1030 Travel Plan（dijsktra + dfs/bfs + 回溯）

 题面意思比较清晰，就是优先最短路，同距离取最小花费。

#include<bits/stdc++.h>
using namespace std;
int n, m, s, d;
typedef pair<int, int> pii;
vector<pii> graph[505];
set<pii> min_heap;
int cost[505][505] = {0};
vector<bool> visited(505, false);
vector<bool> dfs_visited(505, false);
vector<int> dist(505,0x3f3f3f);
vector<int> prefix[505]; //记录前结点的队列
vector<int> result; //记录最终路径
int minimum = 0x3f3f3f; //记录最小花费

void dijkstra(int start) {
    visited[start] = true;
    dist[start] = 0;
    min_heap.insert(make_pair(0,start));
    while(!min_heap.empty()) {
        auto iter = min_heap.begin();
        int root = iter -> second;
        visited[root] = true;
        min_heap.erase(iter);
        for(auto i : graph[root]) {
            int child = i.first;
            int dis = i.second;
            if (!visited[child]) {
                if (dist[child] > dist[root] + dis) {
                    prefix[child].clear();
                    min_heap.erase(make_pair(dist[child], child));
                    dist[child] = dist[root] + dis;
                    min_heap.insert(make_pair(dist[child], child));
                    prefix[child].push_back(root);
                } else if (dist[child] == dist[root] + dis) { //同距离添加到前缀队列中
                    prefix[child].push_back(root);
                }
            }
        }
    }
}
void dfs(int p, int end, int cnt, vector<int> path) {
    dfs_visited[p] = true;
    if (p == end) {
        if (cnt < minimum) {
            result = path;
            minimum = cnt;
        }
        return;
    }

    for (auto i : prefix[p]) {
        if (!dfs_visited[i]) {
            vector<int> temp = path;
            temp.push_back(i);
            dfs(i, end, cnt + cost[p][i], temp);
            dfs_visited[i] = false;
        }
    }
}
int main() {
    cin >> n >> m >> s >> d;
    for (int i = 0; i < m; ++ i) {
        int c1, c2, dis, cos;
        cin >> c1 >> c2 >> dis >> cos;
        graph[c1].push_back(make_pair(c2, dis));
        graph[c2].push_back(make_pair(c1, dis));
        cost[c1][c2] = cos;
        cost[c2][c1] = cos;
    }
    dijkstra(s);
    vector<int> temp;
    temp.push_back(d);
    dfs(d, s, 0, temp); //由于记录的是前结点，遍历时从目的到起点
    reverse(result.begin(),result.end()); //反转一下路径
    for (auto i : result) {
        cout << i << " ";
    }
    cout << dist[d] << " " << minimum;
}