魔術廣場| 偶數訂單 · GeeksForGeeks 中文系列教程

# 魔術廣場| 偶數訂單 > 原文： [https://www.geeksforgeeks.org/magic-square-even-order/](https://www.geeksforgeeks.org/magic-square-even-order/) 階數為 n 的**幻方**是正方形中 n ^ 2 個數字（通常是不同的整數）的排列，以使所有行，所有列和兩個對角線中的 n 個數字求和為相同的常數。幻方包含從 1 到 n ^ 2 的整數。每行，每一列和對角線中的常數之和稱為魔術常數或魔術之和 M。正常魔術方陣的魔術常數僅取決于 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 ``` **有點理論**：魔術方塊根據方塊的順序分為三大類。 1）[奇數階幻方。](https://www.geeksforgeeks.org/magic-square/) 示例：3,5,7，…（2 * n +1） 2）雙偶數階幻方。示例：4,8,12,16，..（4 * n） 3）單雙階幻方。例子：6,10,14,18，..（4 * n +2） **雙偶幻方的算法**： ``` 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]; } ``` **舉例說明：（第 4 階）** 1）定義 4 * 4 階數組，并將其計數值填充為： [![dd1](https://img.kancloud.cn/14/21/1421688c64f5528763db91bf24c54a6b_311x231.png)](https://media.geeksforgeeks.org/wp-content/uploads/array-5.jpg) 2）更改順序（1 * 1）的左上角矩陣的值： [![dd2](https://img.kancloud.cn/f3/f5/f3f594ea7b87ff141bd1eecca506e21c_311x231.png)](https://media.geeksforgeeks.org/wp-content/uploads/array1.jpg) 3）更改順序（1 * 1）的右上角矩陣的值： [![dd3](https://img.kancloud.cn/82/ba/82bad665a22ea68fae43817de1ee115e_311x231.png)](https://media.geeksforgeeks.org/wp-content/uploads/array2-1.jpg) 4）更改順序（1 * 1）的左下角矩陣的值： [![dd4](https://img.kancloud.cn/0c/66/0c66dc914a3546f04fbabddabf04a939_311x231.png)](https://media.geeksforgeeks.org/wp-content/uploads/array3.jpg) 5）更改順序（1 * 1）的右下角矩陣的值： [![dd5](https://img.kancloud.cn/1a/a9/1aa98fa6b1d408c44ac66d20a444b129_311x231.png)](https://media.geeksforgeeks.org/wp-content/uploads/array4.jpg) 6）階數（2 * 2）的中心矩陣的更改值： [![ddf](https://img.kancloud.cn/d8/bf/d8bf2f28ee98e585a86ccb43883621b9_311x231.png)](https://media.geeksforgeeks.org/wp-content/uploads/array5.jpg) **雙偶幻方的實現**： ## 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; }? ```