oj.uz

Submission #719080

# Submission time Handle Problem Language Result Execution time Memory
719080 2023-04-05T10:10:43 Z Cyanmond Aesthetic (NOI20_aesthetic) C++17
100 / 100
 640 ms 96676 KB 
#include <bits/stdc++.h>

using i64 = long long;
constexpr i64 inf64 = 1ll << 60;

struct Edge {
    int to;
    i64 cost;
    int id;
};

void solve() {
    int N, M;
    std::cin >> N >> M;
    std::vector<int> A(M), B(M);
    std::vector<i64> W(M);
    std::vector<std::vector<Edge>> graph(N);
    for (int i = 0; i < M; ++i) {
        std::cin >> A[i] >> B[i] >> W[i];
        --A[i], --B[i];
        graph[A[i]].push_back({B[i], W[i], i});
        graph[B[i]].push_back({A[i], W[i], i});
    }
    std::vector<i64> C(M);
    for (int i = M - 2; i >= 0; --i) {
        C[i] = W[i + 1];
        C[i] = std::max(C[i], C[i + 1]);
    }

    auto calcMinDist = [&](const int f) {
        std::vector<i64> dist(N, inf64);
        std::priority_queue<std::pair<i64, int>, std::vector<std::pair<i64, int>>, std::greater<std::pair<i64, int>>> pq;
        dist[f] = 0;
        pq.push({0, f});
        while (not pq.empty()) {
            const auto [nowDist, v] = pq.top();
            pq.pop();
            if (nowDist > dist[v]) continue;
            for (const auto &[t, cost, id] : graph[v]) {
                const auto newDist = nowDist + cost;
                if (newDist < dist[t]) {
                    dist[t] = newDist;
                    pq.push({newDist, t});
                }
            }
        }
        return dist;
    };
    const auto dist1 = calcMinDist(0), dist2 = calcMinDist(N - 1);
    const auto minDist = dist1[N - 1];

    std::vector<int> edgeType(M);
    std::vector<std::vector<Edge>> sGraph(N);
    for (int i = 0; i < M; ++i) {
        if (dist1[A[i]] > dist1[B[i]]) std::swap(A[i], B[i]);
        const auto x = dist1[A[i]], y = dist2[B[i]];
        if (x + y + W[i] == minDist) {
            edgeType[i] = 1;
            sGraph[A[i]].push_back({B[i], W[i], i});
            sGraph[B[i]].push_back({A[i], W[i], i});
        }
    }
    std::vector<int> distX(N, -1);
    std::queue<int> que;
    distX[0] = 0;
    que.push(0);
    while (not que.empty()) {
        const auto f = que.front();
        que.pop();
        for (const auto &[t, cost, id] : sGraph[f]) {
            if (distX[t] == -1) {
                distX[t] = distX[f] + 1;
                que.push(t);
            }
        }
    }

    std::vector<bool> isSeen(N);
    std::vector<int> order(N), low(N), bridges;
    auto dfsLowlink = [&](auto &&self, const int v, const int p, int k) -> int {
        isSeen[v] = true;
        order[v] = k++;
        low[v] = order[v];
        for (const auto &[t, cost, id] : sGraph[v]) {
            if (not isSeen[t]) {
                k = self(self, t, v, k);
                low[v] = std::min(low[v], low[t]);
                if (order[v] < low[t]) bridges.push_back(id);
            } else if (t != p) {
                low[v] = std::min(low[v], order[t]);
            }
        }
        return k;
    };
    dfsLowlink(dfsLowlink, 0, -1, 0);
    std::sort(bridges.begin(), bridges.end(), [&](const int a, const int b) {
        const auto x = std::min(dist1[A[a]], dist1[B[a]]), y = std::min(dist1[A[b]], dist1[B[b]]);
        if (x != y) return x < y;
        const auto x2 = std::min(distX[A[a]], distX[B[a]]), y2 = std::min(distX[A[b]], distX[B[b]]);
        return x2 < y2;
    });
    std::vector<int> edgeId(M, -1);
    const int P = (int)bridges.size();
    for (int i = 0; i < P; ++i) {
        edgeId[bridges[i]] = i;
        edgeType[bridges[i]] = 2;
    }

    std::vector<i64> dist(N, inf64);
    std::vector<int> lastR(N, -1);
    std::priority_queue<std::pair<i64, int>, std::vector<std::pair<i64, int>>, std::greater<std::pair<i64, int>>> pq;
    dist[0] = 0;
    pq.push({0, 0});
    std::vector<std::vector<i64>> addEvent(P + 1), eraseEvent(P + 1);
    while (not pq.empty()) {
        const auto [nowDist, v] = pq.top();
        pq.pop();
        if (nowDist > dist[v]) continue;
        assert(nowDist == dist1[v]);
        for (const auto &[t, cost, id] : graph[v]) {
            const auto newDist = nowDist + cost;
            if (dist[t] > newDist) {
                dist[t] = newDist;
                pq.push({newDist, t});
            }
            const auto z = edgeId[id];
            const auto y = std::max({lastR[t], z, lastR[v]});
            if (newDist <= dist[t]) lastR[t] = y;
        }
    }
    auto eval = [&](int a, int b, i64 e, int u) {
        // if (dist[a] > dist[b]) return;
        const auto x = lastR[a], y = lastR[b];
        if (x >= y) return;
        addEvent[x + 1].push_back(dist[a] + e + dist2[b]);
        eraseEvent[y + 1 - u].push_back(dist[a] + e + dist2[b]);
    };
    for (int i = 0; i < M; ++i) {
        eval(A[i], B[i], W[i], edgeType[i] == 2 ? 1 : 0);
        eval(B[i], A[i], W[i], edgeType[i] == 2 ? 1 : 0);
    }

    std::multiset<i64> s;
    std::vector<i64> X(P);
    for (int i = 0; i < P; ++i) {
        for (const auto v : addEvent[i]) s.insert(v);
        for (const auto v : eraseEvent[i]) s.erase(s.find(v));
        X[i] = s.empty() ? inf64 : *s.begin();
    }
    i64 answer = minDist;
    for (int i = 0; i < P; ++i) {
        const auto x = minDist + C[bridges[i]], y = X[i];
        answer = std::max(answer, std::min(x, y));
    }
    std::cout << answer << std::endl;
}

int main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    int T = 1;
    while (T--) {
        solve();
    }
}

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 340 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 0 ms 332 KB Output is correct
6 Correct 0 ms 340 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 1 ms 340 KB Output is correct

Subtask #2
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 340 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 0 ms 332 KB Output is correct
6 Correct 0 ms 340 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 1 ms 340 KB Output is correct
9 Correct 2 ms 596 KB Output is correct
10 Correct 2 ms 596 KB Output is correct
11 Correct 2 ms 704 KB Output is correct
12 Correct 2 ms 596 KB Output is correct
13 Correct 2 ms 596 KB Output is correct
14 Correct 2 ms 596 KB Output is correct
15 Correct 2 ms 596 KB Output is correct
16 Correct 2 ms 588 KB Output is correct

Subtask #3
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 535 ms 61900 KB Output is correct
2 Correct 538 ms 62264 KB Output is correct
3 Correct 554 ms 61632 KB Output is correct
4 Correct 527 ms 61588 KB Output is correct
5 Correct 528 ms 61928 KB Output is correct
6 Correct 532 ms 63148 KB Output is correct
7 Correct 544 ms 62896 KB Output is correct
8 Correct 546 ms 63232 KB Output is correct

Subtask #4
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 539 ms 63172 KB Output is correct
2 Correct 517 ms 62216 KB Output is correct
3 Correct 547 ms 62060 KB Output is correct
4 Correct 595 ms 63068 KB Output is correct
5 Correct 539 ms 61892 KB Output is correct
6 Correct 498 ms 62132 KB Output is correct
7 Correct 553 ms 62156 KB Output is correct
8 Correct 570 ms 62592 KB Output is correct

Subtask #5
16.0 / 16.0

# Verdict Execution time Memory Grader output
1 Correct 449 ms 55208 KB Output is correct
2 Correct 221 ms 55840 KB Output is correct
3 Correct 349 ms 72100 KB Output is correct
4 Correct 406 ms 72132 KB Output is correct
5 Correct 364 ms 72144 KB Output is correct
6 Correct 340 ms 72276 KB Output is correct
7 Correct 402 ms 72140 KB Output is correct
8 Correct 391 ms 72464 KB Output is correct
9 Correct 366 ms 72220 KB Output is correct
10 Correct 353 ms 72988 KB Output is correct
11 Correct 390 ms 72380 KB Output is correct
12 Correct 507 ms 56976 KB Output is correct
13 Correct 359 ms 72520 KB Output is correct
14 Correct 211 ms 85040 KB Output is correct
15 Correct 177 ms 79448 KB Output is correct
16 Correct 416 ms 55352 KB Output is correct
17 Correct 451 ms 54152 KB Output is correct
18 Correct 483 ms 54936 KB Output is correct
19 Correct 214 ms 55868 KB Output is correct
20 Correct 254 ms 55944 KB Output is correct
21 Correct 221 ms 55836 KB Output is correct
22 Correct 211 ms 55924 KB Output is correct

Subtask #6
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 449 ms 55208 KB Output is correct
2 Correct 221 ms 55840 KB Output is correct
3 Correct 349 ms 72100 KB Output is correct
4 Correct 406 ms 72132 KB Output is correct
5 Correct 364 ms 72144 KB Output is correct
6 Correct 340 ms 72276 KB Output is correct
7 Correct 402 ms 72140 KB Output is correct
8 Correct 391 ms 72464 KB Output is correct
9 Correct 366 ms 72220 KB Output is correct
10 Correct 353 ms 72988 KB Output is correct
11 Correct 390 ms 72380 KB Output is correct
12 Correct 507 ms 56976 KB Output is correct
13 Correct 359 ms 72520 KB Output is correct
14 Correct 211 ms 85040 KB Output is correct
15 Correct 177 ms 79448 KB Output is correct
16 Correct 416 ms 55352 KB Output is correct
17 Correct 451 ms 54152 KB Output is correct
18 Correct 483 ms 54936 KB Output is correct
19 Correct 214 ms 55868 KB Output is correct
20 Correct 254 ms 55944 KB Output is correct
21 Correct 221 ms 55836 KB Output is correct
22 Correct 211 ms 55924 KB Output is correct
23 Correct 572 ms 58016 KB Output is correct
24 Correct 265 ms 59468 KB Output is correct
25 Correct 276 ms 44440 KB Output is correct
26 Correct 302 ms 47460 KB Output is correct
27 Correct 274 ms 46632 KB Output is correct
28 Correct 268 ms 45644 KB Output is correct
29 Correct 304 ms 47792 KB Output is correct
30 Correct 293 ms 46092 KB Output is correct
31 Correct 273 ms 46772 KB Output is correct
32 Correct 298 ms 46288 KB Output is correct
33 Correct 258 ms 45908 KB Output is correct
34 Correct 573 ms 56928 KB Output is correct
35 Correct 291 ms 47100 KB Output is correct
36 Correct 285 ms 96104 KB Output is correct
37 Correct 257 ms 94596 KB Output is correct
38 Correct 575 ms 57148 KB Output is correct
39 Correct 533 ms 56840 KB Output is correct
40 Correct 572 ms 57772 KB Output is correct
41 Correct 274 ms 59512 KB Output is correct
42 Correct 274 ms 59452 KB Output is correct
43 Correct 294 ms 59484 KB Output is correct
44 Correct 277 ms 59552 KB Output is correct

Subtask #7
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 340 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 0 ms 332 KB Output is correct
6 Correct 0 ms 340 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 1 ms 340 KB Output is correct
9 Correct 2 ms 596 KB Output is correct
10 Correct 2 ms 596 KB Output is correct
11 Correct 2 ms 704 KB Output is correct
12 Correct 2 ms 596 KB Output is correct
13 Correct 2 ms 596 KB Output is correct
14 Correct 2 ms 596 KB Output is correct
15 Correct 2 ms 596 KB Output is correct
16 Correct 2 ms 588 KB Output is correct
17 Correct 535 ms 61900 KB Output is correct
18 Correct 538 ms 62264 KB Output is correct
19 Correct 554 ms 61632 KB Output is correct
20 Correct 527 ms 61588 KB Output is correct
21 Correct 528 ms 61928 KB Output is correct
22 Correct 532 ms 63148 KB Output is correct
23 Correct 544 ms 62896 KB Output is correct
24 Correct 546 ms 63232 KB Output is correct
25 Correct 539 ms 63172 KB Output is correct
26 Correct 517 ms 62216 KB Output is correct
27 Correct 547 ms 62060 KB Output is correct
28 Correct 595 ms 63068 KB Output is correct
29 Correct 539 ms 61892 KB Output is correct
30 Correct 498 ms 62132 KB Output is correct
31 Correct 553 ms 62156 KB Output is correct
32 Correct 570 ms 62592 KB Output is correct
33 Correct 449 ms 55208 KB Output is correct
34 Correct 221 ms 55840 KB Output is correct
35 Correct 349 ms 72100 KB Output is correct
36 Correct 406 ms 72132 KB Output is correct
37 Correct 364 ms 72144 KB Output is correct
38 Correct 340 ms 72276 KB Output is correct
39 Correct 402 ms 72140 KB Output is correct
40 Correct 391 ms 72464 KB Output is correct
41 Correct 366 ms 72220 KB Output is correct
42 Correct 353 ms 72988 KB Output is correct
43 Correct 390 ms 72380 KB Output is correct
44 Correct 507 ms 56976 KB Output is correct
45 Correct 359 ms 72520 KB Output is correct
46 Correct 211 ms 85040 KB Output is correct
47 Correct 177 ms 79448 KB Output is correct
48 Correct 416 ms 55352 KB Output is correct
49 Correct 451 ms 54152 KB Output is correct
50 Correct 483 ms 54936 KB Output is correct
51 Correct 214 ms 55868 KB Output is correct
52 Correct 254 ms 55944 KB Output is correct
53 Correct 221 ms 55836 KB Output is correct
54 Correct 211 ms 55924 KB Output is correct
55 Correct 572 ms 58016 KB Output is correct
56 Correct 265 ms 59468 KB Output is correct
57 Correct 276 ms 44440 KB Output is correct
58 Correct 302 ms 47460 KB Output is correct
59 Correct 274 ms 46632 KB Output is correct
60 Correct 268 ms 45644 KB Output is correct
61 Correct 304 ms 47792 KB Output is correct
62 Correct 293 ms 46092 KB Output is correct
63 Correct 273 ms 46772 KB Output is correct
64 Correct 298 ms 46288 KB Output is correct
65 Correct 258 ms 45908 KB Output is correct
66 Correct 573 ms 56928 KB Output is correct
67 Correct 291 ms 47100 KB Output is correct
68 Correct 285 ms 96104 KB Output is correct
69 Correct 257 ms 94596 KB Output is correct
70 Correct 575 ms 57148 KB Output is correct
71 Correct 533 ms 56840 KB Output is correct
72 Correct 572 ms 57772 KB Output is correct
73 Correct 274 ms 59512 KB Output is correct
74 Correct 274 ms 59452 KB Output is correct
75 Correct 294 ms 59484 KB Output is correct
76 Correct 277 ms 59552 KB Output is correct
77 Correct 595 ms 60092 KB Output is correct
78 Correct 256 ms 58680 KB Output is correct
79 Correct 388 ms 49888 KB Output is correct
80 Correct 328 ms 50056 KB Output is correct
81 Correct 354 ms 49904 KB Output is correct
82 Correct 340 ms 49908 KB Output is correct
83 Correct 407 ms 50420 KB Output is correct
84 Correct 350 ms 50668 KB Output is correct
85 Correct 335 ms 50160 KB Output is correct
86 Correct 452 ms 50340 KB Output is correct
87 Correct 410 ms 50296 KB Output is correct
88 Correct 640 ms 58876 KB Output is correct
89 Correct 399 ms 50776 KB Output is correct
90 Correct 286 ms 96676 KB Output is correct
91 Correct 287 ms 95124 KB Output is correct
92 Correct 632 ms 60168 KB Output is correct
93 Correct 530 ms 58508 KB Output is correct
94 Correct 560 ms 57564 KB Output is correct
95 Correct 252 ms 58832 KB Output is correct
96 Correct 324 ms 58804 KB Output is correct
97 Correct 255 ms 58764 KB Output is correct
98 Correct 269 ms 58648 KB Output is correct