大二（上）离散数学 有补格的判定

#include
#include
#define MAX 50
using namespace std;

int num = 0;  //正整数
int n = 0;
int a[MAX][MAX] = {
      0 };  //关系矩阵
int b[MAX] = {
      0 };       //存1到num中能整除num的数字

int gcd(int x, int y)     //求最大公约数
{
     
	int r;
	if (x < y)
	{
     
		r = x;
		x = y;
		y = r;
	}
	r = 1;
	while (r)
	{
     
		r = x % y;
		x = y;
		y = r;
	}
	return x;
}

int lcm(int x, int y)    //最小公倍数
{
     
	return x * y / gcd(x, y);
}

void calPianXu() //计算偏序集元素
{
     
	for (int i = 1; i < num; i++)    //储存偏序集元素
	{
     
		if (num%i == 0)
		{
     
			b[n++] = i;
		}
	}
   	b[n] = num;
}

void calGuanxi() //计算关系矩阵
{
     
	for (int i = 0; i <= n; i++)
		for (int j = 0; j <= n; j++)
		{
     
			if (b[i] % b[j] == 0)
				a[i][j] = 1;
		}
}

void calGaizhu()     //计算并输出盖住集
{
     
	for (int i = 0; i <= n; i++)
		for (int j = 0; j <= n; j++)
			for (int k = 0; k <= n; k++)
			{
     
				a[k][k] = 0;
				if (a[i][j] && a[j][k])
					a[i][k] = 0;
			}
	a[n][n] = 1;
	cout << "\n盖住集：{ ";
	for (int i = 0; i <= n; i++)  //输出盖住集
		for (int j = 0; j <= n; j++)
		{
     
			if (a[i][j])
				cout << "<" << b[j] << "," << b[i] << "> ";
		}
	cout << "}" << endl << endl;
}

void judge()    //判断是否为补格
{
     
	int flag[MAX] = {
      0 };   //存储是否存在补元
	for (int i = 0; i < n; i++)
	{
     
		for (int j = 0; j < n; j++)
		{
     
			if (gcd(b[i], b[j]) == 1 && lcm(b[i], b[j]) == num)  //最大公约数和最小公倍数
			{
     
				flag[i] = 1;
				printf("%d的补元素是%d；\n", b[i], b[j]);
				break;
			}
		}
	}
	for (int i = 1; i < n; i++)
		if (!flag[i])
		{
     
			cout << "\n不是有补格";
			return;
		}
	cout << "\n是有补格";
}

int main()
{
     
	n = 0;
	cout << "请输入一个正整数：";
	cin >> num;
	calPianXu();
	calGuanxi();
	calGaizhu();
	judge();
	cout << endl;
	return 0;
}