結果

問題 No.2764 Warp Drive Spacecraft
ユーザー t98slider
提出日時 2024-05-18 10:42:58
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 372 ms / 3,000 ms
コード長 3,834 bytes
コンパイル時間 2,459 ms
コンパイル使用メモリ 209,780 KB
最終ジャッジ日時 2025-02-21 15:42:29
ジャッジサーバーID
（参考情報） 		judge2 / judge4
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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;
using ll = long long;
//min_ver
class LiChaoTree{
    struct Line{
        long long a, b;
        long long get(long long x){return a * x + b; }
        Line(long long a, long long b) : a(a), b(b) {}
    };
    struct Node {
        Node *left, *right;
        Line line;
        Node(Line line) : left(nullptr), right(nullptr), line(line) {}
    };
    const long long inf = 1ll << 60;
    const Line inf_line = Line{0, inf};
    Node *root;
    long long lx, rx;
    Node* _add_line(Node *nd, Line line, long long l, long long r){
        if(l == r) return nullptr;
        if(nd == nullptr) return new Node(line);
        long long m = (l + r) >> 1;
        bool left = (line.get(l) <= nd->line.get(l));
        bool mid = (line.get(m) <= nd->line.get(m));
        bool right = (line.get(r) <= nd->line.get(r));
        if(left && right)nd->line = line;
        if(left == right)return nd;
        if(mid) std::swap(nd->line, line);
        if(left != mid){
            nd->left = _add_line(nd->left, line, l, m);
        }else{
            nd->right = _add_line(nd->right, line, m, r);
        }
        return nd;
    }
    Node* _add_segment_line(long long a, long long b, Node *nd, Line line, long long l, long long r) {
        if(r <= a || b <= l) return nd;
        if(a <= l && r <= b) return _add_line(nd, line, l, r);
        if(nd == nullptr) nd = new Node(inf_line);
        long long m = (l + r) >> 1;
        nd->left = _add_segment_line(a, b, nd->left, line, l, m);
        nd->right = _add_segment_line(a, b, nd->right, line, m, r);
        return nd;
    }
    long long query(long long x, long long l, long long r){
        Node *nd = root;
        long long res = inf;
        while(r > l && nd != nullptr) {
            long long m = (l + r) >> 1;
            res = std::min(res, nd->line.get(x));
            if(x < m) {
                r = m;
                nd = nd->left;
            } else {
                l = m;
                nd = nd->right;
            }
        }
        return res;
    }
    public:
    // [xl, xr)
    LiChaoTree(long long lx, long long rx) : lx(lx), rx(rx), root(nullptr) {}
    void add_line(long long a, long long b) {
        Line line(a, b);
        root = _add_line(root, line, lx, rx);
    }
    void add_segment_line(long long a, long long b, long long l, long long r) {
        Line line = Line{a, b};
        root = _add_segment_line(l, r, root, line, lx, rx);
    }
    long long get(long long x) {
        return query(x, lx, rx);
    }
};
int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    int n, m;
    cin >> n >> m;
    vector<int> w(n);
    LiChaoTree LCT(0, 1 << 30);
    vector<ll> dp(n, 1ll << 60);
    vector<vector<pair<int,ll>>> g(n);
    priority_queue<pair<ll,int>, vector<pair<ll,int>>, greater<pair<ll,int>>> pq;
    for(auto &&v : w) cin >> v;
    for(int i = 0; i < m; i++){
        int u, v;
        ll t;
        cin >> u >> v >> t;
        u--, v--;
        g[u].emplace_back(v, t);
        g[v].emplace_back(u, t);
    }
    dp[0] = 0;
    pq.emplace(0, 0);
    while(!pq.empty()){
        auto [d, v] = pq.top();
        pq.pop();
        if(d > dp[v]) continue;
        LCT.add_line(w[v], d);
        for(auto &&[u, w] : g[v]){
            if(d + w >= dp[u]) continue;
            dp[u] = d + w;
            pq.emplace(dp[u], u);
        }
    }
    for(int i = 0; i < n; i++){
        dp[i] = min(dp[i], LCT.get(w[i]));
        pq.emplace(dp[i], i);
    }
    while(!pq.empty()){
        auto [d, v] = pq.top();
        pq.pop();
        if(d > dp[v]) continue;
        LCT.add_line(w[v], d);
        for(auto &&[u, w] : g[v]){
            if(d + w >= dp[u]) continue;
            dp[u] = d + w;
            pq.emplace(dp[u], u);
        }
    }
    cout << dp[n - 1] << '\n';
}
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