oj.uz

Submission #159918

# Submission time Handle Problem Language Result Execution time Memory
159918 2019-10-25T12:02:05 Z XCoder Commuter Pass (JOI18_commuter_pass) C++14
100 / 100
 753 ms 21768 KB 
#include <bits/stdc++.h>

#define FOR(i,s,e) for(int i=(s);i<(int)(e);i++)
#define FOE(i,s,e) for(int i=(s);i<=(int)(e);i++)
#define REP(i,n)   FOR(i,0,n)
#define ALL(x) (x).begin(), (x).end()
#define CLR(s) memset(s,0,sizeof(s))
#define PB push_back
#define ITER(v) __typeof((v).begin())
#define FOREACH(i,v) for(ITER(v) i=(v).begin();i!=(v).end();i++)

#define x first
#define y second

using namespace std;

typedef long long LL;
typedef pair<int,int> pii;
typedef pair<LL, LL> pll;
typedef map<int,int> mii;
typedef vector<int> vi;

const LL INF = 1LL << 60;
using Graph = vector<vector<pii>>;
using Dist = vector<LL>;
using Node = tuple<LL, int>;  // <cost, node_id>

int N, M, S, T, U, V;
Graph G;

Dist compute_shortest_path(Graph &G, vector<int> src_nodes, int N) {
    Dist D(N + 1, INF);
    priority_queue<Node, vector<Node>, greater<Node>> pq;

    for (auto &src : src_nodes) {
        D[src] = 0LL;
        pq.push({D[src], src});
    }

    while (!pq.empty()) {
        LL cur;
        int x;
        tie(cur, x) = pq.top();
        pq.pop();

        if (D[x] > cur) continue;

        for (auto &it : G[x]) {
            LL cost;
            int y;
            tie(y, cost) = it;
            if (cur + cost < D[y]) {
                D[y] = cur + cost;    
                pq.push({D[y], y});
            }
        }
    }
    return D;
}


Dist S_dist, T_dist, U_dist, V_dist;
LL ST_shortest_path_cost;
Graph G_ST; // edges consisting of edges used in any shortest paths


LL dfs(Graph &G, int x, LL u_min_dist, LL v_min_dist) {
    // x : current node
    // DFS - traverse all possible shortest paths

    LL ans = INF;
    // u -> some nodes visited -> x -> v
    u_min_dist = min(u_min_dist, U_dist[x]);
    ans = min(ans, u_min_dist + V_dist[x]);

    // v -> some nodes visited -> x -> u
    v_min_dist = min(v_min_dist, V_dist[x]);
    ans = min(ans, v_min_dist + U_dist[x]);

    for (auto &edge : G[x]) {
        int y = edge.first;
        // S -> x -> y -> T is a possible S-T shortest path
        //cout << x << "->" << y << endl;
        ans = min(ans, dfs(G, y, u_min_dist, v_min_dist));
    }
    return ans;
}


void dfs_2(int x, Dist &u_min_dist, Dist &U_dist) {
    // Already tried
    if (u_min_dist[x] != INF) return;

    // DFS - traverse all possible shortest paths
    // x : current node
    // V ~~> some node visited before -> x ~~> U

    u_min_dist[x] = U_dist[x];
    for (auto &edge : G_ST[x]) {
        // S -> x -> y -> T is a possible S-T shortest path
        //cout << x << "->" << y << endl;
        int y = edge.first;
        dfs_2(y, u_min_dist, U_dist);
        u_min_dist[x] = min(u_min_dist[x], u_min_dist[y]);
    }
}


LL solve() {
    Dist u_min_dist(N + 1, INF);
    Dist v_min_dist(N + 1, INF);

    dfs_2(S, u_min_dist, U_dist);
    dfs_2(S, v_min_dist, V_dist);

    LL ans = INF;
    FOE(x, 1, N) {
        ans = min(ans, u_min_dist[x] + V_dist[x]);
        ans = min(ans, v_min_dist[x] + U_dist[x]);
    }
    return ans;
}


int main() {
    int A, B, C;
    cin >> N >> M >> S >> T >> U >> V;

    G.resize(N + 1);
    FOR(_, 0, M) {
        cin >> A >> B >> C;
        G[A].PB({B, C});
        G[B].PB({A, C});
    }

    S_dist = compute_shortest_path(G, {S}, N);
    T_dist = compute_shortest_path(G, {T}, N);
    U_dist = compute_shortest_path(G, {U}, N);
    V_dist = compute_shortest_path(G, {V}, N);
    //cout << src_dist[T] << " " << dst_dist[S] << endl;

    ST_shortest_path_cost = S_dist[T];
    assert (S_dist[T] == T_dist[S]);

    // Case 1: Travel U -> some nodes along a shortest path -> V
    G_ST.resize(N + 1);
    FOE(x, 1, N) {
        for (auto &edge : G[x]) {
            int y, cost;
            tie(y, cost) = edge;
            if (S_dist[x] + cost + T_dist[y] == ST_shortest_path_cost) {
                G_ST[x].PB(edge);
            } 
        }
    }

    LL ans = solve();
    //cout << ans << endl;

    // Case 2: Travel U -> V via direct shortest path
    ans = min(ans, U_dist[V]);

    cout << ans << endl;

    return 0;
}

Subtask #1
16.0 / 16.0

# Verdict Execution time Memory Grader output
1 Correct 669 ms 16116 KB Output is correct
2 Correct 684 ms 16604 KB Output is correct
3 Correct 722 ms 21668 KB Output is correct
4 Correct 654 ms 15908 KB Output is correct
5 Correct 655 ms 17172 KB Output is correct
6 Correct 688 ms 16124 KB Output is correct
7 Correct 667 ms 17672 KB Output is correct
8 Correct 655 ms 17404 KB Output is correct
9 Correct 701 ms 16144 KB Output is correct
10 Correct 622 ms 15948 KB Output is correct
11 Correct 294 ms 16816 KB Output is correct
12 Correct 697 ms 16072 KB Output is correct

Subtask #2
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 679 ms 18120 KB Output is correct
2 Correct 689 ms 18692 KB Output is correct
3 Correct 713 ms 18116 KB Output is correct
4 Correct 709 ms 18400 KB Output is correct
5 Correct 713 ms 19068 KB Output is correct
6 Correct 695 ms 21164 KB Output is correct
7 Correct 744 ms 21768 KB Output is correct
8 Correct 739 ms 18520 KB Output is correct
9 Correct 732 ms 19116 KB Output is correct
10 Correct 753 ms 18188 KB Output is correct
11 Correct 332 ms 18756 KB Output is correct
12 Correct 736 ms 21452 KB Output is correct

Subtask #3
24.0 / 24.0

# Verdict Execution time Memory Grader output
1 Correct 38 ms 1016 KB Output is correct
2 Correct 3 ms 376 KB Output is correct
3 Correct 3 ms 376 KB Output is correct
4 Correct 70 ms 1672 KB Output is correct
5 Correct 36 ms 1016 KB Output is correct
6 Correct 4 ms 376 KB Output is correct
7 Correct 6 ms 376 KB Output is correct
8 Correct 8 ms 504 KB Output is correct
9 Correct 5 ms 376 KB Output is correct
10 Correct 35 ms 1016 KB Output is correct
11 Correct 3 ms 376 KB Output is correct
12 Correct 3 ms 376 KB Output is correct
13 Correct 3 ms 376 KB Output is correct
14 Correct 4 ms 376 KB Output is correct
15 Correct 4 ms 376 KB Output is correct

Subtask #4
45.0 / 45.0

# Verdict Execution time Memory Grader output
1 Correct 669 ms 16116 KB Output is correct
2 Correct 684 ms 16604 KB Output is correct
3 Correct 722 ms 21668 KB Output is correct
4 Correct 654 ms 15908 KB Output is correct
5 Correct 655 ms 17172 KB Output is correct
6 Correct 688 ms 16124 KB Output is correct
7 Correct 667 ms 17672 KB Output is correct
8 Correct 655 ms 17404 KB Output is correct
9 Correct 701 ms 16144 KB Output is correct
10 Correct 622 ms 15948 KB Output is correct
11 Correct 294 ms 16816 KB Output is correct
12 Correct 697 ms 16072 KB Output is correct
13 Correct 679 ms 18120 KB Output is correct
14 Correct 689 ms 18692 KB Output is correct
15 Correct 713 ms 18116 KB Output is correct
16 Correct 709 ms 18400 KB Output is correct
17 Correct 713 ms 19068 KB Output is correct
18 Correct 695 ms 21164 KB Output is correct
19 Correct 744 ms 21768 KB Output is correct
20 Correct 739 ms 18520 KB Output is correct
21 Correct 732 ms 19116 KB Output is correct
22 Correct 753 ms 18188 KB Output is correct
23 Correct 332 ms 18756 KB Output is correct
24 Correct 736 ms 21452 KB Output is correct
25 Correct 38 ms 1016 KB Output is correct
26 Correct 3 ms 376 KB Output is correct
27 Correct 3 ms 376 KB Output is correct
28 Correct 70 ms 1672 KB Output is correct
29 Correct 36 ms 1016 KB Output is correct
30 Correct 4 ms 376 KB Output is correct
31 Correct 6 ms 376 KB Output is correct
32 Correct 8 ms 504 KB Output is correct
33 Correct 5 ms 376 KB Output is correct
34 Correct 35 ms 1016 KB Output is correct
35 Correct 3 ms 376 KB Output is correct
36 Correct 3 ms 376 KB Output is correct
37 Correct 3 ms 376 KB Output is correct
38 Correct 4 ms 376 KB Output is correct
39 Correct 4 ms 376 KB Output is correct
40 Correct 692 ms 15620 KB Output is correct
41 Correct 720 ms 16008 KB Output is correct
42 Correct 699 ms 16148 KB Output is correct
43 Correct 347 ms 19192 KB Output is correct
44 Correct 343 ms 19228 KB Output is correct
45 Correct 719 ms 19252 KB Output is correct
46 Correct 676 ms 19448 KB Output is correct
47 Correct 659 ms 16068 KB Output is correct
48 Correct 345 ms 17144 KB Output is correct
49 Correct 594 ms 15596 KB Output is correct
50 Correct 666 ms 18432 KB Output is correct
51 Correct 635 ms 19396 KB Output is correct