Check given matrix is magic square or not
Last Updated :
04 Aug, 2022
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.
- Find the sum of prime diagonal and secondary diagonal.
- Calculate the sum of each row and column.
- 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 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 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 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# 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 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;
}
?>
<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>
Time Complexity: O(n2)
Auxiliary Space: O(1), since no extra space has been taken.
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