結果

問題 No.2764 Warp Drive Spacecraft
ユーザー 👑 binap
提出日時 2024-04-29 10:57:11
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 804 ms / 3,000 ms
コード長 3,222 bytes
コンパイル時間 3,275 ms
コンパイル使用メモリ 229,216 KB
最終ジャッジ日時 2025-02-21 09:34:40
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
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ファイルパターン 結果
sample AC * 4
other AC * 35
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

#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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