dijkstra算法c++代码实现

Dijkstra算法是一种用于解决单源最短路径问题的经典算法。下面是Dijkstra算法的C++代码实现：

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

using namespace std;

// 定义图的邻接表表示
typedef pair<int, int> pii;
typedef vector<vector<pii>> Graph;

// Dijkstra算法实现
vector<int> dijkstra(const Graph& graph, int start) {
    int n = graph.size();
    vector<int> dist(n, INT_MAX);  // 存储起点到各个顶点的最短距离
    vector<bool> visited(n, false);  // 记录顶点是否已访问
    priority_queue<pii, vector<pii>, greater<pii>> pq;  // 小顶堆，存储顶点和距离的pair

    dist[start] = 0;  // 起点到自身的距离为0
    pq.push(make_pair(0, start));

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

        if (visited[u]) {
            continue;
        }
        visited[u] = true;

        for (const auto& neighbor : graph[u]) {
            int v = neighbor.first;
            int weight = neighbor.second;

            if (dist[u] + weight < dist[v]) {
                dist[v] = dist[u] + weight;
                pq.push(make_pair(dist[v], v));
            }
        }
    }

    return dist;
}

int main() {
    int n, m;  // n为顶点数，m为边数
    cin >> n >> m;

    Graph graph(n);

    for (int i = 0; i < m; ++i) {
        int u, v, weight;
        cin >> u >> v >> weight;
        graph[u].push_back(make_pair(v, weight));
        graph[v].push_back(make_pair(u, weight));
    }

    int start;
    cin >> start;

    vector<int> shortestDist = dijkstra(graph, start);

    for (int i = 0; i < n; ++i) {
        cout << "Shortest distance from " << start << " to " << i << " is " << shortestDist[i] << endl;
    }

    return 0;
}