提出 #8265493

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ソースコード 拡げる

#include <bits/stdc++.h>
#define REP(i, n) for (int i = 0; (i) < (int)(n); ++ (i))
#define REP3(i, m, n) for (int i = (m); (i) < (int)(n); ++ (i))
#define REP_R(i, n) for (int i = (int)(n) - 1; (i) >= 0; -- (i))
#define REP3R(i, m, n) for (int i = (int)(n) - 1; (i) >= (int)(m); -- (i))
#define ALL(x) std::begin(x), std::end(x)
using namespace std;
template <class T, class U> inline void chmax(T & a, U const & b) { a = max<T>(a, b); }
template <class T, class U> inline void chmin(T & a, U const & b) { a = min<T>(a, b); }

namespace convex_hull_trick_details {
    /**
     * @note y = ax + b
     */
    struct line_t { int64_t a, b; };
    bool operator < (line_t lhs, line_t rhs) {
        return std::make_pair(- lhs.a, lhs.b) < std::make_pair(- rhs.a, rhs.b);
    }

    struct rational_t { int64_t num, den; };
    bool operator < (rational_t lhs, rational_t rhs) {
        if (lhs.num ==   INT64_MAX or rhs.num == - INT64_MAX) return false;
        if (lhs.num == - INT64_MAX or rhs.num ==   INT64_MAX) return true;
        return lhs.num * rhs.den < rhs.num * lhs.den;  // TODO: check overflow
    }
}

class convex_hull_trick {
    typedef convex_hull_trick_details::line_t line_t;
    typedef convex_hull_trick_details::rational_t rational_t;
    static rational_t make_rational(int64_t num, int64_t den = 1) {
        if (den < 0) { num *= -1; den *= -1; }
        return { num, den };  // NOTE: no reduction
    }

public:
    convex_hull_trick() {
        lines.insert({ + INT64_MAX, 0 });  // sentinels
        lines.insert({ - INT64_MAX, 0 });
        cross.emplace(make_rational(- INT64_MAX), (line_t) { - INT64_MAX, 0 });
    }
    /**
     * @note O(log n)
     */
    void add_line(int64_t a, int64_t b) {
        auto it = lines.insert({ a, b }).first;
        if (not is_required(*prev(it), { a, b }, *next(it))) {
            lines.erase(it);
            return;
        }
        cross.erase(cross_point(*prev(it), *next(it)));
        {  // remove right lines
            auto ju = prev(it);
            while (ju != lines.begin() and not is_required(*prev(ju), *ju, { a, b })) -- ju;
            cross_erase(ju, prev(it));
            it = lines.erase(++ ju, it);
        }
        {  // remove left lines
            auto ju = next(it);
            while(next(ju) != lines.end() and not is_required({ a, b }, *ju, *next(ju))) ++ ju;
            cross_erase(++ it, ju);
            it = prev(lines.erase(it, ju));
        }
        cross.emplace(cross_point(*prev(it), *it), *it);
        cross.emplace(cross_point(*it, *next(it)), *next(it));
        assert (not empty());
    }
    bool empty() const {
        return lines.size() <= 2;
    }
    /**
     * @note O(log n)
     */
    int64_t get_min(int64_t x) const {
        assert (not empty());
        line_t f = prev(cross.lower_bound(make_rational(x)))->second;
        return f.a * x + f.b;
    }

private:
    std::set<line_t> lines;
    std::map<rational_t, line_t> cross;
    template <typename Iterator>
    void cross_erase(Iterator first, Iterator last) {
        for (; first != last; ++ first) {
            cross.erase(cross_point(*first, *next(first)));
        }
    }
    rational_t cross_point(line_t f1, line_t f2) const {
        if (f1.a ==   INT64_MAX) return make_rational(- INT64_MAX);
        if (f2.a == - INT64_MAX) return make_rational(  INT64_MAX);
        return make_rational(f1.b - f2.b, f2.a - f1.a);
    }
    bool is_required(line_t f1, line_t f2, line_t f3) const {
        if (f1.a == f2.a and f1.b <= f2.b) return false;
        if (f1.a == INT64_MAX or f3.a == - INT64_MAX) return true;
        return (f2.a - f1.a) * (f3.b - f2.b) < (f2.b - f1.b) * (f3.a - f2.a);
    }
};


struct shop_t {
    int open;
    int close;
    int64_t d;
    int64_t x;
};

vector<int64_t> solve(int n, const vector<shop_t> & shops) {
    int t_max = 0;
    for (auto shop : shops) {
        chmax(t_max, shop.open + 3);
        chmax(t_max, shop.close + 3);
    }

    // CHTs on a segment tree
    int k = 0;
    while ((1 << k) < t_max) {
        ++ k;
    }
    vector<convex_hull_trick> segtree(2 * (1 << k) - 1);
    auto range_update = [&](int l, int r, int64_t a, int64_t b) {
        assert (0 <= l and l < r and r <= (1 << k));
        function<void (int)> go = [&](int i) {
            assert (0 <= i and i < 2 * (1 << k));
            int d = 32 - __builtin_clz(i + 1) - 1;
            int j = i - (1 << d) + 1;
            int il = (1 << (k - d)) * j;
            int ir = (1 << (k - d)) * (j + 1);
            if (ir <= l or r <= il) {
                // nop
            } else if (l <= il and ir <= r) {
                segtree[i].add_line(a, b);
            } else {
                go(2 * i + 1);
                go(2 * i + 2);
            }
        };
        go(0);
    };
    auto point_get = [&](int i, int64_t x) {
        assert (0 <= i and i < (1 << k));
        int64_t y = INT64_MAX;
        i += (1 << k) - 1;
        while (true) {
            if (not segtree[i].empty()) {
                chmin(y, segtree[i].get_min(x));
            }
            if (i == 0) break;
            i = (i - 1) / 2;
        }
        return y;
    };

    // run
    vector<int64_t> p(n);
    REP (i, n) {
        auto shop = shops[i];
        int64_t y = point_get(shop.open, shop.d);
        p[i] = min(shop.x, y == INT64_MAX ? INT64_MAX : shop.d * shop.d + y);
        int64_t a = - 2 * shop.d;
        int64_t b = p[i] + shop.d * shop.d;
        range_update(shop.open + 1, shop.close != -1 ? shop.close + 2 : t_max, a, b);
    }
    return p;
}

int main() {
    int n; cin >> n;
    vector<shop_t> shops(n);
    REP (i, n) {
        cin >> shops[i].open;
        cin >> shops[i].close;
        cin >> shops[i].d;
        cin >> shops[i].x;
    }
    vector<int64_t> prices = solve(n, shops);
    REP (i, n) {
        cout << prices[i] << endl;
    }
    return 0;
}

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