test/data_structure/Segment_Add_Get_Min.test.cpp

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• Last update: 2023-12-28 15:52:36+09:00
• Problem: https://judge.yosupo.jp/problem/segment_add_get_min

Depends on

• Li Chao Tree (data_structure/li_chao_tree.hpp)
• template/int_alias.hpp

Code

#define PROBLEM "https://judge.yosupo.jp/problem/segment_add_get_min"

#include <iostream>
#include <utility>
#include <vector>

#include "../../data_structure/li_chao_tree.hpp"
#include "../../template/int_alias.hpp"

using ebi::i64;

int main() {
    int n, q;
    std::cin >> n >> q;
    std::vector<std::pair<i64, i64>> lr(n);
    std::vector<std::pair<i64, i64>> y(n);
    std::vector<i64> x;
    for (int i = 0; i < n; i++) {
        std::cin >> lr[i].first >> lr[i].second;
        std::cin >> y[i].first >> y[i].second;
    }
    std::vector<std::vector<i64>> query(q);
    for (int i = 0; i < q; i++) {
        i64 t;
        std::cin >> t;
        query[i].emplace_back(t);
        if (t == 0) {
            i64 l, r, a, b;
            std::cin >> l >> r >> a >> b;
            query[i].emplace_back(l);
            query[i].emplace_back(r);
            query[i].emplace_back(a);
            query[i].emplace_back(b);
        } else {
            i64 p;
            std::cin >> p;
            query[i].emplace_back(p);
            x.emplace_back(p);
        }
    }
    if (x.size() == 0) return 0;
    std::sort(x.begin(), x.end());
    x.erase(unique(x.begin(), x.end()), x.end());
    x.emplace_back(1e9 + 10);
    ebi::li_chao_tree<i64> seg(x);
    for (int i = 0; i < n; i++) {
        auto [l, r] = lr[i];
        auto [a, b] = y[i];
        seg.add_segment(a, b, l, r);
    }
    for (int i = 0; i < q; i++) {
        if (query[i][0] == 0) {
            i64 l = query[i][1];
            i64 r = query[i][2];
            i64 a = query[i][3];
            i64 b = query[i][4];
            seg.add_segment(a, b, l, r);
        } else {
            i64 ret = seg.min(query[i][1]);
            if (ret == std::numeric_limits<i64>::max()) {
                std::cout << "INFINITY" << std::endl;
            } else {
                std::cout << ret << std::endl;
            }
        }
    }
}

#line 1 "test/data_structure/Segment_Add_Get_Min.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/segment_add_get_min"

#include <iostream>
#include <utility>
#include <vector>

#line 2 "data_structure/li_chao_tree.hpp"

#include <algorithm>
#include <cassert>
#include <limits>
#line 8 "data_structure/li_chao_tree.hpp"

namespace ebi {

template <class T> struct li_chao_tree {
  private:
    T f(std::pair<T, T> y, T x) const {
        return y.first * x + y.second;
    }

    void add(std::pair<T, T> y, int l, int r, int index) {
        while (l < r) {
            bool left = f(y, xs[l]) < f(data[index], xs[l]);
            bool mid = f(y, xs[(l + r) / 2]) < f(data[index], xs[(l + r) / 2]);
            bool right = f(y, xs[r - 1]) < f(data[index], xs[r - 1]);
            if (left && right) {
                data[index] = y;
                return;
            }
            if (!(left || right)) {
                return;
            }
            if (mid) {
                std::swap(y, data[index]);
                left = !left;
                right = !right;
            }
            if (left) {
                r = (l + r) / 2;
                index *= 2;
            } else {
                l = (l + r) / 2;
                index = 2 * index + 1;
            }
        }
    }

    int get_index(T x) const {
        auto itr = std::lower_bound(xs.begin(), xs.end(), x);
        return itr - xs.begin();
    }

  public:
    li_chao_tree(std::vector<T> &_x) : xs(_x), sz(1) {
        std::sort(xs.begin(), xs.end());
        xs.erase(std::unique(xs.begin(), xs.end()), xs.end());
        while (sz < int(xs.size())) sz <<= 1;
        while (int(xs.size()) < sz) xs.emplace_back(xs.back() + 1);
        data.assign(2 * sz, {0, std::numeric_limits<T>::max()});
    }

    void add_line(T a, T b) {
        add({a, b}, 0, sz, 1);
    }

    void add_segment(T a, T b, T lx, T rx) {
        int l = get_index(lx);
        int r = get_index(rx);
        assert(0 <= l && l <= r && r <= sz);
        int il = l + sz;
        int ir = r + sz;
        int rank = 0;
        while (il < ir) {
            if (il & 1) {
                add({a, b}, l, l + (1 << rank), il++);
                l += (1 << rank);
            }
            if (ir & 1) {
                add({a, b}, r - (1 << rank), r, --ir);
                r -= (1 << rank);
            }
            rank++;
            il >>= 1;
            ir >>= 1;
        }
    }

    T min(T x) {
        int k = get_index(x) + sz;
        T val = std::numeric_limits<T>::max();
        while (k > 0) {
            val = std::min(val, f(data[k], x));
            k >>= 1;
        }
        return val;
    }

  private:
    std::vector<std::pair<T, T>> data;
    std::vector<T> xs;
    int sz;
};

}  // namespace ebi
#line 2 "template/int_alias.hpp"

#include <cstdint>

namespace ebi {

using ld = long double;
using std::size_t;
using i8 = std::int8_t;
using u8 = std::uint8_t;
using i16 = std::int16_t;
using u16 = std::uint16_t;
using i32 = std::int32_t;
using u32 = std::uint32_t;
using i64 = std::int64_t;
using u64 = std::uint64_t;
using i128 = __int128_t;
using u128 = __uint128_t;

}  // namespace ebi
#line 9 "test/data_structure/Segment_Add_Get_Min.test.cpp"

using ebi::i64;

int main() {
    int n, q;
    std::cin >> n >> q;
    std::vector<std::pair<i64, i64>> lr(n);
    std::vector<std::pair<i64, i64>> y(n);
    std::vector<i64> x;
    for (int i = 0; i < n; i++) {
        std::cin >> lr[i].first >> lr[i].second;
        std::cin >> y[i].first >> y[i].second;
    }
    std::vector<std::vector<i64>> query(q);
    for (int i = 0; i < q; i++) {
        i64 t;
        std::cin >> t;
        query[i].emplace_back(t);
        if (t == 0) {
            i64 l, r, a, b;
            std::cin >> l >> r >> a >> b;
            query[i].emplace_back(l);
            query[i].emplace_back(r);
            query[i].emplace_back(a);
            query[i].emplace_back(b);
        } else {
            i64 p;
            std::cin >> p;
            query[i].emplace_back(p);
            x.emplace_back(p);
        }
    }
    if (x.size() == 0) return 0;
    std::sort(x.begin(), x.end());
    x.erase(unique(x.begin(), x.end()), x.end());
    x.emplace_back(1e9 + 10);
    ebi::li_chao_tree<i64> seg(x);
    for (int i = 0; i < n; i++) {
        auto [l, r] = lr[i];
        auto [a, b] = y[i];
        seg.add_segment(a, b, l, r);
    }
    for (int i = 0; i < q; i++) {
        if (query[i][0] == 0) {
            i64 l = query[i][1];
            i64 r = query[i][2];
            i64 a = query[i][3];
            i64 b = query[i][4];
            seg.add_segment(a, b, l, r);
        } else {
            i64 ret = seg.min(query[i][1]);
            if (ret == std::numeric_limits<i64>::max()) {
                std::cout << "INFINITY" << std::endl;
            } else {
                std::cout << ret << std::endl;
            }
        }
    }
}

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