任意N阶幻方算法实现

算法原理请参考：https://www.zhihu.com/question/23531676

先定义一些通用的函数，比如创建空幻方，删除幻方，打印幻方。

创建幻方

int **NewMagicS(int n) {
    int **magic = new int*[n];
    for (int k = 0; k < n; k++)
        magic[k] = new int[n];
    return magic;
}

删除幻方

void DeleteMagicS(int **magic, int n) {
    for (int k = 0; k < n; k++)
        delete[] magic[k];
    delete[] magic;
}

打印幻方

void ShowMagicS(int **magic, int n) {
    int i, j;
    for (i = 0; i < n; i++) {
        for (j = 0; j < n; j++)
            printf("%-6d", magic[i][j]);
        printf("\n");
    }
}

一、奇数幻方算法实现：

辅助函数（实现算法）

void OddMagicSA(int **magic, int n, int value) {
    int i, j, total;
    //初始化二维数组
    for (i = 0; i < n; i++)
        for (j = 0; j < n; j++)
            magic[i][j] = 0;
    i = 0;
    j = n / 2;
    magic[i][j] = value++;
    for (total = 1; total < n*n; total++, value++) {//向右上角移动
        //调整位置
        if (!magic[(i - 1) == -1 ? n - 1 - i : i - 1][(j + 1) % n]) { //空闲
            i = (i - 1) == -1 ? n - 1 - i : i - 1;
            j = (j + 1) % n;
        }
        else //原位置下移一格(行变)
            i = (i + 1) % n;
        magic[i][j] = value;
    }
}

主函数（负责打印）

void OddMagicS(int n) {
    int **magic;
    if (n <= 0 || n == 1 || n == 2 || (n % 2 == 0)) return;
    magic = NewMagicS(n);
    OddMagicSA(magic, n, 1);
    //显示奇数幻方
    ShowMagicS(magic, n);
    DeleteMagicS(magic, n);
}

二、偶数幻方算法实现：

辅助函数（算法实现）

void EvenMagicSA(int **magic, int n, int value) {
    int i, j;
    //初始化二维数组
    for (i = 0; i < n; i++)
        for (j = 0; j < n; j++)
            magic[i][j] = 0;
    //分割为4x4格子，然后填充对角线位置为-1
    for (i = 0; i < n; i += 4)//i, j 表示4x4起点
        for (j = 0; j < n; j += 4) {
            //对角线填充
            for (int k = 0; k < 4; k++) {
                magic[i + k][j + k] = -1;
                magic[i + 3 - k][j + k] = -1;
            }
        }
    i = 0;
    for (; i < n; i++)
        for (j = 0; j < n; j++, value++) {
            //先填充4x4非对角线，从左向右，从上向下
            if (magic[i][j] != -1 && magic[i][j] == 0) magic[i][j] = value;
            //填充4x4对角线,左右向左，从下向上
            if (magic[n - 1 - i][n - 1 - j] == -1) magic[n - 1 - i][n - 1 - j] = value;
        }
}

主要函数（打印幻方）

void EvenMagicS(int n) {
    int **magic;
    if (n <= 0 || n == 1 || n == 2 || n % 4 != 0) return;
    magic = NewMagicS(n);
    EvenMagicSA(magic, n, 1);
    //显示偶数幻方
    ShowMagicS(magic, n);
    DeleteMagicS(magic, n);
}

三、最后一个幻方类型叫做奇偶幻方，算法实现：

增加一个幻方复制

void CopyMagicS(int **dstMagic, int sLine, int sColumn, int **srcMagic, int n) {
    for (int i = sLine, p = 0; p < n; i++, p++)
        for (int j = sColumn, q = 0; q < n; j++, q++)
            dstMagic[i][j] = srcMagic[p][q];
}

 

主要函数（算法实现）

void OddEvenMagicS(int n) {
    int **magic, **magicTemp, i, j, k, mid;
    if (!(n >= 0 && n != 1 && n != 2 && (n % 2 == 0 && n % 4 != 0))) return;
    magic = NewMagicS(n);
    magicTemp = NewMagicS(n / 2);
    //顺时针分成A,B,C,D四个象限，并且按照A, D, B, C的顺序以奇幻方方法填充
    i = j = 0;//A象限
    OddMagicSA(magicTemp, n / 2, 1);
    CopyMagicS(magic, i, j, magicTemp, n / 2);
    i = j = n / 2;//D象限
    OddMagicSA(magicTemp, n / 2, n / 2 * n / 2 + 1);
    CopyMagicS(magic, i, j, magicTemp, n / 2);
    i = 0;
    j = n / 2;//B象限
    OddMagicSA(magicTemp, n / 2, n / 2 * n / 2 * 2 + 1);
    CopyMagicS(magic, i, j, magicTemp, n / 2);
    i = n / 2;
    j = 0;//C象限
    OddMagicSA(magicTemp, n / 2, n / 2 * n / 2 * 3 + 1);
    CopyMagicS(magic, i, j, magicTemp, n / 2);
    k = (n - 2) / 4;
    //A, C象限交换
    for (int l = 0; l < n / 2; l++) 
        for (int m = 0; m < k; m++)
            if (l == n / 4) {//中间行
                mid = magic[l][k + m];
                magic[l][k + m] = magic[n / 2 + l][k + m];
                magic[n / 2 + l][k + m] = mid;
            }
            else {
                mid = magic[l][m];
                magic[l][m] = magic[n / 2 + l][m];
                magic[n / 2 + l][m] = mid;
            }
    //B, D象限交换
    for (int l = 0; l < k - 1; l++) {//列
        for (int m = 0; m < n / 2; m++) {//行
            mid = magic[m][3 * n / 4 - l];
            magic[m][3 * n / 4 - l] = magic[n / 2 + m][3 * n / 4 - l];
            magic[n / 2 + m][3 * n / 4 - l] = mid;
        }
    }
    //显示奇偶数幻方
    ShowMagicS(magic, n);
    DeleteMagicS(magic, n);
    DeleteMagicS(magicTemp, n / 2);
}

所有代码均经过测试，结果正确。