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.
- 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 functionint 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 functionint 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 notimport 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 Codemat = [ [ 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 notusing 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 functionvar 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.
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