输入一个二元关系的关系矩阵,计算它的自反闭包,对称闭包,和传递闭包的代码用C++怎么写
时间: 2024-03-17 13:43:09 浏览: 11
以下是用 C++ 实现计算自反闭包、对称闭包和传递闭包的代码示例:
```c++
#include <iostream>
#include <vector>
using namespace std;
// 计算自反闭包
vector<vector<int>> reflexive_closure(vector<vector<int>> relation_matrix) {
int n = relation_matrix.size();
vector<vector<int>> reflexive(n, vector<int>(n, 0));
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
reflexive[i][j] = relation_matrix[i][j] || (i == j);
}
}
return reflexive;
}
// 计算对称闭包
vector<vector<int>> symmetric_closure(vector<vector<int>> relation_matrix) {
int n = relation_matrix.size();
vector<vector<int>> symmetric(n, vector<int>(n, 0));
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
symmetric[i][j] = relation_matrix[i][j] || relation_matrix[j][i];
}
}
return symmetric;
}
// 计算传递闭包
vector<vector<int>> transitive_closure(vector<vector<int>> relation_matrix) {
int n = relation_matrix.size();
vector<vector<int>> transitive(relation_matrix);
for (int k = 0; k < n; k++) {
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
transitive[i][j] = transitive[i][j] || (transitive[i][k] && transitive[k][j]);
}
}
}
return transitive;
}
// 测试
int main() {
vector<vector<int>> relation_matrix = {{0, 1, 0}, {1, 0, 1}, {0, 1, 0}};
vector<vector<int>> reflexive = reflexive_closure(relation_matrix);
cout << "自反闭包:" << endl;
for (auto row : reflexive) {
for (auto elem : row) {
cout << elem << " ";
}
cout << endl;
}
vector<vector<int>> symmetric = symmetric_closure(relation_matrix);
cout << "对称闭包:" << endl;
for (auto row : symmetric) {
for (auto elem : row) {
cout << elem << " ";
}
cout << endl;
}
vector<vector<int>> transitive = transitive_closure(relation_matrix);
cout << "传递闭包:" << endl;
for (auto row : transitive) {
for (auto elem : row) {
cout << elem << " ";
}
cout << endl;
}
return 0;
}
```
其中,`relation_matrix` 为输入的二元关系的关系矩阵,`reflexive`、`symmetric` 和 `transitive` 分别为计算得到的自反闭包、对称闭包和传递闭包。使用 C++ 中的二维 vector 来表示矩阵。计算传递闭包的部分使用了 Floyd-Warshall 算法,时间复杂度为 O(n^3)。