C++에서 Prim의 알고리즘을 사용하는 방법

#include<iostream>
#include<queue>
#include<vector>
#include<algorithm>
using namespace std;

const int MAX = 100;
const int INF = 9999;

vector<vector<int>> graph(MAX, vector<int>(MAX, INF));

void prim(int start, int n)
{
    vector<int> key(n, INF);  // 存储每个顶点到最小生成树的最小权重
    vector<bool> visited(n, false);  // 标记顶点是否已经加入最小生成树
    priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> pq;  // 优先队列，按权重升序排列

    key[start] = 0;  // 起始顶点到自身的权重置为0
    pq.push(make_pair(0, start));

    while (!pq.empty())
    {
        int u = pq.top().second;
        pq.pop();

        visited[u] = true;

        for (int v = 0; v < n; v++)
        {
            if (graph[u][v] != INF && !visited[v] && graph[u][v] < key[v])
            {
                key[v] = graph[u][v];
                pq.push(make_pair(graph[u][v], v));
            }
        }
    }

    // 输出最小生成树的边
    for (int i = 1; i < n; i++)
    {
        cout << "Edge: " << i << " - " << key[i] << endl;
    }
}

int main()
{
    int n, e;
    cout << "Enter the number of vertices: ";
    cin >> n;
    cout << "Enter the number of edges: ";
    cin >> e;

    cout << "Enter the edges and weights: " << endl;
    int u, v, w;
    for (int i = 0; i < e; i++)
    {
        cin >> u >> v >> w;
        graph[u][v] = w;
        graph[v][u] = w;
    }

    int start;
    cout << "Enter the starting vertex: ";
    cin >> start;

    cout << "Minimum Spanning Tree edges: " << endl;
    prim(start, n);

    return 0;
}