結果

問題 No.2764 Warp Drive Spacecraft
ユーザー 👑 rin204
提出日時 2024-05-18 01:33:31
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 341 ms / 3,000 ms
コード長 14,986 bytes
コンパイル時間 3,395 ms
コンパイル使用メモリ 270,288 KB
実行使用メモリ 26,064 KB
最終ジャッジ日時 2024-07-17 20:24:41
合計ジャッジ時間 10,694 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge3
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

// #pragma GCC target("avx2")
// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")
// #define INTERACTIVE
#include <bits/stdc++.h>
using namespace std;
namespace templates {
// type
using ll  = long long;
using ull = unsigned long long;
using Pii = pair<int, int>;
using Pil = pair<int, ll>;
using Pli = pair<ll, int>;
using Pll = pair<ll, ll>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using qp = priority_queue<T, vector<T>, greater<T>>;
// clang-format off
#define vec(T, A, ...) vector<T> A(__VA_ARGS__);
#define vvec(T, A, h, ...) vector<vector<T>> A(h, vector<T>(__VA_ARGS__));
#define vvvec(T, A, h1, h2, ...) vector<vector<vector<T>>> A(h1, vector<vector<T>>(h2, vector<T>(__VA_ARGS__)));
// clang-format on
// for loop
#define fori1(a) for (ll _ = 0; _ < (a); _++)
#define fori2(i, a) for (ll i = 0; i < (a); i++)
#define fori3(i, a, b) for (ll i = (a); i < (b); i++)
#define fori4(i, a, b, c) for (ll i = (a); ((c) > 0 || i > (b)) && ((c) < 0 || i < (b)); i += (c))
#define overload4(a, b, c, d, e, ...) e
#define fori(...) overload4(__VA_ARGS__, fori4, fori3, fori2, fori1)(__VA_ARGS__)
// declare and input
// clang-format off
#define INT(...) int __VA_ARGS__; inp(__VA_ARGS__);
#define LL(...) ll __VA_ARGS__; inp(__VA_ARGS__);
#define STRING(...) string __VA_ARGS__; inp(__VA_ARGS__);
#define CHAR(...) char __VA_ARGS__; inp(__VA_ARGS__);
#define DOUBLE(...) double __VA_ARGS__; STRING(str___); __VA_ARGS__ = stod(str___);
#define VEC(T, A, n) vector<T> A(n); inp(A);
#define VVEC(T, A, n, m) vector<vector<T>> A(n, vector<T>(m)); inp(A);
// clang-format on
// const value
const ll MOD1   = 1000000007;
const ll MOD9   = 998244353;
const double PI = acos(-1);
// other macro
#if !defined(RIN__LOCAL) && !defined(INTERACTIVE)
#define endl "\n"
#endif
#define spa ' '
#define len(A) ll(A.size())
#define all(A) begin(A), end(A)
// function
vector<char> stoc(string &S) {
    int n = S.size();
    vector<char> ret(n);
    for (int i = 0; i < n; i++) ret[i] = S[i];
    return ret;
}
string ctos(vector<char> &S) {
    int n      = S.size();
    string ret = "";
    for (int i = 0; i < n; i++) ret += S[i];
    return ret;
}
template <class T>
auto min(const T &a) {
    return *min_element(all(a));
}
template <class T>
auto max(const T &a) {
    return *max_element(all(a));
}
template <class T, class S>
auto clamp(T &a, const S &l, const S &r) {
    return (a > r ? r : a < l ? l : a);
}
template <class T, class S>
inline bool chmax(T &a, const S &b) {
    return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
    return (a > b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chclamp(T &a, const S &l, const S &r) {
    auto b = clamp(a, l, r);
    return (a != b ? a = b, 1 : 0);
}
template <typename T>
T sum(vector<T> &A) {
    T tot = 0;
    for (auto a : A) tot += a;
    return tot;
}
template <typename T>
vector<T> compression(vector<T> X) {
    sort(all(X));
    X.erase(unique(all(X)), X.end());
    return X;
}
// input and output
namespace io {
// __int128_t
std::ostream &operator<<(std::ostream &dest, __int128_t value) {
    std::ostream::sentry s(dest);
    if (s) {
        __uint128_t tmp = value < 0 ? -value : value;
        char buffer[128];
        char *d = std::end(buffer);
        do {
            --d;
            *d = "0123456789"[tmp % 10];
            tmp /= 10;
        } while (tmp != 0);
        if (value < 0) {
            --d;
            *d = '-';
        }
        int len = std::end(buffer) - d;
        if (dest.rdbuf()->sputn(d, len) != len) {
            dest.setstate(std::ios_base::badbit);
        }
    }
    return dest;
}
// vector<T>
template <typename T>
istream &operator>>(istream &is, vector<T> &A) {
    for (auto &a : A) is >> a;
    return is;
}
template <typename T>
ostream &operator<<(ostream &os, vector<T> &A) {
    for (size_t i = 0; i < A.size(); i++) {
        os << A[i];
        if (i != A.size() - 1) os << ' ';
    }
    return os;
}
// vector<vector<T>>
template <typename T>
istream &operator>>(istream &is, vector<vector<T>> &A) {
    for (auto &a : A) is >> a;
    return is;
}
template <typename T>
ostream &operator<<(ostream &os, vector<vector<T>> &A) {
    for (size_t i = 0; i < A.size(); i++) {
        os << A[i];
        if (i != A.size() - 1) os << endl;
    }
    return os;
}
// pair<S, T>
template <typename S, typename T>
istream &operator>>(istream &is, pair<S, T> &A) {
    is >> A.first >> A.second;
    return is;
}
template <typename S, typename T>
ostream &operator<<(ostream &os, pair<S, T> &A) {
    os << A.first << ' ' << A.second;
    return os;
}
// vector<pair<S, T>>
template <typename S, typename T>
istream &operator>>(istream &is, vector<pair<S, T>> &A) {
    for (size_t i = 0; i < A.size(); i++) {
        is >> A[i];
    }
    return is;
}
template <typename S, typename T>
ostream &operator<<(ostream &os, vector<pair<S, T>> &A) {
    for (size_t i = 0; i < A.size(); i++) {
        os << A[i];
        if (i != A.size() - 1) os << endl;
    }
    return os;
}
// tuple
template <typename T, size_t N>
struct TuplePrint {
    static ostream &print(ostream &os, const T &t) {
        TuplePrint<T, N - 1>::print(os, t);
        os << ' ' << get<N - 1>(t);
        return os;
    }
};
template <typename T>
struct TuplePrint<T, 1> {
    static ostream &print(ostream &os, const T &t) {
        os << get<0>(t);
        return os;
    }
};
template <typename... Args>
ostream &operator<<(ostream &os, const tuple<Args...> &t) {
    TuplePrint<decltype(t), sizeof...(Args)>::print(os, t);
    return os;
}
// io functions
void FLUSH() {
    cout << flush;
}
void print() {
    cout << endl;
}
template <class Head, class... Tail>
void print(Head &&head, Tail &&...tail) {
    cout << head;
    if (sizeof...(Tail)) cout << spa;
    print(std::forward<Tail>(tail)...);
}
template <typename T, typename S>
void prisep(vector<T> &A, S sep) {
    int n = A.size();
    for (int i = 0; i < n; i++) {
        cout << A[i];
        if (i != n - 1) cout << sep;
    }
    cout << endl;
}
template <typename T, typename S>
void priend(T A, S end) {
    cout << A << end;
}
template <typename T>
void prispa(T A) {
    priend(A, spa);
}
template <typename T, typename S>
bool printif(bool f, T A, S B) {
    if (f)
        print(A);
    else
        print(B);
    return f;
}
template <class... T>
void inp(T &...a) {
    (cin >> ... >> a);
}
} // namespace io
using namespace io;
// read graph
vector<vector<int>> read_edges(int n, int m, bool direct = false, int indexed = 1) {
    vector<vector<int>> edges(n, vector<int>());
    for (int i = 0; i < m; i++) {
        INT(u, v);
        u -= indexed;
        v -= indexed;
        edges[u].push_back(v);
        if (!direct) edges[v].push_back(u);
    }
    return edges;
}
vector<vector<int>> read_tree(int n, int indexed = 1) {
    return read_edges(n, n - 1, false, indexed);
}
template <typename T = long long>
vector<vector<pair<int, T>>> read_wedges(int n, int m, bool direct = false, int indexed = 1) {
    vector<vector<pair<int, T>>> edges(n, vector<pair<int, T>>());
    for (int i = 0; i < m; i++) {
        INT(u, v);
        T w;
        inp(w);
        u -= indexed;
        v -= indexed;
        edges[u].push_back({v, w});
        if (!direct) edges[v].push_back({u, w});
    }
    return edges;
}
template <typename T = long long>
vector<vector<pair<int, T>>> read_wtree(int n, int indexed = 1) {
    return read_wedges<T>(n, n - 1, false, indexed);
}
// yes / no
namespace yesno {
// yes
inline bool yes(bool f = true) {
    cout << (f ? "yes" : "no") << endl;
    return f;
}
inline bool Yes(bool f = true) {
    cout << (f ? "Yes" : "No") << endl;
    return f;
}
inline bool YES(bool f = true) {
    cout << (f ? "YES" : "NO") << endl;
    return f;
}
// no
inline bool no(bool f = true) {
    cout << (!f ? "yes" : "no") << endl;
    return f;
}
inline bool No(bool f = true) {
    cout << (!f ? "Yes" : "No") << endl;
    return f;
}
inline bool NO(bool f = true) {
    cout << (!f ? "YES" : "NO") << endl;
    return f;
}
// possible
inline bool possible(bool f = true) {
    cout << (f ? "possible" : "impossible") << endl;
    return f;
}
inline bool Possible(bool f = true) {
    cout << (f ? "Possible" : "Impossible") << endl;
    return f;
}
inline bool POSSIBLE(bool f = true) {
    cout << (f ? "POSSIBLE" : "IMPOSSIBLE") << endl;
    return f;
}
// impossible
inline bool impossible(bool f = true) {
    cout << (!f ? "possible" : "impossible") << endl;
    return f;
}
inline bool Impossible(bool f = true) {
    cout << (!f ? "Possible" : "Impossible") << endl;
    return f;
}
inline bool IMPOSSIBLE(bool f = true) {
    cout << (!f ? "POSSIBLE" : "IMPOSSIBLE") << endl;
    return f;
}
// Alice Bob
inline bool Alice(bool f = true) {
    cout << (f ? "Alice" : "Bob") << endl;
    return f;
}
inline bool Bob(bool f = true) {
    cout << (f ? "Bob" : "Alice") << endl;
    return f;
}
// Takahashi Aoki
inline bool Takahashi(bool f = true) {
    cout << (f ? "Takahashi" : "Aoki") << endl;
    return f;
}
inline bool Aoki(bool f = true) {
    cout << (f ? "Aoki" : "Takahashi") << endl;
    return f;
}
} // namespace yesno
using namespace yesno;
} // namespace templates
using namespace templates;
template <typename T, T low, T upp, T inf>
struct DynamicLiChaoTree {
    struct Line {
        T a, b;
        Line(T a, T b) : a(a), b(b) {}
        inline T get(T x) const {
            return a * x + b;
        }
    };
    struct Node {
        Line x;
        Node *l, *r;
        Node(const Line &x) : x{x}, l{nullptr}, r{nullptr} {}
    };
    Node *root;
    DynamicLiChaoTree() : root{nullptr} {}
    Node *add_line(Node *t, Line &x, const T &l, const T &r, const T &xl, const T &xr) {
        if (!t) return new Node(x);
        T tl = t->x.get(l);
        T tr = t->x.get(r);
        if (tl <= xl && tr <= xr)
            return t;
        else if (tl >= xl && tr >= xr) {
            t->x = x;
            return t;
        } else {
            T m = (l + r) / 2;
            if (m == r) m--;
            T tm = t->x.get(m);
            T xm = x.get(m);
            if (tm > xm) {
                swap(t->x, x);
                if (xl >= tl)
                    t->l = add_line(t->l, x, l, m, tl, tm);
                else
                    t->r = add_line(t->r, x, m + 1, r, tm + x.a, tr);
            } else {
                if (tl >= xl)
                    t->l = add_line(t->l, x, l, m, xl, xm);
                else
                    t->r = add_line(t->r, x, m + 1, r, xm + x.a, xr);
            }
            return t;
        }
    }
    void add_line(const T &a, const T &b) {
        Line x(a, b);
        root = add_line(root, x, low, upp, x.get(low), x.get(upp));
    }
    Node *add_segment(Node *t, Line &x, const T &a, const T &b, const T &l, const T &r, const T &xl,
                      const T &xr) {
        if (r < a || b < l) return t;
        if (a <= l && r <= b) {
            Line y{x};
            return add_line(t, y, l, r, xl, xr);
        }
        if (t) {
            T tl = t->x.get(l);
            T tr = t->x.get(r);
            if (tl <= xl && tr <= xr) return t;
        } else {
            t = new Node(Line(0, inf));
        }
        T m = (l + r) / 2;
        if (m == r) m--;
        T xm = x.get(m);
        t->l = add_segment(t->l, x, a, b, l, m, xl, xm);
        t->r = add_segment(t->r, x, a, b, m + 1, r, xm + x.a, xr);
        return t;
    }
    void add_segment(const T &l, const T &r, const T &a, const T &b) {
        Line x(a, b);
        root = add_segment(root, x, l, r - 1, low, upp, x.get(low), x.get(upp));
    }
    T query(const Node *t, const T &l, const T &r, const T &x) const {
        if (!t) return inf;
        if (l == r) return t->x.get(x);
        T m = (l + r) / 2;
        if (m == r) m--;
        if (x <= m)
            return min(t->x.get(x), query(t->l, l, m, x));
        else
            return min(t->x.get(x), query(t->r, m + 1, r, x));
    }
    T query(const T &x) const {
        return query(root, low, upp, x);
    }
    ~DynamicLiChaoTree() {
        delete root;
    }
};
void solve() {
    LL(n, m);
    VEC(ll, W, n);
    auto edges = read_wedges(n, m);
    const ll inf = 1LL << 60;
    auto f       = [&](int s) -> vector<ll> {
        vec(ll, dist, n, inf);
        dist[s] = 0;
        qp<Pll> hq;
        hq.push({0, s});
        while (!hq.empty()) {
            auto [d, pos] = hq.top();
            hq.pop();
            if (dist[pos] < d) continue;
            for (auto [to, w] : edges[pos]) {
                if (chmin(dist[to], d + w)) {
                    hq.push({dist[to], to});
                }
            }
        }
        return dist;
    };
    auto ds = f(0);
    auto dt = f(n - 1);
    ll ans  = ds[n - 1];
    DynamicLiChaoTree<ll, 0, 1 << 30, inf> lc;
    fori(j, n) {
        lc.add_line(W[j], dt[j]);
    }
    fori(i, n) {
        auto res = lc.query(W[i]);
        chmin(ans, res + ds[i]);
        ll tmp = inf;
        fori(j, n) {
            chmin(tmp, ds[i] + dt[j] + W[i] * W[j]);
        }
    }
    print(ans);
}
int main() {
#ifndef INTERACTIVE
    cin.tie(0)->sync_with_stdio(0);
#endif
    // cout << fixed << setprecision(12);
    int t;
    t = 1;
    // cin >> t;
    while (t--) solve();
    return 0;
}
// // #pragma GCC target("avx2")
// // #pragma GCC optimize("O3")
// // #pragma GCC optimize("unroll-loops")
// // #define INTERACTIVE
//
// #include "kyopro-cpp/template.hpp"
//
// #include "data_structure/DynamicLiChaoTree.hpp"
//
// void solve() {
//     LL(n, m);
//     VEC(ll, W, n);
//     auto edges = read_wedges(n, m);
//
//     const ll inf = 1LL << 60;
//     auto f       = [&](int s) -> vector<ll> {
//         vec(ll, dist, n, inf);
//         dist[s] = 0;
//         qp<Pll> hq;
//         hq.push({0, s});
//         while (!hq.empty()) {
//             auto [d, pos] = hq.top();
//             hq.pop();
//             if (dist[pos] < d) continue;
//             for (auto [to, w] : edges[pos]) {
//                 if (chmin(dist[to], d + w)) {
//                     hq.push({dist[to], to});
//                 }
//             }
//         }
//         return dist;
//     };
//
//     auto ds = f(0);
//     auto dt = f(n - 1);
//     ll ans  = ds[n - 1];
//     DynamicLiChaoTree<ll, 0, 1 << 30, inf> lc;
//     fori(j, n) {
//         lc.add_line(W[j], dt[j]);
//     }
//     fori(i, n) {
//         auto res = lc.query(W[i]);
//         chmin(ans, res + ds[i]);
//
//         ll tmp = inf;
//         fori(j, n) {
//             chmin(tmp, ds[i] + dt[j] + W[i] * W[j]);
//         }
//     }
//     print(ans);
// }
//
// int main() {
// #ifndef INTERACTIVE
//     cin.tie(0)->sync_with_stdio(0);
// #endif
//     // cout << fixed << setprecision(12);
//     int t;
//     t = 1;
//     // cin >> t;
//     while (t--) solve();
//     return 0;
// }
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