結果

問題 No.2764 Warp Drive Spacecraft
ユーザー apricityapricity
提出日時 2024-05-17 22:45:38
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 361 ms / 3,000 ms
コード長 7,474 bytes
コンパイル時間 1,783 ms
コンパイル使用メモリ 145,372 KB
実行使用メモリ 25,052 KB
最終ジャッジ日時 2024-05-18 00:10:58
合計ジャッジ時間 9,169 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge1
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
6,816 KB
testcase_01 AC 2 ms
6,944 KB
testcase_02 AC 2 ms
6,940 KB
testcase_03 AC 3 ms
6,940 KB
testcase_04 AC 2 ms
6,944 KB
testcase_05 AC 2 ms
6,940 KB
testcase_06 AC 2 ms
6,944 KB
testcase_07 AC 2 ms
6,944 KB
testcase_08 AC 3 ms
6,944 KB
testcase_09 AC 2 ms
6,944 KB
testcase_10 AC 2 ms
6,940 KB
testcase_11 AC 2 ms
6,940 KB
testcase_12 AC 3 ms
6,940 KB
testcase_13 AC 2 ms
6,940 KB
testcase_14 AC 2 ms
6,940 KB
testcase_15 AC 2 ms
6,940 KB
testcase_16 AC 110 ms
21,872 KB
testcase_17 AC 113 ms
21,956 KB
testcase_18 AC 108 ms
21,932 KB
testcase_19 AC 275 ms
19,164 KB
testcase_20 AC 274 ms
20,452 KB
testcase_21 AC 261 ms
20,292 KB
testcase_22 AC 268 ms
20,244 KB
testcase_23 AC 268 ms
19,300 KB
testcase_24 AC 273 ms
20,344 KB
testcase_25 AC 279 ms
20,280 KB
testcase_26 AC 345 ms
24,252 KB
testcase_27 AC 341 ms
24,096 KB
testcase_28 AC 358 ms
24,560 KB
testcase_29 AC 361 ms
24,644 KB
testcase_30 AC 353 ms
24,068 KB
testcase_31 AC 358 ms
24,936 KB
testcase_32 AC 359 ms
25,052 KB
testcase_33 AC 122 ms
15,232 KB
testcase_34 AC 124 ms
15,104 KB
testcase_35 AC 123 ms
15,232 KB
testcase_36 AC 148 ms
22,032 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include<iostream>
#include<string>
#include<vector>
#include<algorithm>
#include<numeric>
#include<cmath>
#include<utility>
#include<tuple>
#include<cstdint>
#include<cstdio>
#include<iomanip>
#include<map>
#include<queue>
#include<set>
#include<stack>
#include<deque>
#include<unordered_map>
#include<unordered_set>
#include<bitset>
#include<cctype>
#include<chrono>
#include<random>
#include<cassert>
#include<cstddef>
#include<iterator>
#include<string_view>
#include<type_traits>

#ifdef LOCAL
#  include "debug_print.hpp"
#  define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)
#else
#  define debug(...) (static_cast<void>(0))
#endif

using namespace std;
#define rep1(a)          for(int i = 0; i < a; i++)
#define rep2(i, a)       for(int i = 0; i < a; i++)
#define rep3(i, a, b)    for(int i = a; i < b; i++)
#define rep4(i, a, b, c) for(int i = a; i < b; i += c)
#define overload4(a, b, c, d, e, ...) e
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define rrep1(a)          for(int i = (a)-1; i >= 0; i--)
#define rrep2(i, a)       for(int i = (a)-1; i >= 0; i--)
#define rrep3(i, a, b)    for(int i = (b)-1; i >= a; i--)
#define rrep4(i, a, b, c) for(int i = (b)-1; i >= a; i -= c)
#define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__)
#define ALL(v) v.begin(), v.end()
#define RALL(v) v.rbegin(), v.rend()
#define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() );
#define pb push_back
using ll = long long;
using D = double;
using LD = long double;
using P = pair<int, int>;
using vi = vector<int>;
using vl = vector<ll>;
template <class T> using vc = vector<T>;
template <class T> using vvc = vector<vc<T>>;
template <class T> using vvvc = vector<vvc<T>>;
template <class T> using vvvvc = vector<vvvc<T>>;
template <class T> using vvvvvc = vector<vvvvc<T>>;
#define vv(type, name, h, ...) \
  vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...)   \
  vector<vector<vector<type>>> name( \
      h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...)       \
  vector<vector<vector<vector<type>>>> name( \
      a, vector<vector<vector<type>>>(       \
             b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))
template<typename T> using PQ = priority_queue<T,vector<T>>;
template<typename T> using minPQ = priority_queue<T, vector<T>, greater<T>>;
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }
void yesno(bool flag) {cout << (flag?"Yes":"No") << "\n";}

template<typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
    os << p.first << " " << p.second;
    return os;
}
template<typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
    is >> p.first >> p.second;
    return is;
}

template<typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
    int s = (int)v.size();
    for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
    return os;
}
template<typename T>
istream &operator>>(istream &is, vector<T> &v) {
    for (auto &x : v) is >> x;
    return is;
}
void in() {}
template<typename T, class... U>
void in(T &t, U &...u) {
    cin >> t;
    in(u...);
}
void out() { cout << "\n"; }
template<typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
    cout << t;
    if (sizeof...(u)) cout << sep;
    out(u...);
}
void outr() {}
template<typename T, class... U, char sep = ' '>
void outr(const T &t, const U &...u) {
    cout << t;
    outr(u...);
}

#line 1 "structure/convex-hull-trick/dynamic-li-chao-tree.hpp"
/**
 * @brief Dynamic-Li-Chao-Tree
 *
 */
template <typename T, T x_low, T x_high, T id>
struct DynamicLiChaoTree {
  struct Line {
    T a, b;

    Line(T a, T b) : a(a), b(b) {}

    inline T get(T x) const { return a * x + b; }
  };

  struct Node {
    Line x;
    Node *l, *r;

    Node(const Line &x) : x{x}, l{nullptr}, r{nullptr} {}
  };

  Node *root;

  DynamicLiChaoTree() : root{nullptr} {}

  Node *add_line(Node *t, Line &x, const T &l, const T &r, const T &x_l,
                 const T &x_r) {
    if (!t) return new Node(x);

    T t_l = t->x.get(l), t_r = t->x.get(r);

    if (t_l <= x_l && t_r <= x_r) {
      return t;
    } else if (t_l >= x_l && t_r >= x_r) {
      t->x = x;
      return t;
    } else {
      T m = (l + r) / 2;
      if (m == r) --m;
      T t_m = t->x.get(m), x_m = x.get(m);
      if (t_m > x_m) {
        swap(t->x, x);
        if (x_l >= t_l)
          t->l = add_line(t->l, x, l, m, t_l, t_m);
        else
          t->r = add_line(t->r, x, m + 1, r, t_m + x.a, t_r);
      } else {
        if (t_l >= x_l)
          t->l = add_line(t->l, x, l, m, x_l, x_m);
        else
          t->r = add_line(t->r, x, m + 1, r, x_m + x.a, x_r);
      }
      return t;
    }
  }

  void add_line(const T &a, const T &b) {
    Line x(a, b);
    root = add_line(root, x, x_low, x_high, x.get(x_low), x.get(x_high));
  }

  Node *add_segment(Node *t, Line &x, const T &a, const T &b, const T &l,
                    const T &r, const T &x_l, const T &x_r) {
    if (r < a || b < l) return t;
    if (a <= l && r <= b) {
      Line y{x};
      return add_line(t, y, l, r, x_l, x_r);
    }
    if (t) {
      T t_l = t->x.get(l), t_r = t->x.get(r);
      if (t_l <= x_l && t_r <= x_r) return t;
    } else {
      t = new Node(Line(0, id));
    }
    T m = (l + r) / 2;
    if (m == r) --m;
    T x_m = x.get(m);
    t->l = add_segment(t->l, x, a, b, l, m, x_l, x_m);
    t->r = add_segment(t->r, x, a, b, m + 1, r, x_m + x.a, x_r);
    return t;
  }

  void add_segment(const T &l, const T &r, const T &a, const T &b) {
    Line x(a, b);
    root = add_segment(root, x, l, r - 1, x_low, x_high, x.get(x_low),
                       x.get(x_high));
  }

  T query(const Node *t, const T &l, const T &r, const T &x) const {
    if (!t) return id;
    if (l == r) return t->x.get(x);
    T m = (l + r) / 2;
    if (m == r) --m;
    if (x <= m)
      return min(t->x.get(x), query(t->l, l, m, x));
    else
      return min(t->x.get(x), query(t->r, m + 1, r, x));
  }

  T query(const T &x) const { return query(root, x_low, x_high, x); }
};

int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    int n,m; in(n,m);
    vector<ll> w(n); in(w);
    vector<vector<pair<int,ll>>> g(n);
    rep(i,m){
        int u,v; ll t; in(u,v,t);
        u--; v--;
        g[u].pb({v,t});
        g[v].pb({u,t});
    }
    const ll INF = 4e18;
    vector<ll> d(n,INF),e(n,INF);
    d[0] = e[n-1] = 0;
    minPQ<pair<ll,int>> pq;
    pq.push({0,0});
    while(pq.size()){
        auto [cd,cv] = pq.top(); pq.pop();
        if(d[cv] > cd) continue;
        for(auto [nv, w] : g[cv]){
            if(d[nv] > w+cd){
                d[nv]=w+cd;
                pq.push({d[nv],nv});
            }
        }
    }
    pq.push({0,n-1});
    while(pq.size()){
        auto [cd,cv] = pq.top(); pq.pop();
        if(e[cv] > cd) continue;
        for(auto [nv, w] : g[cv]){
            if(e[nv] > w+cd){
                e[nv]=w+cd;
                pq.push({e[nv],nv});
            }
        }
    }
    DynamicLiChaoTree<ll,0,1010101010,INF> t;
    rep(i,n)if(e[i]!=INF) t.add_line(w[i],e[i]);
    ll ans = min(w[0]*w[n-1],d[n-1]);
    rep(i,n)if(d[i]!=INF){
        chmin(ans, t.query(w[i])+d[i]);
    }
    out(ans);
}
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