Submission #603015

#	Time	Username	Problem	Language	Result	Execution time	Memory
603015		verngutz	Aesthetic (NOI20_aesthetic)	C++17	36 / 100	2083 ms	74072 KiB

Aesthetic

#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 i, u, v; T w;
    wedge reverse() const { return {i, v, u, w}; }
    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 <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 <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;
}
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);
    for(int i = 0; i < m; i++) {
        int u, v, w;
        cin >> u >> v >> w;
        g.add_edge({i, u, v, w});
    }
    auto [ds, ps] = sssp(g, {1});
    auto [dt, pt] = sssp(g, {n});
    if(all_of(g.edges.begin(), g.edges.end(), [](const wedge<ll>& e) { return e.w == 1; })) {
        graph<0, wedge<ll>, 1> sp_dag(n);
        for(auto [i, u, v, w] : g.edges) {
            if(ds[u] + w + dt[v] == ds[n]) {
                sp_dag.add_edge({i, u, v, w});
            }
        }
        auto [cut_edge, _2eccs] = find_2eccs(sp_dag);
        bool increase = false;
        for(int i = 0; i < sp_dag.edges.size(); i++) {
            wedge<ll>& sp_edge = sp_dag.edges[i];
            increase |= cut_edge[i] and sp_edge.i != m - 1;
        }
        cout << ds[n] + increase << endl;
    } else if(m == n - 1) {
        auto path = construct_path(g, ps, n);
        set<pair<int, int>> in_path;
        for(int i = 0; i < path.size() - 1; i++) {
            in_path.insert({path[i], path[i + 1]});
        }
        ll max_replace = 0;
        ll ans = ds[n];
        for(int ii = g.edges.size() - 1; ii >= 0; ii--) {
            auto [i, u, v, w] = g.edges[ii];
            if(in_path.count({u, v})) {
                ans = max(ans, ds[u] + w + max_replace + dt[v]);
            }
            if(ii % 2 == 0) {
                max_replace = max(max_replace, w);
            }
        }
        cout << ans << endl;
    } else {
        ll max_replace = 0;
        ll ans = ds[n];
        for(int i = m - 1; i >= 0; i--) {
            g.edges[2 * i].w += max_replace;
            g.edges[2 * i + 1].w += max_replace;
            ans = max(ans, sssp(g, {1}).first[n]);
            g.edges[2 * i].w -= max_replace;
            g.edges[2 * i + 1].w -= max_replace;
            max_replace = max(max_replace, g.edges[2 * i].w);
        }
        cout << ans << endl;
    }
    return 0;
}

Compilation message (stderr)

Aesthetic.cpp: In function 'int main()':
Aesthetic.cpp:121:26: 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]
  121 |         for(int i = 0; i < sp_dag.edges.size(); i++) {
      |                        ~~^~~~~~~~~~~~~~~~~~~~~
Aesthetic.cpp:129:26: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  129 |         for(int i = 0; i < path.size() - 1; i++) {
      |                        ~~^~~~~~~~~~~~~~~~~
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:119:52:   required from here
Aesthetic.cpp:81:26: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::vector<int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   81 |     for(int u = Index; u < g.adj.size(); u++) if(not vis[u]) {
      |                        ~~^~~~~~~~~~~~~~

• Subtask 1: 5 / 5
• Subtask 2: 8 / 8
• Subtask 3: 7 / 7
• Subtask 4: 0 / 15
• Subtask 5: 16 / 16
• Subtask 6: 0 / 22
• Subtask 7: 0 / 27