結果

問題 No.2764 Warp Drive Spacecraft
ユーザー pitP
提出日時 2024-05-18 17:55:45
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 283 ms / 3,000 ms
コード長 5,246 bytes
コンパイル時間 4,632 ms
コンパイル使用メモリ 316,908 KB
実行使用メモリ 26,068 KB
最終ジャッジ日時 2024-07-17 20:24:55
合計ジャッジ時間 10,664 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge5
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>
#include <atcoder/all>
using namespace std;
using namespace atcoder;
istream &operator>>(istream &is, modint &a) { long long v; is >> v; a = v; return is; }
ostream &operator<<(ostream &os, const modint &a) { return os << a.val(); }
istream &operator>>(istream &is, modint998244353 &a) { long long v; is >> v; a = v; return is; }
ostream &operator<<(ostream &os, const modint998244353 &a) { return os << a.val(); }
istream &operator>>(istream &is, modint1000000007 &a) { long long v; is >> v; a = v; return is; }
ostream &operator<<(ostream &os, const modint1000000007 &a) { return os << a.val(); } 
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
#define FOR(i,l,r) for (int i = l;i < (int)(r); i++)
#define rep(i,n) for (int i = 0;i < (int)(n); i++)
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define my_sort(x) sort(x.begin(), x.end())
#define my_max(x) *max_element(all(x))
#define my_min(x) *min_element(all(x))
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
const int INF = (1<<30) - 1;
const ll LINF = (1LL<<62) - 1;
const int MOD = 998244353;
const int MOD2 = 1e9+7;
const double PI = acos(-1);
vector<int> di = {1,0,-1,0};
vector<int> dj = {0,1,0,-1};
#ifdef LOCAL
#  include <debug_print.hpp>
#  define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)
#else
#  define debug(...) (static_cast<void>(0))
#endif
using Edge = pair<ll, int>;
using Graph = vector<vector<Edge>>;
vector<ll> dijkstra(int st, Graph &g){
    int N = g.size();
    vector<ll> dist(N, LINF);
    dist[st] = 0ll;
    using P = pair<ll, int>;
    priority_queue<P, vector<P>, greater<P>> pq;
    pq.emplace(P{0ll, st});
    while(!pq.empty()){
        ll time = pq.top().first;
        int now = pq.top().second;
        pq.pop();
        if (time > dist[now])continue;
        for(auto e : g[now]){
            ll c = e.first;
            int nxt = e.second;
            if (c + time < dist[nxt]){
                dist[nxt] = c + time;
                pq.push(P{c + time, nxt});
            }
        }
    }
    return dist;
}
template<typename T> class ConvexHullTrick {
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:
    ConvexHullTrick(const T _lpos, const T _rpos) : lpos(_lpos), rpos(_rpos), root(new node()){
        assert(lpos < rpos);
    }
    // ~ConvexHullTrick(){ 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);
    }
};
// 最大値は add_line(-a, -b) で -query(x)
// https://ei1333.github.io/library/structure/convex-hull-trick/dynamic-li-chao-tree.hpp.html
int main(){
    cin.tie(0);
    ios_base::sync_with_stdio(false);
    int N, M; cin >> N >> M;
    vector<ll> W(N);
    rep(i,N) cin >> W[i];
    Graph g(N);
    rep(i,M){
        int u, v; cin >> u >> v;
        u--;
        v--;
        ll T; cin >> T;
        g[u].push_back({T, v});
        g[v].push_back({T, u});
    }
    auto dist1 = dijkstra(0, g);
    auto distN = dijkstra(N - 1, g);
    debug(dist1, distN);
    ConvexHullTrick<ll> cht(1, (ll)1e9);
    rep(j, N) cht.add_line(W[j], distN[j]);
    ll ans = dist1[N - 1];
    rep(i, N) {
        chmin(ans, dist1[i] + cht.query(W[i]));
        debug(dist1[i], cht.query(W[i]), W[i]);
    }
    cout << ans << endl;
}
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