結果

問題 No.2764 Warp Drive Spacecraft
ユーザー 👑 binap
提出日時 2024-04-29 01:49:20
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 754 ms / 3,000 ms
コード長 4,203 bytes
コンパイル時間 3,075 ms
コンパイル使用メモリ 230,192 KB
最終ジャッジ日時 2025-02-21 09:24:01
ジャッジサーバーID
（参考情報） 		judge1 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 4
other AC * 35
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ソースコード

diff #
プレゼンテーションモードにする

#include<bits/stdc++.h>
using namespace std;
template<typename T> void chmin(T& a, T b){a = min(a, b);}
// thanks for Luzhiled-san's website
// https://ei1333.github.io/luzhiled/snippets/structure/convex-hull-trick-add-monotone.html
template< typename T, bool isMin >
struct ConvexHullTrickAddMonotone {
#define F first
#define S second
  using P = pair< T, T >;
  deque< P > H;
  ConvexHullTrickAddMonotone() = default;
  bool empty() const { return H.empty(); }
  void clear() { H.clear(); }
  inline int sgn(T x) { return x == 0 ? 0 : (x < 0 ? -1 : 1); }
  using D = long double;
  inline bool check(const P &a, const P &b, const P &c) {
    if(b.S == a.S || c.S == b.S)
      return sgn(b.F - a.F) * sgn(c.S - b.S) >= sgn(c.F - b.F) * sgn(b.S - a.S);
    //return (b.F-a.F)*(c.S-b.S) >= (b.S-a.S)*(c.F-b.F);
    return
        D(b.F - a.F) * sgn(c.S - b.S) / D(abs(b.S - a.S)) >=
        D(c.F - b.F) * sgn(b.S - a.S) / D(abs(c.S - b.S));
  }
  void add(T a, T b) {
    if(!isMin) a *= -1, b *= -1;
    P line(a, b);
    if(empty()) {
      H.emplace_front(line);
      return;
    }
    if(H.front().F <= a) {
      if(H.front().F == a) {
        if(H.front().S <= b) return;
        H.pop_front();
      }
      while(H.size() >= 2 && check(line, H.front(), H[1])) H.pop_front();
      H.emplace_front(line);
    } else {
      assert(a <= H.back().F);
      if(H.back().F == a) {
        if(H.back().S <= b) return;
        H.pop_back();
      }
      while(H.size() >= 2 && check(H[H.size() - 2], H.back(), line)) H.pop_back();
      H.emplace_back(line);
    }
  }
  inline T get_y(const P &a, const T &x) {
    return a.F * x + a.S;
  }
  T query_monotone_inc(T x) {
    assert(!empty());
    while(H.size() >= 2 && get_y(H.front(), x) >= get_y(H[1], x)) H.pop_front();
    if(isMin) return get_y(H.front(), x);
    return -get_y(H.front(), x);
  }
#undef F
#undef S
};
const long long INF = 2002002002002002002;
using S = long long;
S _INF(INF);
S _ZERO(0LL);
using F = long long;
S apply(F f, S x){
    return f + x;
}
template<typename S, typename F>
struct Dijkstra{
    struct Edge{
        int from, to;
        F cost;
        Edge(int from, int to, F cost) : from(from), to(to), cost(cost) {};
    };
    int n, m;
    vector<bool> initialized;
    vector<Edge> E;
    vector<vector<int>> G;
    map<int, vector<S>> dist;
    map<int, vector<int>> idx;
    Dijkstra(int _n) : n(_n), m(0), initialized(n, false), G(n){}
    void add_edge(int from, int to, F cost){
        Edge e(from, to, cost);
        E.push_back(e);
        G[from].emplace_back(m);
        m++;
    }
    void calc(int s){
        initialized[s] = true;
        dist[s] = vector<S>(n, _INF);
        idx[s] = vector<int>(n, -1);
        priority_queue<tuple<S, int, int>, vector<tuple<S, int, int>>, greater<tuple<S, int, int>>> pq;
        pq.emplace(_ZERO, s, -1);
        while(pq.size()){
            auto [dist_from, from, index] = pq.top(); pq.pop();
            if(dist[s][from] <= dist_from) continue;
            dist[s][from] = dist_from;
            idx[s][from] = index;
            for(int index : G[from]){
                int to = E[index].to;
                S dist_to = apply(E[index].cost, dist_from);
                if(dist[s][to] <= dist_to) continue;
                pq.emplace(dist_to, to, index);
            }
        }
    }
    S get_dist(int s, int t){
        if(!initialized[s]) calc(s);
        return dist[s][t];
    }
};
int main(){
    int n, m;
    cin >> n >> m;
    vector<long long> w(n);
    for(int i = 0; i < n; i++) cin >> w[i];
    Dijkstra<long long, long long> graph(n);
    for(int i = 0; i < m; i++){
        int u, v;
        long long t;
        cin >> u >> v >> t;
        u--; v--;
        graph.add_edge(u, v, t);
        graph.add_edge(v, u, t);
    }
    vector<long long> dist_s(n);
    vector<long long> dist_t(n);
    for(int i = 0; i < n; i++) dist_s[i] = graph.get_dist(0, i);
    for(int i = 0; i < n; i++) dist_t[i] = graph.get_dist(n - 1, i);
    long long ans = dist_s[n - 1];
    ConvexHullTrickAddMonotone<long long, true> CHT;
    vector<int> asc(n);
    for(int i = 0; i < n; i++) asc[i] = i;
    sort(asc.begin(), asc.end(), [&](int left, int right){
        return w[left] < w[right];
    });
    for(int i = 0; i < n; i++){
        int idx = asc[i];
        if(dist_t[idx] < INF) CHT.add(w[idx], dist_t[idx]);
    }
    for(int i = 0; i < n; i++){
        int idx = asc[i];
        if(dist_s[idx] < INF) chmin(ans, dist_s[idx] + CHT.query_monotone_inc(w[idx]));
    }
    cout << ans << "\n";
    return 0;
}
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