11111-编程知识

11111

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#include <iostream>
#include <vector>
#include <queue>
#include <algorithm>using namespace std;// 边的结构体
struct Edge {int src, dest, weight;// 按照权重进行排序bool operator<(const Edge& other) const {return weight < other.weight;}
};class Graph {
public:int V; // 顶点数vector<Edge> edges; // 边的集合// 构造函数Graph(int v) : V(v) {}// 添加边void addEdge(int src, int dest, int weight) {Edge edge = {src, dest, weight};edges.push_back(edge);}// Prim算法实现void primMST() {vector<int> key(V, INT_MAX); // 用于存储顶点的键值vector<int> parent(V, -1);   // 用于存储MST中的父节点vector<bool> inMST(V, false); // 用于标记顶点是否在MST中// 从第一个顶点开始key[0] = 0;// 创建最小优先队列priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> pq;pq.push({0, 0}); // {键值, 顶点}while (!pq.empty()) {int u = pq.top().second;pq.pop();inMST[u] = true;// 遍历u的邻居for (const Edge& edge : edges) {int v = (edge.src == u) ? edge.dest : edge.src;int weight = edge.weight;if (!inMST[v] && weight < key[v]) {key[v] = weight;parent[v] = u;pq.push({key[v], v});}}}// 输出MSTcout << "Prim MST:" << endl;for (int i = 1; i < V; ++i)cout << parent[i] << " - " << i << endl;}// Kruskal算法实现void kruskalMST() {// 对边按照权重进行排序sort(edges.begin(), edges.end());vector<int> parent(V, -1); // 用于存储每个集合的父节点// 查找根节点function<int(int)> find = [&](int i) {while (parent[i] != -1)i = parent[i];return i;};// 合并两个集合function<void(int, int)> unionSets = [&](int x, int y) {int rootX = find(x);int rootY = find(y);parent[rootX] = rootY;};// 输出MSTcout << "Kruskal MST:" << endl;for (const Edge& edge : edges) {int rootSrc = find(edge.src);int rootDest = find(edge.dest);// 如果加入这条边不会形成环，则加入MSTif (rootSrc != rootDest) {cout << edge.src << " - " << edge.dest << endl;unionSets(rootSrc, rootDest);}}}// Dijkstra算法实现void dijkstra(int src) {// 创建最小优先队列priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> pq;vector<int> dist(V, INT_MAX); // 用于存储最短路径dist[src] = 0;pq.push({0, src});while (!pq.empty()) {int u = pq.top().second;pq.pop();for (const Edge& edge : edges) {if (edge.src == u) {int v = edge.dest;int weight = edge.weight;// 更新最短路径if (dist[u] != INT_MAX && dist[u] + weight < dist[v]) {dist[v] = dist[u] + weight;pq.push({dist[v], v});}}}}// 输出最短路径cout << "Dijkstra Shortest Paths from vertex " << src << ":" << endl;for (int i = 0; i < V; ++i)cout << "To " << i << ": " << dist[i] << endl;}// Bellman-Ford算法实现void bellmanFord(int src) {vector<int> dist(V, INT_MAX); // 用于存储最短路径dist[src] = 0;// 松弛操作for (int i = 1; i < V; ++i) {for (const Edge& edge : edges) {int u = edge.src;int v = edge.dest;int weight = edge.weight;if (dist[u] != INT_MAX && dist[u] + weight < dist[v]) {dist[v] = dist[u] + weight;}}}// 检测负权环for (const Edge& edge : edges) {int u = edge.src;int v = edge.dest;int weight = edge.weight;if (dist[u] != INT_MAX && dist[u] + weight < dist[v]) {cout << "Graph contains negative weight cycle!" << endl;return;}}// 输出最短路径cout << "Bellman-Ford Shortest Paths from vertex " << src << ":" << endl;for (int i = 0; i < V; ++i)cout << "To " << i << ": " << dist[i] << endl;}// Floyd算法实现void floydWarshall() {vector<vector<int>> dist(V, vector<int>(V, INT_MAX));// 初始化邻接矩阵for (int i = 0; i < V; ++i)dist[i][i] = 0;for (const Edge& edge : edges)dist[edge.src][edge.dest] = edge.weight;// Floyd算法核心for (int k = 0; k < V; ++k) {for (int i = 0; i < V; ++i) {for (int j = 0; j < V; ++j) {if (dist[i][k] != INT_MAX && dist[k][j] != INT_MAX &&dist[i][k] + dist[k][j] < dist[i][j]) {dist[i][j] = dist[i][k] + dist[k][j];}}}}// 输出最短路径cout << "Floyd Shortest Paths:" << endl;for (int i = 0; i < V; ++i) {for (int j = 0; j < V; ++j) {cout << dist[i][j] << "\t";}cout << endl;}}
};int main() {Graph g(6);// 添加边g.addEdge(0, 1, 4);g.addEdge(0, 2, 3);g.addEdge(1, 2, 1);g.addEdge(1, 3, 2);g.addEdge(2, 3, 4);g.addEdge(3, 4, 2);g.addEdge(4, 5, 6);// 执行算法g.primMST();g.kruskalMST();g.dijkstra(0);g.bellmanFord(0);g.floydWarshall();return 0;
}