# 檢查給定矩陣是否為幻方 > 原文： [https://www.geeksforgeeks.org/check-given-matrix-is-magic-square-or-not/](https://www.geeksforgeeks.org/check-given-matrix-is-magic-square-or-not/) 給定一個矩陣，檢查它是否為 [Magic Square](https://www.geeksforgeeks.org/magic-square/) 。 幻方是從 1 到 n ² 的不同元素的 n x n 矩陣，其中任何行，列或對角線的總和始終等于相同的數字。 例子： ``` 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.找到主要對角線和次要對角線的和。 2.計算每行和每列的總和。 3.如果主要對角線和輔助對角線的總和等于每一行的總和和每一列的總和，則它是幻矩陣。 ## C++ ```cpp // C++ program to check whether a given? // matrix is magic matrix or not #include <bits/stdc++.h> #define N 3 using namespace std; // Returns true if mat[][] is magic // square, else returns false. bool isMagicSquare(int mat[][N]) {? ????// calculate the sum of? ????// the prime diagonal ????int sum = 0,sum2=0;? ????for (int i = 0; i < N; i++) ????????sum = sum + mat[i][i]; ????// the secondary diagonal ????for (int i = 0; i < N; i++) ????????sum2 = sum2 + mat[i][N-1-i]; ????if(sum!=sum2)? ????????return false; ????// For sums of Rows? ????for (int i = 0; i < N; i++) { ????????int rowSum = 0;????? ????????for (int j = 0; j < N; j++) ????????????rowSum += mat[i][j]; ????????// check if every row sum is ????????// equal to prime diagonal sum ????????if (rowSum != sum) ????????????return false; ????} ????// For sums of Columns ????for (int i = 0; i < N; i++) { ????????int colSum = 0;????? ????????for (int j = 0; j < N; j++) ????????????colSum += mat[j][i]; ????????// check if every column sum is? ????????// equal to prime diagonal sum ????????if (sum != colSum)? ????????return false; ????} ????return true; } // driver program to? // test above function int main() { ????int mat[][N] = {{ 2, 7, 6 }, ????????????????????{ 9, 5, 1 }, ????????????????????{ 4, 3, 8 }}; ????if (isMagicSquare(mat)) ????????cout << "Magic Square"; ????else ????????cout << "Not a magic Square"; ????return 0; } ``` ## Java ```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[][]) ????{ ????????// calculate the sum of ????????// the prime diagonal ?????????int sum = 0,sum2=0;? ????????for (int i = 0; i < N; i++) ????????????sum = sum + mat[i][i]; ????????// the secondary diagonal ????????for (int i = 0; i < N; i++) ????????????sum2 = sum2 + mat[i][N-1-i]; ????????if(sum!=sum2)? ????????????return false; ????????// For sums of Rows ????????for (int i = 0; i < N; i++) { ????????????int rowSum = 0; ????????????for (int j = 0; j < N; j++) ????????????????rowSum += mat[i][j]; ????????????// check if every row sum is ????????????// equal to prime diagonal sum ????????????if (rowSum != sum) ????????????????return false; ????????} ????????// For sums of Columns ????????for (int i = 0; i < N; i++) { ????????????int colSum = 0; ????????????for (int j = 0; j < N; j++) ????????????????colSum += mat[j][i]; ????????????// check if every column sum is ????????????// equal to prime diagonal sum ????????????if (sum != colSum) ????????????????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"); ????} } // This code is contributed by vt_m ``` ## Python3 ```py # Python3 program to check whether a given? # matrix is magic matrix or not N = 3 # Returns true if mat[][] is magic # square, else returns false. def isMagicSquare( mat) : ????# calculate the sum of? ????# the prime diagonal ????s = 0? ????for i in range(0, N) : ????????s = s + mat[i][i] ????# the secondary diagonal ????s2 = 0 ????for i in range(0, N) : ????????s2 = s2 + mat[i][N-i-1] ????if(s!=s2) : ????????return False ????# For sums of Rows? ????for i in range(0, N) : ????????rowSum = 0;????? ????????for j in range(0, N) : ????????????rowSum += mat[i][j] ????????# check if every row sum is ????????# equal to prime diagonal sum ????????if (rowSum != s) : ????????????return False ????# For sums of Columns ????for i in range(0, N): ????????colSum = 0 ????????for j in range(0, N) : ????????????colSum += mat[j][i] ????????# check if every column sum is? ????????# equal to prime diagonal sum ????????if (s != colSum) : ????????????return False ????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") # This code is contributed by Nikita Tiwari.???? ``` ## C# ```cs // 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) ????{ ????????// calculate the sum of ????????// the prime diagonal ????????int sum = 0, sum2 = 0; ????????for (int i = 0; i < N; i++) ????????????sum = sum + mat[i, i]; ????????// the secondary diagonal ????????for (int i = 0; i < N; i++) ????????????sum2 = sum2 + mat[i, N-1-i]; ????????if(sum!=sum2) ????????????return false; ????????// For sums of Rows ????????for (int i = 0; i < N; i++) { ????????????int rowSum = 0; ????????????for (int j = 0; j < N; j++) ????????????????rowSum += mat[i, j]; ????????????// check if every row sum is ????????????// equal to prime diagonal sum ????????????if (rowSum != sum) ????????????????return false; ????????} ????????// For sums of Columns ????????for (int i = 0; i < N; i++)? ????????{ ????????????int colSum = 0; ????????????for (int j = 0; j < N; j++) ????????????????colSum += mat[j,i]; ????????????// check if every column sum is ????????????// equal to prime diagonal sum ????????????if (sum != colSum) ????????????????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"); ????} } // This code is contributed by KRV. ``` ## PHP ```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($mat) { ????// calculate the sum of? ????// the prime diagonal ????$sum = 0; $N=3; ????for($i = 0; $i < $N; $i++) ????????$sum = $sum + $mat[$i][$i]; ????// the secondary diagonal ????$sum2 = 0; $N=3; ????for($i = 0; $i < $N; $i++) ????????$sum2 = $sum2 + $mat[$i][$N-$i-1]; ????if( $sum != $sum2) ????????return false; ????// For sums of Rows? ????for($i = 0; $i < $N; $i++)? ????{ ????????$rowSum = 0;????? ????????for ($j = 0; $j < $N; $j++) ????????????$rowSum += $mat[$i][$j]; ????????// check if every row sum is ????????// equal to prime diagonal sum ????????if ($rowSum != $sum) ????????????return false; ????} ????// For sums of Columns ????for ($i = 0; $i < $N; $i++) ????{ ????????$colSum = 0;????? ????????for ($j = 0; $j < $N; $j++) ????????????$colSum += $mat[$j][$i]; ????????// check if every column sum is? ????????// equal to prime diagonal sum ????????if ($sum != $colSum)? ????????return false; ????} ????return true; } // Driver Code { ????$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; } ?> // This code is contributed by nitin mittal ``` ``` Magic square ``` * * * * * *