結果

問題 No.2764 Warp Drive Spacecraft
ユーザー 👑 binapbinap
提出日時 2024-04-29 10:57:11
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 691 ms / 3,000 ms
コード長 3,222 bytes
コンパイル時間 3,196 ms
コンパイル使用メモリ 241,684 KB
実行使用メモリ 36,140 KB
最終ジャッジ日時 2024-05-18 00:09:31
合計ジャッジ時間 16,582 ms
ジャッジサーバーID
(参考情報)
judge1 / judge4
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
6,812 KB
testcase_01 AC 2 ms
6,944 KB
testcase_02 AC 2 ms
6,944 KB
testcase_03 AC 2 ms
6,944 KB
testcase_04 AC 2 ms
6,940 KB
testcase_05 AC 2 ms
6,944 KB
testcase_06 AC 2 ms
6,940 KB
testcase_07 AC 2 ms
6,944 KB
testcase_08 AC 2 ms
6,940 KB
testcase_09 AC 2 ms
6,940 KB
testcase_10 AC 3 ms
6,940 KB
testcase_11 AC 2 ms
6,940 KB
testcase_12 AC 3 ms
6,944 KB
testcase_13 AC 3 ms
6,940 KB
testcase_14 AC 2 ms
6,940 KB
testcase_15 AC 2 ms
6,940 KB
testcase_16 AC 320 ms
36,140 KB
testcase_17 AC 319 ms
35,592 KB
testcase_18 AC 311 ms
35,308 KB
testcase_19 AC 515 ms
24,036 KB
testcase_20 AC 517 ms
25,352 KB
testcase_21 AC 521 ms
24,596 KB
testcase_22 AC 515 ms
24,420 KB
testcase_23 AC 516 ms
25,740 KB
testcase_24 AC 515 ms
24,472 KB
testcase_25 AC 522 ms
26,104 KB
testcase_26 AC 674 ms
33,672 KB
testcase_27 AC 647 ms
34,268 KB
testcase_28 AC 665 ms
34,408 KB
testcase_29 AC 691 ms
34,976 KB
testcase_30 AC 662 ms
33,596 KB
testcase_31 AC 670 ms
35,344 KB
testcase_32 AC 673 ms
35,512 KB
testcase_33 AC 367 ms
22,168 KB
testcase_34 AC 367 ms
23,492 KB
testcase_35 AC 375 ms
21,028 KB
testcase_36 AC 317 ms
35,552 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<bits/stdc++.h>
using namespace std;

template<typename T> void chmin(T& a, T b){a = min(a, b);}

// thanks for Luzhiled's memo
// https://ei1333.github.io/luzhiled/snippets/dp/monotone-minima.html
template<typename T, typename Compare = less<T>>
pair<vector<int>, vector<T>> monotone_minima(int H, int W, const function<T(int, int)> &f, const Compare &comp = Compare()) {
	vector<int> idx(H);
	vector<T> res(H);
	function<void(int, int, int, int)> dfs = [&](int top, int bottom, int left, int right) {
		if(top > bottom) return;
		int line = (top + bottom) / 2;
		T ma = 0;
		int mi = -1;
		for(int i = left; i <= right; i++) {
			T cst = f(line, i);
			if(mi == -1 || comp(cst, ma)) {
				ma = cst;
				mi = i;
			}
		}
		idx[line] = mi;
		res[line] = ma;
		dfs(top, line - 1, left, mi);
		dfs(line + 1, bottom, mi, right);
	};
	dfs(0, H - 1, 0, W - 1);
	return make_pair(idx, res);
}

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;
	vector<long long> w(n);
	for(int i = 0; i < n; i++) cin >> w[i];
	Dijkstra<long long, long long> graph(n);
	for(int i = 0; i < m; i++){
		int u, v;
		long long t;
		cin >> u >> v >> t;
		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];
	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];
	});
	// W_pi * W_pj + dist(pj, N)
	// W[p1] <= W[p2] <= ... <= W[pN]
	function<long long(int, int)> f = [&](int i, int j){
		return w[asc[i]] * w[asc[(n - 1) - j]] + dist_t[asc[(n - 1) - j]];
	};
	auto [idx, val] = monotone_minima(n, n, f);
	for(int i = 0; i < n; i++){
		chmin(ans, dist_s[asc[i]] + val[i]);
	}
	cout << ans << "\n";
	return 0;
}
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