c++集合论实验：编程实现关系性质的判断

#include 
using namespace std;
typedef int Func;
int arr[100][2];//集合元素
int matrix[100][100];//二元关系矩阵
int n, m, c;

//1--自反性
Func function1() {
	for (int i = 0; i < m; i++) {
		if (matrix[i][i] != 1) {
			cout << "二元关系不具有自反性。" << endl;
			return 0;
		}
	}
	cout << "二元关系具有自反性。" << endl;
	return 0;
}
//2--反自反性
Func function2() {
	for (int i = 0; i < m; i++) {
		if (matrix[i][i] == 1) {
			cout << "二元关系不具有反自反性。" << endl;
			return 0;
		}
	}
	cout << "二元关系具有反自反性。" << endl;
	return 0;
}
//3--对称性
Func function3() {
	for (int i = 0; i < m; i++) {
		for (int j = i+1;j < m;j++)
		{
			if (matrix[i][j] == 1&& matrix[j][i] != 1) {
				cout << "二元关系不具有对称性。" << endl;
				return 0;
			}
		}
	}
	cout << "二元关系具有对称性。" << endl;
	return 0;
}
//4--反对称性
Func function4() {
	for (int i = 0; i < m; i++) {
		for (int j = i+1; j < m; j++)
		{
			if (matrix[i][j] == 1&&matrix[j][i] ==1) {
				cout << "二元关系不具有反对称性。" << endl;
				return 0;
			}
		}
	}
	cout << "二元关系具有反对称性。" << endl;
	return 0;
}
//5--传递性
Func function5() {
	for (int i = 0; i < m; i++) {
		for (int j = 0; j < m; j++) {
			if (matrix[i][j] == 1) {//找到(i,j)，继续寻找是否存在(j,k),并且判断是否存在(i,k),同时i!=k
				for (int k = 0; k < m; k++) {
					if (k != i && matrix[j][k] == 1 && matrix[i][k] != 1) {
						cout << "二元关系不具有传递性。" << endl;
						return 0;
					}
				}
			}
		}
	}
	cout << "二元关系具有传递性。" << endl;
	return 0;
}
int main()
{
	cout << "请输入集合中元素的个数：" << endl;
	cin >> m;
	cout << "请输入集合中有元素对的个数：" << endl;
	cin >> n;
	cout << "请输入元素关系：（输入格式：元素1【空格】元素2【回车】）" << endl;
	for (int i = 0; i < n; i++) {
		cin >> arr[i][0] >> arr[i][1];
		matrix[arr[i][0]-1][arr[i][1]-1] = 1;
	}
	cout << "二元关系的矩阵表示为：" << endl;
	for (int i = 0; i < m; i++) {
		for (int j = 0; j < m; j++) {
			cout << matrix[i][j] << " ";
		}
		cout << endl;
	}
	cout << endl;
	cout << "1--判断自反性" << endl;
	cout << "2--判断反自反性" << endl;
	cout << "3--判断对称性" << endl;
	cout << "4--判断反对称性" << endl;
	cout << "5--判断传递性" << endl;
	cout << "quit--输入其他数字退出" << endl;
	cout << "请选择功能:" << endl;
	cin >> c;
	while (c <= 5 && c >= 1) {
		switch (c)
		{
		case 1:
			function1();
			break;
		case 2:
			function2();
			break;
		case 3:
			function3();
			break;
		case 4:
			function4();
			break;
		case 5:
			function5();
			break;
		default:
			break;
		}
		cout << "请输入选项：" << endl;
		cin >> c;
	}
	cout << "Bye~" << endl;
}