#977904 (C++17) No.2764 Warp Drive Spacecraft

提出ソース

結果

問題	No.2764 Warp Drive Spacecraft
ユーザー	👑 binap
提出日時	2024-04-28 23:52:11
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	905 ms / 3,000 ms
コード長	5,823 bytes
コンパイル時間	5,413 ms
コンパイル使用メモリ	297,772 KB
実行使用メモリ	43,880 KB
最終ジャッジ日時	2024-07-17 20:22:21
合計ジャッジ時間	24,945 ms
ジャッジサーバーID （参考情報）	judge5 / judge3

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 6,940 KB
testcase_02	AC	2 ms 6,940 KB
testcase_03	AC	2 ms 6,944 KB
testcase_04	AC	2 ms 6,944 KB
testcase_05	AC	2 ms 6,944 KB
testcase_06	AC	2 ms 6,940 KB
testcase_07	AC	2 ms 6,940 KB
testcase_08	AC	2 ms 6,940 KB
testcase_09	AC	2 ms 6,944 KB
testcase_10	AC	4 ms 6,944 KB
testcase_11	AC	2 ms 6,940 KB
testcase_12	AC	3 ms 6,940 KB
testcase_13	AC	3 ms 6,944 KB
testcase_14	AC	2 ms 6,940 KB
testcase_15	AC	2 ms 6,944 KB
testcase_16	AC	371 ms 40,564 KB
testcase_17	AC	371 ms 40,472 KB
testcase_18	AC	371 ms 41,892 KB
testcase_19	AC	741 ms 34,204 KB
testcase_20	AC	764 ms 34,152 KB
testcase_21	AC	748 ms 34,580 KB
testcase_22	AC	768 ms 34,000 KB
testcase_23	AC	736 ms 33,956 KB
testcase_24	AC	746 ms 34,068 KB
testcase_25	AC	727 ms 34,596 KB
testcase_26	AC	871 ms 41,496 KB
testcase_27	AC	844 ms 41,936 KB
testcase_28	AC	840 ms 42,276 KB
testcase_29	AC	855 ms 42,044 KB
testcase_30	AC	829 ms 40,868 KB
testcase_31	AC	905 ms 43,880 KB
testcase_32	AC	887 ms 42,760 KB
testcase_33	AC	594 ms 30,424 KB
testcase_34	AC	586 ms 30,180 KB
testcase_35	AC	598 ms 30,748 KB
testcase_36	AC	358 ms 40,296 KB
testcase_37	AC	384 ms 36,848 KB
testcase_38	AC	306 ms 30,752 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

raw source code

#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(2 <= 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;
}

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結果

テストケース

ソースコード