Prim算法

Prim算法，适用于密集的结构

#include <iostream>
#include <vector>
#include <climits>

using namespace std;

void primMST(const vector<vector<int>> &graph) {
    int vertices = graph.size();
    vector<int> key(vertices, INT_MAX); // 每个顶点的最小权值
    vector<bool> inMST(vertices, false); // 是否包含在MST中
    vector<int> parent(vertices, -1); // 最小生成树的父节点

    key[0] = 0; // 从第一个顶点开始

    for (int count = 0; count < vertices - 1; ++count) {
        int u = -1, minKey = INT_MAX;

        // 找到未包含在MST中且key值最小的顶点
        for (int v = 0; v < vertices; ++v) {
            if (!inMST[v] && key[v] < minKey) {
                minKey = key[v];
                u = v;
            }
        }

        inMST[u] = true; // 将该顶点加入MST

        // 更新与u相邻的顶点的key值
        for (int v = 0; v < vertices; ++v) {
            if (graph[u][v] && !inMST[v] && graph[u][v] < key[v]) {
                key[v] = graph[u][v];
                parent[v] = u;
            }
        }
    }

    // 输出MST
    cout << "Edge \tWeight" << endl;
    for (int i = 1; i < vertices; ++i) {
        cout << parent[i] << " - " << i << "\t" << graph[i][parent[i]] << endl;
    }
}

int main() {
    vector<vector<int>> graph = {
        {0, 2, 0, 6, 0},
        {2, 0, 3, 8, 5},
        {0, 3, 0, 0, 7},
        {6, 8, 0, 0, 9},
        {0, 5, 7, 9, 0}
    };

    cout << "Prim's Minimum Spanning Tree:" << endl;
    primMST(graph);

    return 0;
}