結果
| 問題 |
No.2764 Warp Drive Spacecraft
|
| コンテスト | |
| ユーザー |
👑  binap
|
| 提出日時 | 2024-04-28 23:33:49 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 761 ms / 3,000 ms |
| コード長 | 5,823 bytes |
| コンパイル時間 | 4,650 ms |
| コンパイル使用メモリ | 285,220 KB |
| 最終ジャッジ日時 | 2025-02-21 09:22:25 |
|
ジャッジサーバーID （参考情報） |
judge5 / judge4 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 4 |
| other | AC * 35 |
ソースコード
#include<bits/stdc++.h>
#include<atcoder/all>
#define rep(i,n) for(int i=0;i<n;i++)
using namespace std;
using namespace atcoder;
typedef long long ll;
typedef vector<int> vi;
typedef vector<long long> vl;
typedef vector<vector<int>> vvi;
typedef vector<vector<long long>> vvl;
typedef long double ld;
typedef pair<int, int> P;
ostream& operator<<(ostream& os, const modint& a) {os << a.val(); return os;}
template <int m> ostream& operator<<(ostream& os, const static_modint<m>& a) {os << a.val(); return os;}
template <int m> ostream& operator<<(ostream& os, const dynamic_modint<m>& a) {os << a.val(); return os;}
template<typename T> istream& operator>>(istream& is, vector<T>& v){int n = v.size(); assert(n > 0); rep(i, n) is >> v[i]; return is;}
template<typename U, typename T> ostream& operator<<(ostream& os, const pair<U, T>& p){os << p.first << ' ' << p.second; return os;}
template<typename T> ostream& operator<<(ostream& os, const vector<T>& v){int n = v.size(); rep(i, n) os << v[i] << (i == n - 1 ? "\n" : " "); return os;}
template<typename T> ostream& operator<<(ostream& os, const vector<vector<T>>& v){int n = v.size(); rep(i, n) os << v[i] << (i == n - 1 ? "\n" : ""); return os;}
template<typename T> void chmin(T& a, T b){a = min(a, b);}
template<typename T> void chmax(T& a, T b){a = max(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;
assert(1 <= n && n <= 200000);
assert(0 <= m && m <= 200000);
vector<long long> w(n);
for(int i = 0; i < n; i++) cin >> w[i];
for(int i = 0; i < n; i++) assert(1 <= w[i] && w[i] <= 1000000000);
set<pair<int, int>> set_for_assert;
Dijkstra<long long, long long> graph(n);
for(int i = 0; i < m; i++){
int u, v;
long long t;
cin >> u >> v >> t;
if(cin.fail()) assert(false);
assert(1 <= u && u < v && v <= n);
assert(1 <= t && t <= 1000000000000);
if(set_for_assert.find(make_pair(u, v)) != set_for_assert.end()) assert(false);
set_for_assert.insert(make_pair(u, v));
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;
}