oj.uz

Submission #603484

# Submission time Handle Problem Language Result Execution time Memory
603484 2022-07-24T07:33:31 Z verngutz Aesthetic (NOI20_aesthetic) C++17
100 / 100
 1852 ms 122032 KB 
#include <bits/stdc++.h>
#define err(args...) {}
#ifdef DEBUG
#include "_debug.cpp"
#endif
using namespace std;
using ll = long long;
using ld = long double;
template <typename T> using lim = numeric_limits<T>;
template <typename T> istream& operator>>(istream& is, vector<T>& a) { for(T& x : a) { is >> x; } return is; }
template <typename X, typename Y> istream& operator>>(istream& is, pair<X, Y>& p) { return is >> p.first >> p.second; }
template <typename T> struct wedge {
    int u, v; T w;
    int i; T dw;
    wedge reverse() const { return {v, u, w, i, dw}; }
    friend ostream& operator<<(ostream& os, const wedge& e) {
        return os << "{u: " << e.u << ", v: " << e.v << ", w: " << e.w << "}";
    }
};
template <bool Directed, typename TEdge, bool Index> struct graph {
    using EType = TEdge;
    vector<TEdge> edges;
    vector<vector<int>> adj;
    graph(int n) : adj(n + Index) {}
    graph(int n, int m) : graph(n) { edges.reserve(m << not Directed); }
    TEdge& operator()(int e) { return edges[e]; }
    vector<int>& operator[](int u) { return adj[u]; }
    int size() { return adj.size() - Index; }
    void append(int u, const TEdge& e) {
        adj[u].push_back(edges.size());
        edges.push_back(e);
    }
    void add_edge(const TEdge& e) {
        append(e.u, e);
        if(not Directed) append(e.v, e.reverse());
    }
};
template <bool Directed, typename T, bool Index>
pair<vector<T>, vector<int>> sssp(graph<Directed, wedge<T>, Index>& g, const vector<int>& s) {
    vector<int> vis(g.adj.size()), p(g.adj.size(), -1);
    vector<T> d(g.adj.size(), lim<T>::max());
    priority_queue<pair<T, int>> pq;
    for(int u : s) {
        pq.push({d[u] = 0, u});
    }
    while(not pq.empty()) {
        int u = pq.top().second; pq.pop();
        if(not vis[u]) {
            vis[u] = true;
            for(int e : g[u]) {
                if(not vis[g(e).v] and d[g(e).v] > d[u] + g(e).w) {
                    pq.push({-(d[g(e).v] = d[u] + g(e).w), g(p[g(e).v] = e).v});
                }
            }
        }
    }
    return {move(d), move(p)};
}
template <bool Directed, typename TEdge, bool Index>
vector<int> construct_path(graph<Directed, TEdge, Index>& g, const vector<int>& parent, int t) {
    vector<int> ans = {t};
    while(parent[ans.back()] != -1) {
        ans.push_back(g(parent[ans.back()]).u);
    }
    reverse(ans.begin(), ans.end());
    return ans;
}
template <typename TEdge, bool Index> pair<vector<int>, vector<vector<int>>> find_2eccs(graph<0, TEdge, Index>& g) {
    vector<int> vis(g.adj.size()), low(g.adj.size()), cut_edge(g.edges.size()), s;
    vector<vector<int>> _2eccs = {};
    int timer = 1;
    function<void(int, int)> dfs = [&](int u, int from) {
        vis[u] = low[u] = timer++;
        s.push_back(u);
        for(int e : g[u]) {
            if(not vis[g(e).v]) {
                dfs(g(e).v, e & ~1);
                if(vis[u] < low[g(e).v]) {
                    cut_edge[e] = cut_edge[e ^ 1] = true;
                    _2eccs.push_back(vector<int>());
                    do {
                        _2eccs.back().push_back(s.back()), s.pop_back();
                    } while(_2eccs.back().back() != g(e).v);
                }
                low[u] = min(low[u], low[g(e).v]);
            } else if((e & ~1) != from and vis[u] > vis[g(e).v]) {
                low[u] = min(low[u], vis[g(e).v]);
            }
        }
    };
    for(int u = Index; u < g.adj.size(); u++) if(not vis[u]) {
        dfs(u, -1);
        _2eccs.push_back(vector<int>());
        while(not s.empty()) {
            _2eccs.back().push_back(s.back()), s.pop_back();
        }
    }
    return {move(cut_edge), move(_2eccs)};
}
template <typename TEdge, bool Index> pair<vector<int>, graph<0, TEdge, Index>> build_bridge_tree(graph<0, TEdge, Index>& g,
const vector<int>& cut_edge, const vector<vector<int>>& _2eccs) {
    vector<int> _2ecc_id(g.adj.size());
    for(int i = 0; i < _2eccs.size(); i++) {
        for(int u : _2eccs[i]) {
            _2ecc_id[u] = i + Index;
        }
    }
    graph<0, TEdge, Index> bridge_tree(_2eccs.size());
    for(int e = 0; e < g.edges.size(); e++) {
        if(cut_edge[e] and g(e).u < g(e).v) {
            bridge_tree.add_edge({_2ecc_id[g(e).u], _2ecc_id[g(e).v]});
        }
    }
    return {move(_2ecc_id), move(bridge_tree)};
}
template <typename TEdge, bool Index> pair<vector<int>, graph<0, TEdge, Index>> build_bridge_tree(graph<0, TEdge, Index>& g) {
    auto [cut_edge, _2eccs] = find_2eccs(g);
    return build_bridge_tree(g, cut_edge, _2eccs);
}
template <typename T, typename Can> T bsearch(T L, T R, const Can& can, bool left_feasible = true) {
    static_assert(is_convertible<decltype(can), function<bool(T)>>::value);
    T& feasible = left_feasible ? L : R;
    T& infeasible = left_feasible ? R : L;
    while(R - L > 1) {
        T M = L + (R - L) / 2;
        (can(M) ? feasible : infeasible) = M;
    }
    return feasible;
}
int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    int n, m;
    cin >> n >> m;
    graph<0, wedge<ll>, 1> g(n, m);
    int max_w = 0;
    for(int i = 0; i < m; i++) {
        int u, v, w;
        cin >> u >> v >> w;
        g.add_edge({u, v, w, i});
        max_w = max(max_w, w);
    }
    ll max_dw = 0;
    for(int i = m - 1; i >= 0; i--) {
        g.edges[2 * i].dw = g.edges[2 * i + 1].dw = max_dw;
        max_dw = max(max_dw, g.edges[2 * i].w);
    }
    auto [ds, ps] = sssp(g, {1});
    auto [dt, pt] = sssp(g, {n});
    cout << ds[n] + bsearch(0, max_w + 1, [&, &ds=ds, &dt=dt](int delta) {
        graph<0, wedge<ll>, 1> sp_dag(n);
        for(int ii = 0; ii < g.edges.size(); ii += 2) {
            auto [u, v, w, i, dw] = g.edges[ii];
            if(min(ds[u] + w + dt[v], ds[v] + w + dt[u]) < ds[n] + delta) {
                sp_dag.add_edge({u, v, w, i, dw});
            }
        }
        auto [cut_edge, _2eccs] = find_2eccs(sp_dag);
        auto [_2ecc_id, bridge_tree] = build_bridge_tree(sp_dag, cut_edge, _2eccs);
        auto [d, p] = sssp(bridge_tree, {_2ecc_id[1]});
        auto path = construct_path(bridge_tree, p, {_2ecc_id[n]});
        set<pair<int, int>> on_path;
        for(int i = 1; i < path.size(); i++) {
            on_path.insert({path[i - 1], path[i]});
        }
        bool increase = false;
        for(int ii = 0; ii < sp_dag.edges.size(); ii++) {
            auto [u, v, w, i, dw] = sp_dag.edges[ii];
            increase |= cut_edge[ii]
                and on_path.count({_2ecc_id[u], _2ecc_id[v]})
                and ds[u] + w + dw + dt[v] >= ds[n] + delta;
        }
        return increase;
    }) << endl;
    return 0;
}

Compilation message

Aesthetic.cpp: In lambda function:
Aesthetic.cpp:152:28: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<wedge<long long int>, std::allocator<wedge<long long int> > >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  152 |         for(int ii = 0; ii < g.edges.size(); ii += 2) {
      |                         ~~~^~~~~~~~~~~~~~~~
Aesthetic.cpp:163:26: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  163 |         for(int i = 1; i < path.size(); i++) {
      |                        ~~^~~~~~~~~~~~~
Aesthetic.cpp:167:28: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<wedge<long long int>, std::allocator<wedge<long long int> > >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  167 |         for(int ii = 0; ii < sp_dag.edges.size(); ii++) {
      |                         ~~~^~~~~~~~~~~~~~~~~~~~~
Aesthetic.cpp: In instantiation of 'std::pair<std::vector<int>, std::vector<std::vector<int> > > find_2eccs(graph<false, TEdge, Index>&) [with TEdge = wedge<long long int>; bool Index = true]':
Aesthetic.cpp:158:52:   required from here
Aesthetic.cpp:91:26: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::vector<int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   91 |     for(int u = Index; u < g.adj.size(); u++) if(not vis[u]) {
      |                        ~~^~~~~~~~~~~~~~
Aesthetic.cpp: In instantiation of 'std::pair<std::vector<int>, graph<false, TEdge, Index> > build_bridge_tree(graph<false, TEdge, Index>&, const std::vector<int>&, const std::vector<std::vector<int> >&) [with TEdge = wedge<long long int>; bool Index = true]':
Aesthetic.cpp:159:82:   required from here
Aesthetic.cpp:103:22: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::vector<int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  103 |     for(int i = 0; i < _2eccs.size(); i++) {
      |                    ~~^~~~~~~~~~~~~~~
Aesthetic.cpp:109:22: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<wedge<long long int>, std::allocator<wedge<long long int> > >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  109 |     for(int e = 0; e < g.edges.size(); e++) {
      |                    ~~^~~~~~~~~~~~~~~~

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 1 ms 340 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 1 ms 340 KB Output is correct
7 Correct 1 ms 340 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 1 ms 340 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 1 ms 340 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 1 ms 340 KB Output is correct
7 Correct 1 ms 340 KB Output is correct
8 Correct 1 ms 340 KB Output is correct
9 Correct 5 ms 724 KB Output is correct
10 Correct 6 ms 724 KB Output is correct
11 Correct 11 ms 868 KB Output is correct
12 Correct 9 ms 852 KB Output is correct
13 Correct 4 ms 856 KB Output is correct
14 Correct 4 ms 904 KB Output is correct
15 Correct 4 ms 852 KB Output is correct
16 Correct 4 ms 856 KB Output is correct

Subtask #3
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 1806 ms 79352 KB Output is correct
2 Correct 1633 ms 80536 KB Output is correct
3 Correct 1674 ms 78752 KB Output is correct
4 Correct 1693 ms 79116 KB Output is correct
5 Correct 1789 ms 79516 KB Output is correct
6 Correct 1713 ms 80504 KB Output is correct
7 Correct 1726 ms 80280 KB Output is correct
8 Correct 1722 ms 81040 KB Output is correct

Subtask #4
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1852 ms 80752 KB Output is correct
2 Correct 1785 ms 79696 KB Output is correct
3 Correct 1678 ms 79444 KB Output is correct
4 Correct 1634 ms 80368 KB Output is correct
5 Correct 1706 ms 79376 KB Output is correct
6 Correct 1664 ms 79496 KB Output is correct
7 Correct 1691 ms 86232 KB Output is correct
8 Correct 1747 ms 86824 KB Output is correct

Subtask #5
16.0 / 16.0

# Verdict Execution time Memory Grader output
1 Correct 463 ms 60456 KB Output is correct
2 Correct 206 ms 72400 KB Output is correct
3 Correct 372 ms 69868 KB Output is correct
4 Correct 308 ms 69740 KB Output is correct
5 Correct 330 ms 69712 KB Output is correct
6 Correct 376 ms 69936 KB Output is correct
7 Correct 345 ms 70028 KB Output is correct
8 Correct 356 ms 70368 KB Output is correct
9 Correct 365 ms 70088 KB Output is correct
10 Correct 349 ms 70508 KB Output is correct
11 Correct 367 ms 70060 KB Output is correct
12 Correct 453 ms 60736 KB Output is correct
13 Correct 347 ms 69984 KB Output is correct
14 Correct 219 ms 95492 KB Output is correct
15 Correct 214 ms 95528 KB Output is correct
16 Correct 438 ms 59800 KB Output is correct
17 Correct 442 ms 57324 KB Output is correct
18 Correct 445 ms 59196 KB Output is correct
19 Correct 213 ms 72752 KB Output is correct
20 Correct 217 ms 72792 KB Output is correct
21 Correct 232 ms 72720 KB Output is correct
22 Correct 216 ms 72624 KB Output is correct

Subtask #6
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 463 ms 60456 KB Output is correct
2 Correct 206 ms 72400 KB Output is correct
3 Correct 372 ms 69868 KB Output is correct
4 Correct 308 ms 69740 KB Output is correct
5 Correct 330 ms 69712 KB Output is correct
6 Correct 376 ms 69936 KB Output is correct
7 Correct 345 ms 70028 KB Output is correct
8 Correct 356 ms 70368 KB Output is correct
9 Correct 365 ms 70088 KB Output is correct
10 Correct 349 ms 70508 KB Output is correct
11 Correct 367 ms 70060 KB Output is correct
12 Correct 453 ms 60736 KB Output is correct
13 Correct 347 ms 69984 KB Output is correct
14 Correct 219 ms 95492 KB Output is correct
15 Correct 214 ms 95528 KB Output is correct
16 Correct 438 ms 59800 KB Output is correct
17 Correct 442 ms 57324 KB Output is correct
18 Correct 445 ms 59196 KB Output is correct
19 Correct 213 ms 72752 KB Output is correct
20 Correct 217 ms 72792 KB Output is correct
21 Correct 232 ms 72720 KB Output is correct
22 Correct 216 ms 72624 KB Output is correct
23 Correct 589 ms 62808 KB Output is correct
24 Correct 417 ms 84728 KB Output is correct
25 Correct 283 ms 45124 KB Output is correct
26 Correct 287 ms 43160 KB Output is correct
27 Correct 273 ms 43680 KB Output is correct
28 Correct 298 ms 45824 KB Output is correct
29 Correct 294 ms 43276 KB Output is correct
30 Correct 283 ms 45116 KB Output is correct
31 Correct 327 ms 44868 KB Output is correct
32 Correct 299 ms 44048 KB Output is correct
33 Correct 278 ms 45648 KB Output is correct
34 Correct 582 ms 61904 KB Output is correct
35 Correct 281 ms 44728 KB Output is correct
36 Correct 298 ms 109188 KB Output is correct
37 Correct 259 ms 109224 KB Output is correct
38 Correct 568 ms 60320 KB Output is correct
39 Correct 549 ms 59320 KB Output is correct
40 Correct 602 ms 60696 KB Output is correct
41 Correct 426 ms 82708 KB Output is correct
42 Correct 402 ms 84568 KB Output is correct
43 Correct 469 ms 82788 KB Output is correct
44 Correct 417 ms 82796 KB Output is correct

Subtask #7
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 1 ms 340 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 1 ms 340 KB Output is correct
7 Correct 1 ms 340 KB Output is correct
8 Correct 1 ms 340 KB Output is correct
9 Correct 5 ms 724 KB Output is correct
10 Correct 6 ms 724 KB Output is correct
11 Correct 11 ms 868 KB Output is correct
12 Correct 9 ms 852 KB Output is correct
13 Correct 4 ms 856 KB Output is correct
14 Correct 4 ms 904 KB Output is correct
15 Correct 4 ms 852 KB Output is correct
16 Correct 4 ms 856 KB Output is correct
17 Correct 1806 ms 79352 KB Output is correct
18 Correct 1633 ms 80536 KB Output is correct
19 Correct 1674 ms 78752 KB Output is correct
20 Correct 1693 ms 79116 KB Output is correct
21 Correct 1789 ms 79516 KB Output is correct
22 Correct 1713 ms 80504 KB Output is correct
23 Correct 1726 ms 80280 KB Output is correct
24 Correct 1722 ms 81040 KB Output is correct
25 Correct 1852 ms 80752 KB Output is correct
26 Correct 1785 ms 79696 KB Output is correct
27 Correct 1678 ms 79444 KB Output is correct
28 Correct 1634 ms 80368 KB Output is correct
29 Correct 1706 ms 79376 KB Output is correct
30 Correct 1664 ms 79496 KB Output is correct
31 Correct 1691 ms 86232 KB Output is correct
32 Correct 1747 ms 86824 KB Output is correct
33 Correct 463 ms 60456 KB Output is correct
34 Correct 206 ms 72400 KB Output is correct
35 Correct 372 ms 69868 KB Output is correct
36 Correct 308 ms 69740 KB Output is correct
37 Correct 330 ms 69712 KB Output is correct
38 Correct 376 ms 69936 KB Output is correct
39 Correct 345 ms 70028 KB Output is correct
40 Correct 356 ms 70368 KB Output is correct
41 Correct 365 ms 70088 KB Output is correct
42 Correct 349 ms 70508 KB Output is correct
43 Correct 367 ms 70060 KB Output is correct
44 Correct 453 ms 60736 KB Output is correct
45 Correct 347 ms 69984 KB Output is correct
46 Correct 219 ms 95492 KB Output is correct
47 Correct 214 ms 95528 KB Output is correct
48 Correct 438 ms 59800 KB Output is correct
49 Correct 442 ms 57324 KB Output is correct
50 Correct 445 ms 59196 KB Output is correct
51 Correct 213 ms 72752 KB Output is correct
52 Correct 217 ms 72792 KB Output is correct
53 Correct 232 ms 72720 KB Output is correct
54 Correct 216 ms 72624 KB Output is correct
55 Correct 589 ms 62808 KB Output is correct
56 Correct 417 ms 84728 KB Output is correct
57 Correct 283 ms 45124 KB Output is correct
58 Correct 287 ms 43160 KB Output is correct
59 Correct 273 ms 43680 KB Output is correct
60 Correct 298 ms 45824 KB Output is correct
61 Correct 294 ms 43276 KB Output is correct
62 Correct 283 ms 45116 KB Output is correct
63 Correct 327 ms 44868 KB Output is correct
64 Correct 299 ms 44048 KB Output is correct
65 Correct 278 ms 45648 KB Output is correct
66 Correct 582 ms 61904 KB Output is correct
67 Correct 281 ms 44728 KB Output is correct
68 Correct 298 ms 109188 KB Output is correct
69 Correct 259 ms 109224 KB Output is correct
70 Correct 568 ms 60320 KB Output is correct
71 Correct 549 ms 59320 KB Output is correct
72 Correct 602 ms 60696 KB Output is correct
73 Correct 426 ms 82708 KB Output is correct
74 Correct 402 ms 84568 KB Output is correct
75 Correct 469 ms 82788 KB Output is correct
76 Correct 417 ms 82796 KB Output is correct
77 Correct 1496 ms 70196 KB Output is correct
78 Correct 1680 ms 91372 KB Output is correct
79 Correct 1027 ms 103576 KB Output is correct
80 Correct 1040 ms 103420 KB Output is correct
81 Correct 1081 ms 103576 KB Output is correct
82 Correct 1004 ms 104056 KB Output is correct
83 Correct 1002 ms 102928 KB Output is correct
84 Correct 1149 ms 104284 KB Output is correct
85 Correct 1075 ms 103400 KB Output is correct
86 Correct 1027 ms 102480 KB Output is correct
87 Correct 1144 ms 103860 KB Output is correct
88 Correct 1607 ms 69172 KB Output is correct
89 Correct 981 ms 103872 KB Output is correct
90 Correct 983 ms 122032 KB Output is correct
91 Correct 1020 ms 118048 KB Output is correct
92 Correct 1474 ms 68976 KB Output is correct
93 Correct 1555 ms 68984 KB Output is correct
94 Correct 1421 ms 67428 KB Output is correct
95 Correct 1662 ms 91912 KB Output is correct
96 Correct 1664 ms 92400 KB Output is correct
97 Correct 1821 ms 91776 KB Output is correct
98 Correct 1777 ms 91660 KB Output is correct