結果

問題 No.2764 Warp Drive Spacecraft
ユーザー 👑 binap
提出日時 2024-04-29 01:59:02
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 754 ms / 3,000 ms
コード長 4,482 bytes
コンパイル時間 2,810 ms
コンパイル使用メモリ 221,792 KB
最終ジャッジ日時 2025-02-21 09:24:25
ジャッジサーバーID
（参考情報） 		judge3 / judge5
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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);}
// https://kopricky.github.io/code/DataStructure_Advanced/dynamic_convex_hull_trick.html
template<typename T> class CHT {
private:
    struct node {
        node *left, *right;
        static const T inf = numeric_limits<T>::max();
        T a, b;
        node() : node(0, inf){}
        node(const T _a, const T _b)
            : left(nullptr), right(nullptr), a(_a), b(_b){}
        T f(const T x) const { return a * x + b; }
    };
    static void swap(node *x, node *y){
        std::swap(x->a, y->a), std::swap(x->b, y->b);
    }
    void _add_line(node *cur, node *nw, T l, T r){
        while(true){
            if(nw->f(l) < cur->f(l)) swap(cur, nw);
            if(cur->f(r - 1) <= nw->f(r - 1)) break;
            const T mid = (l + r) / 2;
            if(cur->f(mid) <= nw->f(mid)){
                if(!cur->right){
                    cur->right = new node(*nw);
                    break;
                }else{
                    cur = cur->right, l = mid;
                }
            }else{
                swap(cur, nw);
                if(!cur->left){
                    cur->left = new node(*nw);
                    break;
                }else{
                    cur = cur->left, r = mid;
                }
            }
        }
    }
    T query(node *cur, const T k, T l, T r) const {
        T ans = numeric_limits<T>::max();
        while(cur){
            ans = min(ans, cur->f(k));
            const T mid = (l + r) / 2;
            if(k < mid){
                cur = cur->left, r = mid;
            }else{
                cur = cur->right, l = mid;
            }
        }
        return ans;
    }
    void clear(node *cur){
        if(cur->left) clear(cur->left);
        if(cur->right) clear(cur->right);
        delete cur;
    }
    const T lpos, rpos;
    node *root;
public:
    CHT(const T _lpos, const T _rpos) : lpos(_lpos), rpos(_rpos), root(new node()){
        assert(lpos < rpos);
    }
    // ~CHT(){ clear(root); }
    // f(x) = a * x + b を挿入
    void add_line(const T a, const T b){
        node nw(a, b);
        return _add_line(root, &nw, lpos, rpos);
    }
    // x = k での最小値
    T query(const T k) const {
        return query(root, k, lpos, rpos);
    }
};
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];
    CHT<long long> cht(0, 1000000000);
    vector<int> asc(n);
    for(int i = 0; i < n; i++) asc[i] = i;
    for(int i = 0; i < n; i++){
        if(dist_t[i] < INF) cht.add_line(w[i], dist_t[i]);
    }
    for(int i = 0; i < n; i++){
        if(dist_s[i] < INF) chmin(ans, dist_s[i] + cht.query(w[i]));
    }
    cout << ans << "\n";
    return 0;
}
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