# 魔术广场| 偶数订单 > 原文： [https://www.geeksforgeeks.org/magic-square-even-order/](https://www.geeksforgeeks.org/magic-square-even-order/) 阶数为 n 的**幻方**是正方形中 n ^ 2 个数字（通常是不同的整数）的排列，以使所有行，所有列和两个对角线中的 n 个数字求和为相同的常数。 幻方包含从 1 到 n ^ 2 的整数。 每行，每一列和对角线中的常数之和称为魔术常数或魔术之和 M。正常魔术方阵的魔术常数仅取决于 n，并且具有以下值： M = n（n ^ 2 + 1）/ 2。 **示例**： ``` Magic Square of order 3: ----------------------- 2 7 6 9 5 1 4 3 8 Magic Square of order 4: ----------------------- 16 2 3 13 5 11 10 8 9 7 6 12 4 14 15 1 Magic Square of order 8: ----------------------- 64 63 3 4 5 6 58 57 56 55 11 12 13 14 50 49 17 18 46 45 44 43 23 24 25 26 38 37 36 35 31 32 33 34 30 29 28 27 39 40 41 42 22 21 20 19 47 48 16 15 51 52 53 54 10 9 8 7 59 60 61 62 2 1 ``` **有点理论**： 魔术方块根据方块的顺序分为三大类。 1）[奇数阶幻方。](https://www.geeksforgeeks.org/magic-square/) 示例：3,5,7，…（2 * n +1） 2）双偶数阶幻方。 示例：4,8,12,16，..（4 * n） 3）单双阶幻方。 例子：6,10,14,18，..（4 * n +2） **双偶幻方的算法**： ``` define an 2-D array of order n*n // fill array with their index-counting // starting from 1 for ( i = 0; i<n; i++) { for ( j = 0; j<n; j++) // filling array with its count value // starting from 1; arr[i][j] = (n*i) + j + 1; } // change value of Array elements // at fix location as per rule // (n*n+1)-arr[i][j] // Top Left corner of Matrix // (order (n/4)*(n/4)) for ( i = 0; i<n/4; i++) { for ( j = 0; j<n/4; j++) arr[i][j] = (n*n + 1) - arr[i][j]; } // Top Right corner of Matrix // (order (n/4)*(n/4)) for ( i = 0; i< n/4; i++) { for ( j = 3* (n/4); j<n; j++) arr[i][j] = (n*n + 1) - arr[i][j]; } // Bottom Left corner of Matrix // (order (n/4)*(n/4)) for ( i = 3* n/4; i<n; i++) { for ( j = 0; j<n/4; j++) arr[i][j] = (n*n + 1) - arr[i][j]; } // Bottom Right corner of Matrix // (order (n/4)*(n/4)) for ( i = 3* n/4; i<n; i++) { for ( j = 3* n/4; j<n; j++) arr[i][j] = (n*n + 1) - arr[i][j]; } // Centre of Matrix (order (n/2)*(n/2)) for ( i = n/4; i<3* n/4; i++) { for ( j = n/4; j<3* n/4; j++) arr[i][j] = (n*n + 1) - arr[i][j]; } ``` **举例说明：（第 4 阶）** 1）定义 4 * 4 阶数组，并将其计数值填充为： [](https://media.geeksforgeeks.org/wp-content/uploads/array-5.jpg) 2）更改顺序（1 * 1）的左上角矩阵的值： [](https://media.geeksforgeeks.org/wp-content/uploads/array1.jpg) 3）更改顺序（1 * 1）的右上角矩阵的值： [](https://media.geeksforgeeks.org/wp-content/uploads/array2-1.jpg) 4）更改顺序（1 * 1）的左下角矩阵的值： [](https://media.geeksforgeeks.org/wp-content/uploads/array3.jpg) 5）更改顺序（1 * 1）的右下角矩阵的值： [](https://media.geeksforgeeks.org/wp-content/uploads/array4.jpg) 6）阶数（2 * 2）的中心矩阵的更改值： [](https://media.geeksforgeeks.org/wp-content/uploads/array5.jpg) **双偶幻方的实现**： ## C/C++ ``` // C++ Program to print Magic square // of Doubly even order #include<iostream> using namespace std; // Function for calculating Magic square  void doublyEven( int n ) {      int arr[n][n], i, j;     // filling matrix with its count value      // starting from 1;     for ( i = 0; i < n; i++)         for ( j = 0; j < n; j++)             arr[i][j] = (n*i) + j + 1;     // change value of Array elements     // at fix location as per rule      // (n*n+1)-arr[i][j]     // Top Left corner of Matrix      // (order (n/4)*(n/4))     for ( i = 0; i < n/4; i++)         for ( j = 0; j < n/4; j++)             arr[i][j] = (n*n + 1) - arr[i][j];     // Top Right corner of Matrix      // (order (n/4)*(n/4))     for ( i = 0; i < n/4; i++)         for ( j = 3 * (n/4); j < n; j++)             arr[i][j] = (n*n + 1) - arr[i][j];      // Bottom Left corner of Matrix     // (order (n/4)*(n/4))     for ( i = 3 * n/4; i < n; i++)         for ( j = 0; j < n/4; j++)             arr[i][j] = (n*n+1) - arr[i][j];     // Bottom Right corner of Matrix      // (order (n/4)*(n/4))     for ( i = 3 * n/4; i < n; i++)         for ( j = 3 * n/4; j < n; j++)             arr[i][j] = (n*n + 1) - arr[i][j];     // Centre of Matrix (order (n/2)*(n/2))     for ( i = n/4; i < 3 * n/4; i++)         for ( j = n/4; j < 3 * n/4; j++)             arr[i][j] = (n*n + 1) - arr[i][j];     // Printing the magic-square     for (i = 0; i < n; i++)     {         for ( j = 0; j < n; j++)             cout << arr[i][j] << " ";         cout << "\n";     } } // driver program int main() {     int n=8;     doublyEven(n); //Function call     return 0; }  ```