結果

問題 No.2764 Warp Drive Spacecraft
ユーザー apricityapricity
提出日時 2024-08-07 16:44:59
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
TLE  
実行時間 -
コード長 7,525 bytes
コンパイル時間 1,953 ms
コンパイル使用メモリ 153,420 KB
実行使用メモリ 25,796 KB
最終ジャッジ日時 2024-08-07 16:45:12
合計ジャッジ時間 13,108 ms
ジャッジサーバーID
(参考情報)
judge3 / judge2
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 1 ms
13,880 KB
testcase_01 AC 1 ms
5,376 KB
testcase_02 AC 2 ms
5,376 KB
testcase_03 AC 1 ms
5,376 KB
testcase_04 AC 2 ms
5,376 KB
testcase_05 AC 1 ms
5,376 KB
testcase_06 AC 2 ms
5,376 KB
testcase_07 AC 2 ms
5,376 KB
testcase_08 AC 1 ms
5,376 KB
testcase_09 AC 2 ms
5,376 KB
testcase_10 AC 2 ms
5,376 KB
testcase_11 AC 2 ms
5,376 KB
testcase_12 AC 2 ms
5,376 KB
testcase_13 AC 2 ms
5,376 KB
testcase_14 AC 1 ms
5,376 KB
testcase_15 AC 2 ms
5,376 KB
testcase_16 AC 112 ms
22,828 KB
testcase_17 AC 105 ms
22,772 KB
testcase_18 AC 100 ms
22,756 KB
testcase_19 AC 192 ms
19,420 KB
testcase_20 AC 199 ms
20,452 KB
testcase_21 AC 207 ms
20,420 KB
testcase_22 AC 210 ms
20,316 KB
testcase_23 AC 209 ms
19,424 KB
testcase_24 AC 235 ms
20,340 KB
testcase_25 AC 203 ms
20,272 KB
testcase_26 AC 294 ms
24,248 KB
testcase_27 AC 308 ms
24,220 KB
testcase_28 AC 284 ms
24,388 KB
testcase_29 AC 324 ms
24,520 KB
testcase_30 AC 284 ms
24,200 KB
testcase_31 AC 309 ms
24,932 KB
testcase_32 AC 293 ms
25,052 KB
testcase_33 AC 110 ms
15,104 KB
testcase_34 AC 99 ms
15,232 KB
testcase_35 AC 105 ms
15,104 KB
testcase_36 AC 117 ms
22,784 KB
testcase_37 TLE -
testcase_38 -- -
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/convex-hull-trick-add-monotone.hpp"
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(); }

  static constexpr int sgn(T x) { return x == 0 ? 0 : (x < 0 ? -1 : 1); }

  static constexpr T floor_div(T n, T d) {
    return n / d - ((n ^ d) < 0 and n % d != 0);
  }

  static constexpr 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);
    if constexpr (is_integral<T>::value) {
      return floor_div(b.S - a.S, a.F - b.F) >= floor_div(c.S - b.S, b.F - c.F);
    } else {
      return (b.F - a.F) * sgn(c.S - b.S) / abs(b.S - a.S) >=
             (c.F - b.F) * sgn(b.S - a.S) / 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);
    }
  }

  static constexpr T get_y(const P &a, const T &x) { return a.F * x + a.S; }

  T query(T x) const {
    assert(!empty());
    int l = -1, r = H.size() - 1;
    while (l + 1 < r) {
      int m = (l + r) >> 1;
      if (get_y(H[m], x) >= get_y(H[m + 1], x))
        l = m;
      else
        r = m;
    }
    if (isMin) return get_y(H[r], x);
    return -get_y(H[r], x);
  }

  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);
  }

  T query_monotone_dec(T x) {
    assert(!empty());
    while (H.size() >= 2 && get_y(H.back(), x) >= get_y(H[H.size() - 2], x))
      H.pop_back();
    if (isMin) return get_y(H.back(), x);
    return -get_y(H.back(), x);
  }

#undef F
#undef S
};

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});
            }
        }
    }
    ConvexHullTrickAddMonotone<ll,true> t;
    vector<int> idx(n); iota(ALL(idx),0);
    sort(ALL(idx), [&] (const int i, const int j){
        return w[i] < w[j];
    });
    rep(i,n)if(e[idx[i]]!=INF) t.add(w[idx[i]],e[idx[i]]);
    ll ans = min(w[0]*w[n-1],d[n-1]);
    rep(i,n)if(d[idx[i]]!=INF and !t.empty()){
        chmin(ans, t.query_monotone_inc(w[idx[i]])+d[idx[i]]);
    }
    out(ans);
}
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