Submission #1265180

#	Time	Username	Problem	Language	Result	Execution time	Memory
1265180		andyo	Commuter Pass (JOI18_commuter_pass)	C++20	31 / 100	334 ms	33928 KiB

commuter_pass

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

typedef long long ll;
typedef pair<ll, int> pli;

const ll INF = 1e18;

int main() {
    int n, m;
    cin >> n >> m;
    
    int s, t, u, v;
    cin >> s >> t;
    cin >> u >> v;
    
    // Store graph edges
    vector<vector<pair<int, ll>>> graph(n + 1);
    vector<tuple<int, int, ll>> railways(m);
    
    for (int i = 0; i < m; i++) {
        int a, b;
        ll c;
        cin >> a >> b >> c;
        
        railways[i] = {a, b, c};
        graph[a].push_back({b, c});
        graph[b].push_back({a, c});
    }
    
    // Dijkstra function to compute shortest distances
    auto dijkstra = [&](int start, vector<ll>& dist) {
        dist.assign(n + 1, INF);
        dist[start] = 0;
        priority_queue<pli, vector<pli>, greater<pli>> pq;
        pq.push({0, start});
        
        while (!pq.empty()) {
            auto [d, node] = pq.top();
            pq.pop();
            
            if (d > dist[node]) continue;
            
            for (auto [next, weight] : graph[node]) {
                if (dist[node] + weight < dist[next]) {
                    dist[next] = dist[node] + weight;
                    pq.push({dist[next], next});
                }
            }
        }
    };
    
    // Compute distances from S to all nodes
    vector<ll> dist_from_s(n + 1);
    dijkstra(s, dist_from_s);
    
    // Compute distances from all nodes to T
    vector<ll> dist_to_t(n + 1);
    dijkstra(t, dist_to_t);
    
    // Find shortest path distance from S to T
    ll min_st_dist = dist_from_s[t];
    
    // Create a new graph where railways on min-cost S-T paths have cost 0
    vector<vector<pair<int, ll>>> modified_graph(n + 1);
    
    for (auto [a, b, c] : railways) {
        // Check if this railway is on some minimum cost path from S to T
        bool on_min_path = (dist_from_s[a] + c + dist_to_t[b] == min_st_dist) ||
                           (dist_from_s[b] + c + dist_to_t[a] == min_st_dist);
        
        // If on minimum path, cost is 0; otherwise, original cost
        ll new_cost = on_min_path ? 0 : c;
        
        modified_graph[a].push_back({b, new_cost});
        modified_graph[b].push_back({a, new_cost});
    }
    
    // Find shortest path from U to V in the modified graph
    vector<ll> dist_from_u(n + 1, INF);
    dist_from_u[u] = 0;
    
    priority_queue<pli, vector<pli>, greater<pli>> pq;
    pq.push({0, u});
    
    while (!pq.empty()) {
        auto [d, node] = pq.top();
        pq.pop();
        
        if (d > dist_from_u[node]) continue;
        
        for (auto [next, weight] : modified_graph[node]) {
            if (dist_from_u[node] + weight < dist_from_u[next]) {
                dist_from_u[next] = dist_from_u[node] + weight;
                pq.push({dist_from_u[next], next});
            }
        }
    }
    
    // Output the minimum cost from U to V
    cout << dist_from_u[v] << endl;
    
    return 0;
}

• Subtask 1: 16 / 16
• Subtask 2: 15 / 15
• Subtask 3: 0 / 24
• Subtask 4: 0 / 45