【离散数学】实验二 集合上二元关系性质判定的实现

先打个草稿，今晚看书理解下，明天实现。

内容：

编程实现任意集合上二元关系的性质判定。

要求：

能正确判定任意二元关系的自反性、对称性、传递性、反自反性和反对称性。

代码：

/* * Author  : Tob_yuhong * Function: 集合上二元关系性质判定的实现,能正确判定任意二元关系的自反性、对称性、传递性、反自反性和反对称性。 * 编译环境: Code::Blocks 13.12 *///分别将自反性、对称性、传递性、反自反性和反对称性编号为Func1、Func2,...,一直到Func5。#include <iostream>#include <cstdio>#include <cstdlib>#include <cstring>#include <cmath>#include <cstring>#include <vector>#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();void Func4();void Func5();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 << "请输入集合中的关系元素，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));    memset(relation, 0, sizeof(relation));    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();    //判断是否满足反自反性    Func4();    //判断是否满足反对称性    Func5();    return 0;}void Func1(){    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(){    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(){    bool flag = true;    for(int i = 1; i <= num - 1; i++)    {        for(int j = 2; j <= num; j++)        {            if(arr[i][2] == arr[j][1])            {                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;    }}void Func4(){    bool flag = true;    for(int i = 1; i <= nnn; i++)    {        if(relation[i][i] != 0)        {            flag = false;            break;        }    }    if(flag == true)    {        cout << "满足反自反性" << endl;    }    else    {        cout << "不满足反自反性" << endl;    }}void Func5(){    bool flag = true;    for(int i = 1; i <= nnn - 1; i++)    {        for(int j = i + 1; j <= nnn; j++)        {            if(relation[i][j] == 1 && relation[j][i] == 1 && i != j)            {                flag = false;                break;            }        }    }    if(flag == true)    {        cout << "满足反对称性" << endl;    }    else    {        cout << "不满足反对称性" << endl;    }}

运行结果示意：

测试样例：

/*

4
8
1 1 
1 3 
2 2 
3 3
3 1
3 4
4 3
4 4

*/