图论09

47. 参加科学大会（第六期模拟笔试）

dijkstra（堆优化版）精讲

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

using namespace std;

class mycomparison {
public:
    bool operator()(const pair<int, int>& lhs, const pair<int, int>& rhs) {
        return lhs.second > rhs.second;
    }
};

struct Edges {
    int to;
    int val;
    Edges(int x, int y): to(x), val(y){}
};

int main() {

    int n, m;
    cin >> n >> m;
    int s, e, v;
    vector<list<Edges>> grid(n + 1);
    for (int i = 0; i < m; i++) {
        cin >> s >> e >> v;
        grid[s].push_back(Edges(e, v));

    }
    priority_queue<pair<int, int>, vector<pair<int, int>>, mycomparison> pq;
   
    int start = 1, end = n;
    vector<int> visited(n + 1, 0);
    vector<int> minDist(n + 1, INT_MAX);
    minDist[start] = 0;
    pq.push(pair<int, int>(start, 0)); 
    while (!pq.empty()) {
        // 1. 第一步，选源点到哪个节点近且该节点未被访问过 （通过优先级队列来实现）
        // <节点， 源点到该节点的距离>
        pair<int, int> cur = pq.top(); pq.pop();

        if (visited[cur.first]) continue;

        // 2. 第二步，该最近节点被标记访问过
        visited[cur.first] = true;

        // 3. 第三步，更新非访问节点到源点的距离（即更新minDist数组）
        for (Edges edge : grid[cur.first]) { // 遍历 cur指向的节点，cur指向的节点为 edge
            // cur指向的节点edge.to，这条边的权值为 edge.val
            if (!visited[edge.to] && minDist[cur.first] + edge.val < minDist[edge.to]) { // 更新minDist
                minDist[edge.to] = minDist[cur.first] + edge.val;
                pq.push(pair<int, int>(edge.to, minDist[edge.to]));
            }
        }

    }
    if (minDist[end] == INT_MAX) cout << -1;
    else {
        cout << minDist[end];
    } 
    return 0;
}

94. 城市间货物运输 I

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

using namespace std;

int main() {
    int n, m;
    cin >> n >> m;
    int s, t, v;
    vector<vector<int>> grid;
    vector<int> minDist(n + 1, INT_MAX);
    for (int i = 0; i < m; i++) {
        cin >> s >> t >> v;
        grid.push_back({s, t, v});
    }
    minDist[1] = 0;
    for (int i = 0; i < n - 1; i++) {
        for (auto &edge: grid) {
            int from = edge[0], to = edge[1], value = edge[2];
            if (minDist[from] != INT_MAX && minDist[to] > minDist[from] + value) {
                minDist[to] = minDist[from] + value;
            }
        }
    }
    if (minDist[n] == INT_MAX) cout << "unconnected";
    else cout << minDist[n];

    return 0;
}