离散数学：编程实现关系性质的判断

实验内容：编程实现关系性质的判断

提示：

¨用矩阵表示二元关系

¨通过矩阵的特征判断二元关系所具有的性质

¨运用二维数组实现矩阵的输入，然后判断自反性，反自反性，对称性，反对称性，传递性

#include<iostream>
using namespace std;

void main()
{
	int N;
	int ElemNum = 0;
	cout << "请输入矩阵的维数：" << endl;
	cin >> N;

	//根据维数生成矩阵
	int** p = (int**)malloc(N * sizeof(int*));
	for (int i = 0; i < N; i++)
	{
		p[i] = (int*)malloc(N * sizeof(int*));
	}

	//矩阵数据输入
	cout << "请输入矩阵的数据：" << endl;
	for (int i = 0; i < N; i++)
	{
		for (int j = 0; j < N; j++)
		{
			cin >> p[i][j];
			if (p[i][j] == 1)
				ElemNum++;
		}
	}

	//自反性
	cout << "自反性：";
	bool self_reflexivity = true;//默认为自反
	for (int i = 0; i < N; i++)
	{
		if (p[i][i] != 1)//遍历对角线元素，有一个不为1则说明不存在自反
		{
			self_reflexivity = false;
			break;
		}
	}
	if (self_reflexivity == true)
		cout << "具有自反性！" << endl;
	else if (self_reflexivity == false)
		cout << "不具有自反性。" << endl;

	//反自反性
	cout << "反自反性：";
	bool irreflexive = true;//默认具有
	for (int i = 0; i < N; i++)
	{
		if (p[i][i] != 0)//遍历对角线元素，对角线必须全为0说明具有反自反性
		{
			irreflexive = false;
			break;
		}
	}
	if (irreflexive == true)
		cout << "具有反自反性！" << endl;
	else
		cout << "不具有反自反性。" << endl;

	//对称性
	cout << "对称性：";
	bool symmetry = true;
	for (int i = 0; i < N; i++)
	{
		for (int j = 0; j < N; j++)
		{
			if (p[i][j] == 1 && p[i][j] != p[j][i])
			{
				symmetry = false;
			}
		}
	}
	if (symmetry == true)
		cout << "具有对称性！" << endl;
	else
		cout << "不具有对称性。" << endl;

	//反对称性
	cout << "反对称性：";
	bool irsymmetry = true;
	for (int i = 0; i < N; i++)
	{
		for (int j = 0; j <= i; j++)//寻找对角线的一侧
		{
			if (i != j && p[i][j] == 1 && p[i][j] == p[j][i])
			{
				irsymmetry = false;
			}
		}
	}
	if (irsymmetry == true)
		cout << "具有反对称性！" << endl;
	else
		cout << "不具有反对称性。" << endl;

	//传递性
	cout << "传递性：";
	bool delivery = true;
	for (int i = 0; i < N; i++)
	{
		if (ElemNum == 1)//只有一个元素时
			break;
		for (int j = 0; j < N; j++)
		{
			for (int k = 0; k < N; k++)
			{
				if (p[i][j] == 1 && p[j][k] == 1)//具有可传递元素
				{
					if (p[i][k] != 1)
					{
						delivery = false;
					}
				}
			}
		}
	}
	if (delivery == true)
		cout << "具有传递性！" << endl;
	else
		cout << "不具有传递性。" << endl;
}