【离散数学实验】相容关系的极大相容类的计算

相容关系的极大相容类的计算.cpp

运行环境VisualStudio2013及以上版本

//=============================================================================//    离散数学实验（3）_相容关系的极大相容类的计算//          2015/11/09       ZkP//=============================================================================#include<iostream>#include<vector>#include<sstream>//基于字符串的流#include <stdlib.h> using namespace std;//=============================================================================void InputA(vector<int> &A,int &num){ cout << "请输入集合A的元素个数num：" << endl; cin >> num; cout << "请输入集合A的元素：" << endl; for (int i = 0; i < num; i++)  A.push_back(getchar());}void Inputmat(vector<vector<int>> &mat,int num){ cout << "请输入关系矩阵：" << endl; for (int i = 0; i < num; i++)  for (int j = 0; j < num; j++)  {   vector<int>temp(1);   cin >> temp[0];   mat.push_back(temp);  }}//Inputmat//=============================================================================void DeleteRepeat(vector<vector < int > > &mat)//删除集类中的重复元素{ int i, j, k, l, m, n, o; for (i = 0; i < mat.size(); i++) {  for (j = 0; j < mat[i].size(); j++)  {   for (k = 0; k < mat.size(); k++)   {    for (l = 0; l < mat[k].size(); l++)    {     if (i >= mat.size() || k >= mat.size())      break;     if (i != k&&mat[i][j] == mat[k][l])     {      vector<int> v1(10), v2(10);      v1 = mat[i];      v2 = mat[k];      int count = 0;      for (m = 0; m < v1.size(); m++)       for (n = 0; n < v2.size(); n++)        if (v1[m] == v2[n])        {         count++;         break;        }      if (count == v1.size())//若v2是v1的子集      {       for (o = i; o < mat.size() - 1; o++)        mat[o] = mat[o + 1];       mat.pop_back();      }      else if (count == v2.size())//若v1是v2的子集      {       for (o = k; o < mat.size() - 1; o++)        mat[o] = mat[o + 1];       mat.pop_back();      }     }     if (k >= mat.size())      break;    }   }   if (i >= mat.size())    break;  } }}//DeleteRepeat//=============================================================================void MaximalCompatibleClass(vector<int> A, vector<vector<int>> mat)//求相容类的极大相容类{ vector< vector< int>> mat1; int size_A = A.size(); int i, j, k, m; for (i = 0; i < size_A; i++)//①； {  vector<int> temp1(1);  temp1[0] = A[i];  mat1.push_back(temp1); } for (i = size_A - 2; i > -1; i--)//②③ {  int count = 0;  vector<int> temp2(10);  for (j = size_A - 1; j > i; j--)//④   if (mat[j][i] == 1)   {    temp2[count] = A[j];    count++;   }  if (count != 0)//⑤  {   int size_mat1 = mat1.size();   for (j = 0; j < size_mat1; j++)   {    vector<int> v3(10);    int num = 0;    for (k = 0; k < mat1[j].size(); k++)     for (m = 0; m < count; m++)      if (mat1[j][k] == temp2[m])      {       v3[num] = temp2[m];       num++;       break;      }    if (num != 0)    {     v3[num] = A[i];     while (num < 9)     {      v3.pop_back();      num++;     }     mat1.push_back(v3);    }   }   DeleteRepeat(mat1);//⑥  } } cout << "所有极大相容类有：" << endl; for (i = 0; i < mat1.size(); i++)//输出R中所有的极大相容类 {  cout << "{";  for (j = 0; j < mat1[i].size(); j++)  {   cout << mat1[i][j];   if (j < mat1[i].size() - 1)    cout << ",";  }  cout << "}" << endl; }}//MaximalCompatibleClass//=============================================================================int Reflexivity(vector<vector<int>> mat)//判断关系R是否具有自反性{ int r = 1; for (int i = 0; i < mat.size(); i++)  for (int j = 0; j < mat[i].size(); j++)   if (i == j&&mat[i][j] != 1)   {    r = 0;    return r;   } return r;}//Reflexivity//=============================================================================int Symmetry(vector<vector<int>> mat)//判断关系R是否具有对称性{ int s = 1; for (int i = 0; i < mat.size(); i++)  for (int j = 0; j < mat[i].size(); j++)   if (i != j&&mat[i][j] != mat[j][i])   {    s = 0;    return s;   } return s;}//Symmetry//=============================================================================void PrintA(vector<int> A){ cout << "集合A的元素为：" << endl; for (int i = 0; i < A.size(); i++)  cout << A[i] << " "; cout << endl;}//PrintA//=============================================================================void PrintMat(vector<vector<int>> mat){ cout << "关系矩阵为：" << endl; for (int i = 0; i < mat.size(); i++) {  for (int j = 0; j < mat[i].size(); j++)   cout << mat[i][j] << " ";  cout << endl; }}//PrintMat//=============================================================================void main(){ vector<int> A(10); vector<vector<int>> mat; int d; cout << "请输入产生集合A及关系矩阵的方式 1）--键盘输入 2）--系统定义" << endl; cin >> d; switch (d) { case 1: {  int num;  InputA(A,num);  Inputmat(mat,num); } case 2: {  A = { 1, 2, 3, 4, 5, 6 };  mat = { { 1, 1, 1, 0, 0, 0 },           { 1, 1, 1, 1, 1, 0 },          { 1, 1, 1, 1, 0, 0 },          { 0, 1, 1, 1, 1, 0 },    { 0, 1, 0, 1, 1, 0 },    { 0, 0, 0, 0, 0, 1 } }; } }//switch PrintA(A); cout << endl; PrintMat(mat); cout << endl; if (Reflexivity(mat) && Symmetry(mat)) {  cout << "关系R是集合A上的相容关系！" << endl << endl;;  MaximalCompatibleClass(A, mat); } else  cout << "关系R不是集合A上的相容关系！" << endl; cout << endl;}//main//=============================================================================