結果

問題 No.2764 Warp Drive Spacecraft
ユーザー tokusakuraitokusakurai
提出日時 2024-05-17 22:57:20
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 345 ms / 3,000 ms
コード長 8,623 bytes
コンパイル時間 2,499 ms
コンパイル使用メモリ 218,032 KB
実行使用メモリ 26,176 KB
最終ジャッジ日時 2024-07-17 20:24:10
合計ジャッジ時間 10,157 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge5
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
6,816 KB
testcase_01 AC 2 ms
6,940 KB
testcase_02 AC 2 ms
6,940 KB
testcase_03 AC 2 ms
6,940 KB
testcase_04 AC 2 ms
6,940 KB
testcase_05 AC 2 ms
6,940 KB
testcase_06 AC 2 ms
6,940 KB
testcase_07 AC 2 ms
6,944 KB
testcase_08 AC 2 ms
6,940 KB
testcase_09 AC 2 ms
6,940 KB
testcase_10 AC 2 ms
6,944 KB
testcase_11 AC 2 ms
6,940 KB
testcase_12 AC 3 ms
6,940 KB
testcase_13 AC 3 ms
6,944 KB
testcase_14 AC 2 ms
6,940 KB
testcase_15 AC 2 ms
6,940 KB
testcase_16 AC 108 ms
21,936 KB
testcase_17 AC 108 ms
22,004 KB
testcase_18 AC 106 ms
21,872 KB
testcase_19 AC 239 ms
20,068 KB
testcase_20 AC 250 ms
21,208 KB
testcase_21 AC 254 ms
20,288 KB
testcase_22 AC 250 ms
21,144 KB
testcase_23 AC 245 ms
20,072 KB
testcase_24 AC 253 ms
21,220 KB
testcase_25 AC 246 ms
21,164 KB
testcase_26 AC 345 ms
25,108 KB
testcase_27 AC 337 ms
25,104 KB
testcase_28 AC 335 ms
25,512 KB
testcase_29 AC 335 ms
25,456 KB
testcase_30 AC 328 ms
24,964 KB
testcase_31 AC 344 ms
26,064 KB
testcase_32 AC 341 ms
26,176 KB
testcase_33 AC 112 ms
15,344 KB
testcase_34 AC 111 ms
15,224 KB
testcase_35 AC 114 ms
15,360 KB
testcase_36 AC 101 ms
21,840 KB
testcase_37 AC 125 ms
19,252 KB
testcase_38 AC 99 ms
17,408 KB
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 # 

#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (n); i++)
#define per(i, n) for (int i = (n) - 1; i >= 0; i--)
#define rep2(i, l, r) for (int i = (l); i < (r); i++)
#define per2(i, l, r) for (int i = (r) - 1; i >= (l); 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()
using ll = long long;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;

template <typename T>
using minheap = priority_queue<T, vector<T>, greater<T>>;

template <typename T>
using maxheap = priority_queue<T>;

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 <typename T>
int flg(T x, int i) {
    return (x >> i) & 1;
}

int pct(int x) { return __builtin_popcount(x); }
int pct(ll x) { return __builtin_popcountll(x); }
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int botbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int botbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }

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';
}

template <typename T>
void printn(const vector<T> &v, T x = 0) {
    int n = v.size();
    for (int i = 0; i < n; i++) cout << v[i] + x << '\n';
}

template <typename T>
void err_print(const vector<T> &v, T x = 0) {
    int n = v.size();
    for (int i = 0; i < n; i++) cerr << v[i] + x << ' ';
    cerr << endl;
}

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));
}

template <typename T>
vector<int> id_sort(const vector<T> &v, bool greater = false) {
    int n = v.size();
    vector<int> ret(n);
    iota(begin(ret), end(ret), 0);
    sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; });
    return ret;
}

template <typename T>
void reorder(vector<T> &a, const vector<int> &ord) {
    int n = a.size();
    vector<T> b(n);
    for (int i = 0; i < n; i++) b[i] = a[ord[i]];
    swap(a, b);
}

template <typename T>
T floor(T x, T y) {
    assert(y != 0);
    if (y < 0) x = -x, y = -y;
    return (x >= 0 ? x / y : (x - y + 1) / y);
}

template <typename T>
T ceil(T x, T y) {
    assert(y != 0);
    if (y < 0) x = -x, y = -y;
    return (x >= 0 ? (x + y - 1) / y : x / y);
}

template <typename S, typename T>
pair<S, T> operator+(const pair<S, T> &p, const pair<S, T> &q) {
    return make_pair(p.first + q.first, p.second + q.second);
}

template <typename S, typename T>
pair<S, T> operator-(const pair<S, T> &p, const pair<S, T> &q) {
    return make_pair(p.first - q.first, p.second - q.second);
}

template <typename S, typename T>
istream &operator>>(istream &is, pair<S, T> &p) {
    S a;
    T b;
    is >> a >> b;
    p = make_pair(a, b);
    return is;
}

template <typename S, typename T>
ostream &operator<<(ostream &os, const pair<S, T> &p) {
    return os << p.first << ' ' << p.second;
}

struct io_setup {
    io_setup() {
        ios_base::sync_with_stdio(false);
        cin.tie(NULL);
        cout << fixed << setprecision(15);
        cerr << fixed << setprecision(15);
    }
} io_setup;

constexpr int inf = (1 << 30) - 1;
constexpr ll INF = (1LL << 60) - 1;
// constexpr int MOD = 1000000007;
constexpr int MOD = 998244353;

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;
    }
};

void solve() {
    int N, M;
    cin >> N >> M;

    vector<ll> W(N);
    rep(i, N) cin >> W[i];

    vector<vector<pil>> es(N);
    rep(i, M) {
        int u, v;
        ll w;
        cin >> u >> v >> w;
        u--, v--;
        es[u].eb(v, w), es[v].eb(u, w);
    }

    auto dijkstra = [&](int s) {
        vector<ll> d(N, INF);
        minheap<pli> que;
        que.emplace(d[s] = 0, s);
        while (!empty(que)) {
            auto [t, i] = que.top();
            que.pop();
            if (t > d[i]) continue;
            for (auto [e, l] : es[i]) {
                if (chmin(d[e], d[i] + l)) que.emplace(d[e], e);
            }
        }
        return d;
    };

    auto d1 = dijkstra(0), d2 = dijkstra(N - 1);

    ll ans = d1[N - 1];

    Li_Chao_Tree<ll, 0, inf, true> lct;
    rep(i, N) lct.add_line(W[i], d1[i]);

    rep(i, N) {
        ll tmp = lct.query(W[i]) + d2[i];
        chmin(ans, tmp);
    }

    cout << ans << '\n';

    // Li_Chao_Tree<ll, 0, inf, true> lct;

    // set<pli> s;
    // rep2(i, 0, N) s.emplace(W[i], i);

    // vector<ll> d(N, INF);
    // minheap<pli> que;
    // que.emplace(d[0] = 0, 0);

    // auto add = [&]() {
    //     if (empty(s)) return;
    //     auto [w, i] = *begin(s);
    //     ll tmp = lct.query(w);
    //     if (chmin(d[i], tmp)) que.emplace(d[i], i);
    // };

    // while (!empty(que)) {
    //     auto [t, i] = que.top();
    //     que.pop();
    //     if (t > d[i]) continue;

    //     lct.add_line(W[i], d[i]);
    //     s.erase(pli(W[i], i));
    //     add();

    //     for (auto [e, l] : es[i]) {
    //         if (chmin(d[e], t + l)) que.emplace(d[e], e);
    //     }
    // }

    // cout << d[N - 1] << '\n';
}

int main() {
    int T = 1;
    // cin >> T;
    while (T--) solve();
}
0