結果

問題 No.2764 Warp Drive Spacecraft
コンテスト
ユーザー torisasami4
提出日時 2024-05-17 22:49:35
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 365 ms / 3,000 ms
コード長 9,419 bytes
コンパイル時間 2,409 ms
コンパイル使用メモリ 211,236 KB
最終ジャッジ日時 2025-02-21 15:14:25
ジャッジサーバーID
（参考情報） 		judge2 / judge3
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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 # 

// #define _GLIBCXX_DEBUG
// #pragma GCC optimize("O2,unroll-loops")
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < int(n); i++)
#define per(i, n) for (int i = (n)-1; 0 <= i; i--)
#define rep2(i, l, r) for (int i = (l); i < int(r); i++)
#define per2(i, l, r) for (int i = (r)-1; int(l) <= i; i--)
#define each(e, v) for (auto &e : v)
#define MM << " " <<
#define pb push_back
#define eb emplace_back
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define sz(x) (int)x.size()
template <typename T>
void print(const vector<T> &v, T x = 0) {
    int n = v.size();
    for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' ');
    if (v.empty()) cout << '\n';
}
using ll = long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
template <typename T>
bool chmax(T &x, const T &y) {
    return (x < y) ? (x = y, true) : false;
}
template <typename T>
bool chmin(T &x, const T &y) {
    return (x > y) ? (x = y, true) : false;
}
template <class T>
using minheap = std::priority_queue<T, std::vector<T>, std::greater<T>>;
template <class T>
using maxheap = std::priority_queue<T>;
template <typename T>
int lb(const vector<T> &v, T x) {
    return lower_bound(begin(v), end(v), x) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, T x) {
    return upper_bound(begin(v), end(v), x) - begin(v);
}
template <typename T>
void rearrange(vector<T> &v) {
    sort(begin(v), end(v));
    v.erase(unique(begin(v), end(v)), end(v));
}

// __int128_t gcd(__int128_t a, __int128_t b) {
//     if (a == 0)
//         return b;
//     if (b == 0)
//         return a;
//     __int128_t cnt = a % b;
//     while (cnt != 0) {
//         a = b;
//         b = cnt;
//         cnt = a % b;
//     }
//     return b;
// }

struct Union_Find_Tree {
    vector<int> data;
    const int n;
    int cnt;

    Union_Find_Tree(int n) : data(n, -1), n(n), cnt(n) {}

    int root(int x) {
        if (data[x] < 0) return x;
        return data[x] = root(data[x]);
    }

    int operator[](int i) { return root(i); }

    bool unite(int x, int y) {
        x = root(x), y = root(y);
        if (x == y) return false;
        // if (data[x] > data[y]) swap(x, y);
        data[x] += data[y], data[y] = x;
        cnt--;
        return true;
    }

    int size(int x) { return -data[root(x)]; }

    int count() { return cnt; };

    bool same(int x, int y) { return root(x) == root(y); }

    void clear() {
        cnt = n;
        fill(begin(data), end(data), -1);
    }
};

template <int mod>
struct Mod_Int {
    int x;

    Mod_Int() : x(0) {}

    Mod_Int(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

    static int get_mod() { return mod; }

    Mod_Int &operator+=(const Mod_Int &p) {
        if ((x += p.x) >= mod) x -= mod;
        return *this;
    }

    Mod_Int &operator-=(const Mod_Int &p) {
        if ((x += mod - p.x) >= mod) x -= mod;
        return *this;
    }

    Mod_Int &operator*=(const Mod_Int &p) {
        x = (int)(1LL * x * p.x % mod);
        return *this;
    }

    Mod_Int &operator/=(const Mod_Int &p) {
        *this *= p.inverse();
        return *this;
    }

    Mod_Int &operator++() { return *this += Mod_Int(1); }

    Mod_Int operator++(int) {
        Mod_Int tmp = *this;
        ++*this;
        return tmp;
    }

    Mod_Int &operator--() { return *this -= Mod_Int(1); }

    Mod_Int operator--(int) {
        Mod_Int tmp = *this;
        --*this;
        return tmp;
    }

    Mod_Int operator-() const { return Mod_Int(-x); }

    Mod_Int operator+(const Mod_Int &p) const { return Mod_Int(*this) += p; }

    Mod_Int operator-(const Mod_Int &p) const { return Mod_Int(*this) -= p; }

    Mod_Int operator*(const Mod_Int &p) const { return Mod_Int(*this) *= p; }

    Mod_Int operator/(const Mod_Int &p) const { return Mod_Int(*this) /= p; }

    bool operator==(const Mod_Int &p) const { return x == p.x; }

    bool operator!=(const Mod_Int &p) const { return x != p.x; }

    Mod_Int inverse() const {
        assert(*this != Mod_Int(0));
        return pow(mod - 2);
    }

    Mod_Int pow(long long k) const {
        Mod_Int now = *this, ret = 1;
        for (; k > 0; k >>= 1, now *= now) {
            if (k & 1) ret *= now;
        }
        return ret;
    }

    friend ostream &operator<<(ostream &os, const Mod_Int &p) {
        return os << p.x;
    }

    friend istream &operator>>(istream &is, Mod_Int &p) {
        long long a;
        is >> a;
        p = Mod_Int<mod>(a);
        return is;
    }
};

ll mpow(ll x, ll n, ll mod) {
    ll ans = 1;
    x %= mod;
    while (n != 0) {
        if (n & 1) ans = ans * x % mod;
        x = x * x % mod;
        n = n >> 1;
    }
    ans %= mod;
    return ans;
}

template <typename T>
T modinv(T a, const T &m) {
    T b = m, u = 1, v = 0;
    while (b > 0) {
        T t = a / b;
        swap(a -= t * b, b);
        swap(u -= t * v, v);
    }
    return u >= 0 ? u % m : (m - (-u) % m) % m;
}

ll divide_int(ll a, ll b) {
    if (b < 0) a = -a, b = -b;
    return (a >= 0 ? a / b : (a - b + 1) / b);
}

// const int MOD = 1000000007;
const int MOD = 998244353;
using mint = Mod_Int<MOD>;

// ----- library -------
template <typename T, T min_x, T max_x, bool is_min = true>
struct Li_Chao_Tree {
    struct Line {
        T a, b;

        Line(const T &a, const T &b) : a(a), b(b) {}

        T get(const T &x) const { return a * x + b; }
    };

    struct Node {
        Node *lch, *rch;
        Line l;

        Node(const Line &l) : lch(NULL), rch(NULL), l(l) {}

        Node(const T &a, const T &b) : lch(NULL), rch(NULL), l(a, b) {}
    };

    Node *root;
    const T INF_T = numeric_limits<T>::max() / 2;

    Li_Chao_Tree() : root(NULL) {}

    ~Li_Chao_Tree() { rec_delete(root); }

    void rec_delete(Node *now) {
        if (!now) return;
        rec_delete(now->lch), rec_delete(now->rch);
        delete now;
    }

    Node *add_line(const Line &k, Node *now, const T &l, const T &r) {
        if (!now) return new Node(k);
        T l1 = now->l.get(l), l2 = k.get(l);
        T r1 = now->l.get(r), r2 = k.get(r);
        if (l1 <= l2 && r1 <= r2) return now;
        if (l1 >= l2 && r1 >= r2) {
            now->l = k;
            return now;
        }
        T m = (l + r - 1) / 2;
        T m1 = now->l.get(m), m2 = k.get(m);
        if (m1 > m2) {
            if (l1 <= l2) {
                now->lch = add_line(now->l, now->lch, l, m);
            } else {
                now->rch = add_line(now->l, now->rch, m + 1, r);
            }
            now->l = k;
        } else {
            if (l1 >= l2) {
                now->lch = add_line(k, now->lch, l, m);
            } else {
                now->rch = add_line(k, now->rch, m + 1, r);
            }
        }
        return now;
    }

    // 直線 y = ax+b を追加
    void add_line(const T &a, const T &b) {
        Line k(is_min ? a : -a, is_min ? b : -b);
        root = add_line(k, root, min_x, max_x);
    }

    Node *add_segment(const T &s, const T &t, const Line &k, Node *now, const T &l, const T &r) {
        if (r < s || t < l) return now;
        if (s <= l && r <= t) return add_line(k, now, l, r);
        T m = (l + r - 1) / 2;
        if (!now) now = new Node(0, INF_T);
        now->lch = add_segment(s, t, k, now->lch, l, m);
        now->rch = add_segment(s, t, k, now->rch, m + 1, r);
        return now;
    }

    // [l,r) に直線 y = ax+b を追加
    void add_segment(const T &l, const T &r, const T &a, const T &b) {
        Line k(is_min ? a : -a, is_min ? b : -b);
        root = add_segment(l, r - 1, k, root, min_x, max_x);
    }

    T query(const T &x, Node *now, const T &l, const T &r) const {
        if (!now) return INF_T;
        if (l == r) return now->l.get(x);
        T m = (l + r - 1) / 2;
        if (x <= m) return min(now->l.get(x), query(x, now->lch, l, m));
        return min(now->l.get(x), query(x, now->rch, m + 1, r));
    }

    T query(const T &x) const {
        T ret = query(x, root, min_x, max_x);
        return is_min ? ret : -ret;
    }
};
// ----- library -------

int main() {
    ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    cout << fixed << setprecision(15);

    int n, m;
    cin >> n >> m;
    vector<ll> w(n);
    rep(i, n) cin >> w[i];
    vector<vector<pair<int, ll>>> g(n);
    rep(i, m) {
        int u, v;
        ll t;
        cin >> u >> v >> t;
        u--, v--;
        g[u].eb(v, t);
        g[v].eb(u, t);
    }
    vector<ll> d1(n, 3e18), dn(n, 3e18);
    minheap<pair<ll, int>> que;
    auto upd1 = [&](int i, ll d) {
        if (chmin(d1[i], d))
            que.emplace(d, i);
    };
    upd1(0, 0);
    while (sz(que)) {
        auto [nd, now] = que.top();
        que.pop();
        if (d1[now] != nd)
            continue;
        for (auto [to, cost] : g[now]) {
            upd1(to, nd + cost);
        }
    }
    auto updn = [&](int i, ll d) {
        if (chmin(dn[i], d))
            que.emplace(d, i);
    };
    updn(n - 1, 0);
    while (sz(que)) {
        auto [nd, now] = que.top();
        que.pop();
        if (dn[now] != nd)
            continue;
        for (auto [to, cost] : g[now]) {
            updn(to, nd + cost);
        }
    }
    Li_Chao_Tree<ll, 0, ll(2e9)> lct;
    rep(i, n) lct.add_line(w[i], dn[i]);
    ll ans = dn[0];
    rep(i, n) chmin(ans, lct.query(w[i]) + d1[i]);
    cout << ans << endl;
}
0