离散数学-自反性-对称性-传递性，关系的性质

暂时当草稿存放在这里，后面再补充

//分别将自反性、对称性、传递性的编号为Func1、Func2,Func3。
#include <iostream>
#include <cstring>
#include <fstream>
using namespace std;

const int LEN = 140 + 10;
int arr[LEN][2+10];      //存储集合元素
int relation[LEN][LEN];  //关系矩阵
int nnn; //集合元素个数
int num; //集合关系个数
void Func1();
void Func2();
void Func3();

int main()
{
 //   freopen("datain.txt", "r", stdin);
    cout << "请输入集合中的元素个数 : " << endl;
    cin >> nnn;
    cout << "请输入集合中的关系个数 : " << endl;
    cin >> num;
    cout << "集合中一共有" << num << "对关系" << "," << num*2 <<"个元素(请以整数形式输入) : " << endl;
    memset(arr, 0, sizeof(arr));   //用数组做参数传递给标准函数memset()，以让其将数组设置成全0：
    memset(relation, 0, sizeof(relation)); //这里不懂得话可以参考https://blog.csdn.net/qq_37796444/article/details/80181632
    int num1, num2;
    for(int i = 1; i <= num; i++)
    {
        cin >> num1 >> num2;
        arr[i][1] = num1;
        arr[i][2] = num2;
        relation[num1][num2] = 1;
    }

    cout << "输出关系矩阵 : " << endl;
    for(int i = 1; i <= nnn; i++)
    {
        for(int j = 1; j <= nnn; j++)
        {
            cout << relation[i][j] << "     ";
        }
        cout << endl;
    }
    cout << endl;

    cout << "判断结论 : " << endl;
    //判断是否满足自反性
    Func1();
    //判断是否满足对称性
    Func2();
    //判断是否满足传递性
    Func3();
    return 0;
}

void Func1()   //判断是否满足自反性
{
    bool flag = true;
    for(int i = 1; i <= nnn; i++)
    {
        if(relation[i][i] != 1)
        {
            flag = false;
            break;
        }
    }
    if(flag == true)
    {
        cout << "满足自反性" << endl;
    }
    else
    {
        cout << "不满足自反性" << endl;
    }
}

void Func2()  //判断是否满足对称性
{
    bool flag = true;
    for(int i = 1; i <= nnn; i++)
    {
        for(int j = 1; j <=nnn; j++)
        {
            if(relation[i][j] != relation[j][i])
            {
                flag = false;
            }
        }
    }
    if(flag == true)
    {
        cout << "满足对称性" << endl;
    }
    else
    {
        cout << "不满足对称性" << endl;
    }
}

void Func3()  //判断是否满足传递性
{
    bool flag = true;
    for(int i = 1; i <= num - 1; i++)  //num表示关系个数
    {
        for(int j = 2; j <= num; j++)
        {
            if(arr[i][2] == arr[j][1])   //arr数组表示存储集合元素
            {
                int num1 = arr[i][1], num2 = arr[j][2];
                if(relation[num1][num2] != 1)
                {
                    flag = false;
                    break;
                }
            }
        }
        if(flag == false)
            break;
    }
    if(flag == true)
    {
        cout << "满足传递性" << endl;
    }
    else
    {
        cout << "不满足传递性" << endl;
    }
}