C++求解N阶幻方

由一道数学题的联想
然后根据网上的做法瞎jb乱打了一下，居然对了
代码精心附上了注释，有兴趣的童鞋可以看一看。。
不说了，上代码！(自认为结构很清晰易懂)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171

#include <cstdlib> #include <cmath> #include <cstdio> #define MAXN 10000 using namespace std; int matrix[MAXN][MAXN] = { 0 }; void (int n) { int x = 0, y, mun = 1; y = n / 2; while (mun <= n * n) { matrix[x][y] = mun; //通过x0、y0检测右上的是否已经填入数字 int x0 = x; int y0 = y; x0--; y0++; //超界处理 if (x0 < 0) x0 += n; if (y0 == n) y0 = n - y0; if (!matrix[x0][y0]) { x = x0; y = y0; } else { //若有数字填入之前数字的下方 x++; if (x == n) x = 0; } mun++; } } //生成双偶幻方 void CreateDoubleEvenMagicSqure(int n) { int num = 1; //从1到n的平方依次赋值 for (int i = 0; i<n; i++) for (int j = 0; j<n; j++) matrix[i][j] = num++; //小正方形的对角线上的数字取其补数 for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) { if (i % 4 == 0 && 大专栏  C++求解N阶幻方an class="built_in">abs(i - j) % 4 == 0) for (int k = 0; k<4; k++) matrix[i + k][j + k] = abs(n * n + 1 - matrix[i + k][j + k]); else if (i % 4 == 3 && (i + j) % 4 == 3) for (int k = 0; k<4; k++) matrix[i - k][j + k] = abs(n * n + 1 - matrix[i - k][j + k]); } } //生成单偶幻方 void CreateSingleEvenMagicSqure(int n) { int k = n / 2; CreateOddMagicSquare(k); //赋初值，左上最小，右下其次，右上再次，左下最大 for (int i = 0; i < k; i++) for (int j = 0; j < k; j++) { matrix[i + k][j + k] = matrix[i][j] + k * k; matrix[i][j + k] = matrix[i][j] + k * k * 2; matrix[i + k][j] = matrix[i][j] + k * k * 3; } //公式 n=4m+2 int m = (n - 2) / 4; //交换x方向正中行的从左至右m-1个 for (int i = 0; i<m - 1; i++) { int buf = matrix[k / 2][i]; matrix[k / 2][i] = matrix[k / 2 + k][i]; matrix[k / 2 + k][i] = buf; } int buf = matrix[k / 2][k / 2]; //以及正中间的数 matrix[k / 2][k / 2] = matrix[k / 2 + k][k / 2]; matrix[k / 2 + k][k / 2] = buf; //交换除x正中间行的其他行对应数字m个 for (register int i = 0; i<k; i++) for (register int j = 0; j<k / 2; j++) { if (i != k / 2) { int buf = matrix[i][j]; matrix[i][j] = matrix[i + k][j]; matrix[i + k][j] = buf; } } //交换最右边m-1个数字 for (register int i = 0; i < k; i++) for (register int j = n - 1; j > n - 1 - (m - 1); j--) swap(matrix[i][j], matrix[i + k][j]); } bool Check(int n) { int sum = (n*(n*n + 1)) / 2; int SumA = 0, SumB = 0; for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) SumA += matrix[i][j]; if (SumA != sum) return false; SumA = 0; } for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) SumA += matrix[j][i]; if (SumA != sum) return false; SumA = 0; } for (int i = 0; i<n; i++) { SumA += matrix[i][i]; SumB += matrix[i][n - i - 1]; } if (SumA != sum || SumB != sum) return false; return true; } int main() { int n; cin >> n; if (n % 2 != 0) CreateOddMagicSquare(n); else if (n % 4 == 0) CreateDoubleEvenMagicSqure(n); else if (n % 2 == 0) CreateSingleEvenMagicSqure(n); for (int i = 0; i<n; i++) { for (int j = 0; j<n; j++) cout << matrix[i][j] << "t"; cout << endl; } if (!Check(n)) cout << "Failed to generate!" << endl; getchar(), getchar(); return 0; }