結果

問題 No.2764 Warp Drive Spacecraft
ユーザー ecottea
提出日時 2024-07-16 22:41:43
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
TLE  
(最新)
AC  
(最初)
実行時間 -
コード長 14,027 bytes
コンパイル時間 4,902 ms
コンパイル使用メモリ 282,656 KB
実行使用メモリ 26,064 KB
最終ジャッジ日時 2024-07-17 10:03:30
合計ジャッジ時間 16,463 ms
ジャッジサーバーID
(参考情報)
judge2 / judge1
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 4
other AC * 33 TLE * 1
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 #
プレゼンテーションモードにする

#ifndef HIDDEN_IN_VS //
//
#define _CRT_SECURE_NO_WARNINGS
//
#include <bits/stdc++.h>
using namespace std;
//
using ll = long long; using ull = unsigned long long; // -2^63 2^63 = 9 * 10^18int -2^31 2^31 = 2 * 10^9
using pii = pair<int, int>; using pll = pair<ll, ll>; using pil = pair<int, ll>; using pli = pair<ll, int>;
using vi = vector<int>; using vvi = vector<vi>; using vvvi = vector<vvi>; using vvvvi = vector<vvvi>;
using vl = vector<ll>; using vvl = vector<vl>; using vvvl = vector<vvl>; using vvvvl = vector<vvvl>;
using vb = vector<bool>; using vvb = vector<vb>; using vvvb = vector<vvb>;
using vc = vector<char>; using vvc = vector<vc>; using vvvc = vector<vvc>;
using vd = vector<double>; using vvd = vector<vd>; using vvvd = vector<vvd>;
template <class T> using priority_queue_rev = priority_queue<T, vector<T>, greater<T>>;
using Graph = vvi;
//
const double PI = acos(-1);
int DX[4] = {1, 0, -1, 0}; // 4
int DY[4] = {0, 1, 0, -1};
int INF = 1001001001; ll INFL = 4004004003094073385LL; // (int)INFL = INF, (int)(-INFL) = -INF;
//
struct fast_io { fast_io() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } fastIOtmp;
//
#define all(a) (a).begin(), (a).end()
#define sz(x) ((int)(x).size())
#define lbpos(a, x) (int)distance((a).begin(), std::lower_bound(all(a), x))
#define ubpos(a, x) (int)distance((a).begin(), std::upper_bound(all(a), x))
#define Yes(b) {cout << ((b) ? "Yes\n" : "No\n");}
#define rep(i, n) for(int i = 0, i##_len = int(n); i < i##_len; ++i) // 0 n-1
#define repi(i, s, t) for(int i = int(s), i##_end = int(t); i <= i##_end; ++i) // s t
#define repir(i, s, t) for(int i = int(s), i##_end = int(t); i >= i##_end; --i) // s t
#define repe(v, a) for(const auto& v : (a)) // a
#define repea(v, a) for(auto& v : (a)) // a
#define repb(set, d) for(int set = 0, set##_ub = 1 << int(d); set < set##_ub; ++set) // d
#define repis(i, set) for(int i = lsb(set), bset##i = set; i >= 0; bset##i -= 1 << i, i = lsb(bset##i)) // set
#define repp(a) sort(all(a)); for(bool a##_perm = true; a##_perm; a##_perm = next_permutation(all(a))) // a
#define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());} //
#define EXIT(a) {cout << (a) << endl; exit(0);} //
#define inQ(x, y, u, l, d, r) ((u) <= (x) && (l) <= (y) && (x) < (d) && (y) < (r)) //
//
template <class T> inline ll powi(T n, int k) { ll v = 1; rep(i, k) v *= n; return v; }
template <class T> inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; } // true
    
template <class T> inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; } // true
    
template <class T> inline T getb(T set, int i) { return (set >> i) & T(1); }
template <class T> inline T smod(T n, T m) { n %= m; if (n < 0) n += m; return n; } // mod
//
template <class T, class U> inline istream& operator>>(istream& is, pair<T, U>& p) { is >> p.first >> p.second; return is; }
template <class T> inline istream& operator>>(istream& is, vector<T>& v) { repea(x, v) is >> x; return is; }
template <class T> inline vector<T>& operator--(vector<T>& v) { repea(x, v) --x; return v; }
template <class T> inline vector<T>& operator++(vector<T>& v) { repea(x, v) ++x; return v; }
#endif //
#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
#ifdef _MSC_VER
#include "localACL.hpp"
#endif
//using mint = modint1000000007;
using mint = modint998244353;
//using mint = modint; // mint::set_mod(m);
namespace atcoder {
inline istream& operator>>(istream& is, mint& x) { ll x_; is >> x_; x = x_; return is; }
inline ostream& operator<<(ostream& os, const mint& x) { os << x.val(); return os; }
}
using vm = vector<mint>; using vvm = vector<vm>; using vvvm = vector<vvm>; using vvvvm = vector<vvvm>; using pim = pair<int, mint>;
#endif
#ifdef _MSC_VER // Visual Studio
#include "local.hpp"
#else // gcc
inline int popcount(int n) { return __builtin_popcount(n); }
inline int popcount(ll n) { return __builtin_popcountll(n); }
inline int lsb(int n) { return n != 0 ? __builtin_ctz(n) : -1; }
inline int lsb(ll n) { return n != 0 ? __builtin_ctzll(n) : -1; }
template <size_t N> inline int lsb(const bitset<N>& b) { return b._Find_first(); }
inline int msb(int n) { return n != 0 ? (31 - __builtin_clz(n)) : -1; }
inline int msb(ll n) { return n != 0 ? (63 - __builtin_clzll(n)) : -1; }
#define dump(...)
#define dumpel(v)
#define dump_list(v)
#define dump_mat(v)
#define input_from_file(f)
#define output_to_file(f)
#define Assert(b) { if (!(b)) { vc MLE(1<<30); EXIT(MLE.back()); } } // RE MLE
#endif
//
/*
* to :
* cost :
*/
struct WEdge {
// verify : https://judge.yosupo.jp/problem/shortest_path
int to; //
ll cost; //
WEdge() : to(-1), cost(-INFL) {}
WEdge(int to, ll cost) : to(to), cost(cost) {}
//
operator int() const { return to; }
#ifdef _MSC_VER
friend ostream& operator<<(ostream& os, const WEdge& e) {
os << '(' << e.to << ',' << e.cost << ')';
return os;
}
#endif
};
//
/*
* WGraph g
* g[v] : v
*
* verify : https://judge.yosupo.jp/problem/shortest_path
*/
using WGraph = vector<vector<WEdge>>;
//O(n + m)
/*
* (, , ) n m
*
* n :
* m : n-1
* directed : false
* zero_indexed : 0-indexed false
*/
WGraph read_WGraph(int n, int m = -1, bool directed = false, bool zero_indexed = false) {
// verify : https://judge.yosupo.jp/problem/shortest_path
WGraph g(n);
if (m == -1) m = n - 1;
rep(j, m) {
int u, v; ll c;
cin >> u >> v >> c;
if (!zero_indexed) { --u; --v; }
g[u].push_back({ v, c });
if (!directed && u != v) g[v].push_back({ u, c });
}
return g;
}
//O(n + m log n)
/*
* g st INFL
*/
vl dijkstra(const WGraph& g, int st) {
// : https://snuke.hatenablog.com/entry/2021/02/22/102734
// verify : https://atcoder.jp/contests/tessoku-book/tasks/tessoku_book_bl
int n = sz(g);
vl dist(n, INFL); // st
dist[st] = 0;
// (st , )
priority_queue_rev<pli> q;
q.push({ 0, st });
while (!q.empty()) {
auto [c, s] = q.top(); q.pop();
// O(n^2)
// if (dist[s] < c) continue;
// 辿
repe(e, g[s]) if (chmin(dist[e.to], dist[s] + e.cost)) q.push({ dist[e.to], e.to });
}
return dist;
}
//Convex-Hull Trick
/*
* Convex_hull_trick<T>(bool max_flag = false) : O(1)
* max_flag = false[true] []
* T
*
* insert(T a, T b) : O(log n)
* y = a x + b
*
* T get(T x) : O(log n)
* a x + b []
*
*/
template <class T = ll>
class Convex_hull_trick_integer {
// : https://noshi91.hatenablog.com/entry/2021/03/23/200810
// 1
struct Line {
// y = a x + b
T a, b;
//
bool is_line;
// ()
mutable function<const Line* ()> getSuc;
Line(T a_, T b_, bool is_line = true) : a(a_), b(b_), is_line(is_line) {}
bool operator<(const Line& rhs) const {
// set lower_bound
//
//set 使
//
if (!rhs.is_line) {
const Line* suc = getSuc();
if (suc == nullptr) return false;
const T& x = rhs.a;
return (suc->a - a) * x + (suc->b - b) < T(0);
}
//
if (!is_line) {
const Line* suc = rhs.getSuc();
if (suc == nullptr) return true;
const T& x = a;
return (suc->a - rhs.a) * x + (suc->b - rhs.b) > T(0);
}
//
return a > rhs.a;
}
#ifdef _MSC_VER
friend ostream& operator<<(ostream& os, const Line& l) {
os << "y=";
if (l.a == T(1)) os << "x";
else if (l.a == T(0));
else if (l.a == T(-1)) os << "-x";
else os << l.a << "x";
if (l.a == T(0) || l.b < T(0)) os << l.b;
else if (l.b > T(0)) os << "+" << l.b;
return os;
}
#endif
};
set<Line> lines; //
// false true
bool max_flag;
public:
//
Convex_hull_trick_integer(bool max_flag = false) : max_flag(max_flag) {
// verify : https://judge.yosupo.jp/problem/line_add_get_min
}
// l : y = a x + b
void insert(T a, T b) {
// verify : https://judge.yosupo.jp/problem/line_add_get_min
// -1
if (max_flag) {
a = -a;
b = -b;
}
// nit : l lines.end()
auto nit = lines.lower_bound({ a, b });
// pit : l lines.end()
auto pit = (nit != lines.begin() ? prev(nit) : lines.end());
// pit l
if (pit != lines.end() && pit->a == a) {
// pit l
if (pit->b <= b) return;
// l pit
lines.erase(pit);
}
// l nit
else if (nit != lines.end() && a == nit->a) {
// nit l
if (nit->b <= b) return;
// l nit
lines.erase(nit);
}
// pit, l, nit
else if (pit != lines.end() && nit != lines.end()) {
// l
if ((b - pit->b) / (pit->a - a) >= (nit->b - b) / (a - nit->a)) return;
}
// l
auto it = lines.insert({ a, b }).first;
it->getSuc = [=] { return (next(it) == lines.end() ? nullptr : &*next(it)); };
// l l
if (it != lines.begin()) {
auto pit = prev(it);
while (pit != lines.begin()) {
// pit : l
// ppit : l
auto ppit = prev(pit);
// pit
if ((pit->b - ppit->b) / (ppit->a - pit->a) < (b - pit->b) / (pit->a - a)) break;
// pit
pit = prev(lines.erase(pit));
}
}
// l l
if (next(it) != lines.end()) {
auto nit = next(it);
while (next(nit) != lines.end()) {
// nit : l
// nnit : l
auto nnit = next(nit);
// nit
if ((nit->b - b) / (a - nit->a) < (nnit->b - nit->b) / (nit->a - nnit->a)) break;
// nit
nit = lines.erase(nit);
}
}
}
// a x + b []
T get(T x) {
// verify : https://judge.yosupo.jp/problem/line_add_get_min
Assert(!lines.empty());
auto it = lines.lower_bound(Line{ x, x, false });
if (!max_flag) return it->a * x + it->b;
else return -(it->a * x + it->b); // -1
}
#ifdef _MSC_VER
friend ostream& operator<<(ostream& os, const Convex_hull_trick_integer& cht) {
for (auto it = cht.lines.begin(); it != cht.lines.end(); it++) {
os << *it << (next(it) != cht.lines.end() ? "," : "");
}
return os;
}
#endif
};
int main() {
// input_from_file("input.txt");
// output_to_file("output.txt");
int n, m;
cin >> n >> m;
vl w(n);
cin >> w;
auto g = read_WGraph(n, m);
auto a = dijkstra(g, 0);
auto b = dijkstra(g, n - 1);
Convex_hull_trick_integer<ll> C;
rep(t, n) C.insert(w[t], b[t]);
ll res = a[n - 1];
rep(s, n) chmin(res, a[s] + C.get(w[s]));
cout << res << endl;
}
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