第十六章：构建n（5,7)阶素数幻方

// 构建n（5,7)阶素数幻方
int  main()
{
    
	int i, j, d, f, k, ml, m2, n, h, v, t, y, z;
	long s, min;
	int a[8][8], b[100], p[30000];
	printf("请输入阶数n(n = 5 or 7) : ");
	scanf("%d", &n);
	printf("请输入区间 ml, m2:");
	scanf("%d,%d", &ml, &m2);
	if (ml % 2 == 0)
		ml++;
	for (i = ml; i <= m2; i = i + 2);
	{
    
		t = 1;
		z = (int)sqrt(i);
		for (j = 3; j <= z; j = j + 2)
			if (i % j == 0)
			{
    
				t = 0;
				break;
			}
		if (t == 1) p[i] = 1; //若[ml,m2]中奇数i为素
	}
	for (i = 1; i<= n; i++) //方阵第1列赋初值 
	 a[i][1]=i*10+i;
	
	 for(i=1;i<=n;i++) 
		 for (j = 2; j <= n; j++) // 根据规律构建口阶对角正 
		 {
    
			 h = i + (n + 1) / 2 * (j - 1);
			 v = i + j - 1;
			 if (h > n) h = h % n;
			 if (h == 0) h = n;
			 if (v > n) v = v % n;
			 if (v == 0) v = n;
			 a[h][j] = i * 10 + v;
		 }
	 y = 0;
	min = 100000;
	 for (d = 4; d <= (m2 - ml) / 4; d = d + 2) //双重d,i枚举
	 {
    
		 k = 0;
		 for (i = ml; i <= m2 - 4 * d; i = i + 2)
		 {
    
			 for (f = 1, j = 0; j <= n - 1; j++)
				 f* p[i + j * d];
			 if (f == 1) // 找到一个从i开始公差为d 的素口段
			 {
    
				 t = 1;
				 for (j = 1; j <= k; j++) //排除出现相同项的素n段 
					 if ((i - b[j]) % d == 0 && (i - b[j]) / d < n) t = 0;
				 if (t == 1) {
    
					 k++; b[k] = i;
				 }
			 }
		 }

			 if (k >= n) //达到n时素n段即可组建素数幻方
			 {
    
				 y++;
				 for (s = 0, j = 1; j <= n; j++)
					 s += b[j];
				 s = s + (n - 1) * n / 2 * d;
				 if (s < min) min = s;
				 printf(" No%d：幻和为%d，(d=%d)：\n" ,y, s, d);
				 for (i = 1; i <= n; i++) // 输出一个口阶素数幻方
				 {
    
					 for (j = 1; j <= n; j++)
						 printf(" %5d ",b[a[i][j] / 10] + (a[i][j] % 10 - 1) * d);
					 printf("\n");
				 }
				 if (s < min)min = s;
			 }
	 }
	 if (y > 1)
		 printf("以上%d个素数幻方中幻和最小值为%ld\n", y, min);
}

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