{ 2, 7, 6 },
                       { 9, 5, 1 },
                       { 4, 3, 8 }};

        if (isMagicSquare(mat))
            System.out.println("Magic Square");
        else
            System.out.println("Not a magic" +
                                    " Square");
    }
}

Python3

# Python3 program to check whether a given
# matrix is magic matrix or not
# Returns true if mat[][] is magic
# square, else returns false.
def isMagicSquare( mat) :
  n = len(mat)
  # sumd1 and sumd2 are the sum of the two diagonals
  sumd1=0
  sumd2=0
  for i in range(n):
    # (i, i) is the diagonal from top-left -> bottom-right
    # (i, n - i - 1) is the diagonal from top-right -> bottom-left
    sumd1+=mat[i][i]
    sumd2+=mat[i][n-i-1]
    # if the two diagonal sums are unequal then it is not a magic square
  if not(sumd1==sumd2):
    return False
  for i in range(n):
    #sumr is rowsum and sumc is colsum
    sumr=0
    sumc=0
    for j in range(n):
      sumr+=mat[i][j]
      sumc+=mat[j][i]
    if not(sumr==sumc==sumd1):
      return False
    #if all the conditions are satisfied then it is a magic square
  return True





# Driver Code
mat = [ [ 2, 7, 6 ],
        [ 9, 5, 1 ],
        [ 4, 3, 8 ] ]

if (isMagicSquare(mat)) :
    print( "Magic Square")
else :
    print( "Not a magic Square")

C#

// C# program to check whether a given
// matrix is magic matrix or not
using System;

class GFG
{

    static int N = 3;

    // Returns true if mat[][] is magic
    // square, else returns false.
    static bool isMagicSquare(int[,] mat)
    {

        // sumd1 and sumd2 are the sum of the two diagonals
        int sumd1 = 0, sumd2 = 0;

        for (int i = 0; i < N; i++)
        {
            // (i, i) is the diagonal from top-left -> bottom-right
                // (i, N - i - 1) is the diagonal from top-right -> bottom-left
                    sumd1 = sumd1 + mat[i, i];
                    sumd2 = sumd2 + mat[i, N-1-i];
        }
        // if the two diagonal sums are unequal then it is not a magic square
        if(sumd1!=sumd2)
            return false;

        // For sums of Rows
        for (int i = 0; i < N; i++) {

            int rowSum = 0, colSum = 0;
            for (int j = 0; j < N; j++)
            {
                rowSum += mat[i, j];
                  colSum += mat[j,i];
            }
            if (rowSum != colSum || colSum != sumd1)
                return false;
        }

        return true;
    }

    // Driver Code
    public static void Main()
    {
        int[,] mat =new int [,] {{ 2, 7, 6 },
                                { 9, 5, 1 },
                                { 4, 3, 8 }};

        if (isMagicSquare(mat))
            Console.WriteLine("Magic Square");
        else
            Console.WriteLine("Not a magic" +
                            " Square");
    }
}

PHP

<?php
// PHP program to check whether a given
// matrix is magic matrix or not

// Returns true if mat[][] is magic
// square, else returns false.
function isMagicSquare($mat)
{

    // sumd1 and sumd2 are the sum of the two diagonals
    $sumd1 = 0; $sumd2 = 0;
       $N= count($mat);
    for($i = 0; $i < $N; $i++)
    {
        // (i, i) is the diagonal from top-left -> bottom-right
            // (i, N - i - 1) is the diagonal from top-right -> bottom-left
            $sumd1 = $sumd1 + $mat[$i][$i];
            $sumd2 = $sumd2 + $mat[$i][$N-$i-1];
    }
    // if the two diagonal sums are unequal then it is not a magic square
    if( $sumd1 != $sumd2)
        return false;

    for($i = 0; $i < $N; $i++)
    {
        $rowSum = 0;    $colSum = 0;
        for ($j = 0; $j < $N; $j++)
        {
                $rowSum += $mat[$i][$j];
                  $colSum += $mat[$j][$i];
        }
        if ($rowSum != $colSum || $colSum != $sumd1)
            return false;
    }
    return true;
}

// Driver Code
{
    $mat = array(array(2, 7, 6),
                array(9, 5, 1),
                array(4, 3, 8));

    if (isMagicSquare($mat))
        echo "Magic Square";
    else
        echo "Not a magic Square";

    return 0;
}

?>

Javascript

<script>

// Javascript program to check whether a given
// matrix is magic matrix or not


// Returns true if mat[][] is magic
// square, else returns false.
function isMagicSquare(mat)
{
    var N = mat.length
    // sumd1 and sumd2 are the sum of the two diagonals
    var sumd1 = 0,sumd2=0;
    for (var i = 0; i < N; i++)
    {
        // (i, i) is the diagonal from top-left -> bottom-right
        // (i, N - i - 1) is the diagonal from top-right -> bottom-left
        sumd1 = sumd1 + mat[i][i];
        sumd2 = sumd2 + mat[i][N-1-i];
    }
    // if the two diagonal sums are unequal then it is not a magic square
    if(sumd1!=sumd2)
        return false;


    for (var i = 0; i < N; i++) {
        var colSum = 0;
        var rowSum = 0;
        for (var j = 0; j < N; j++)
        {
            rowSum += mat[i][j];
            colSum += mat[j][i];
        }
        if (rowSum != colSum || colSum != sumd1)
            return false;
    }
    return true;
}

// driver program to
// test above function
var mat = [[ 2, 7, 6 ],
           [ 9, 5, 1 ],
           [ 4, 3, 8 ]];

if (isMagicSquare(mat))
    document.write( "Magic Square");
else
    document.write( "Not a magic Square");


</script>

Output

Magic Square

Time Complexity: O(n²)
Auxiliary Space: O(1),  since no extra space has been taken.

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