cp-library

C++ Library for Competitive Programming

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:heavy_check_mark: 動的計画法/Li Chao tree（最大値）
(test/dynamic_programming/li_chao_tree.2.test.cpp)

Depends on

Code

/*
 * @title 動的計画法/Li Chao tree（最大値）
 *
 * verification-helper: PROBLEM https://judge.yosupo.jp/problem/segment_add_get_min
 */

#include <iostream>
#include <vector>

#include "emthrm/dynamic_programming/li_chao_tree.hpp"

int main() {
  constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL;
  int n, q;
  std::cin >> n >> q;
  std::vector<int> query(q), l(n + q), r(n + q), a(n + q), p(q);
  std::vector<long long> b(n + q), xs;
  for (int i = 0; i < n; ++i) {
    std::cin >> l[i] >> r[i] >> a[i] >> b[i];
  }
  for (int i = 0; i < q; ++i) {
    std::cin >> query[i];
    if (query[i] == 0) {
      std::cin >> l[n + i] >> r[n + i] >> a[n + i] >> b[n + i];
    } else if (query[i] == 1) {
      std::cin >> p[i];
      xs.emplace_back(p[i]);
    }
  }
  if (xs.empty()) return 0;
  emthrm::LiChaoTree<long long, false> li_chao_tree(xs, LINF);
  for (int i = 0; i < n; ++i) {
    li_chao_tree.add(-a[i], -b[i], l[i], r[i]);
  }
  for (int i = 0; i < q; ++i) {
    if (query[i] == 0) {
      li_chao_tree.add(-a[n + i], -b[n + i], l[n + i], r[n + i]);
    } else if (query[i] == 1) {
      const long long ans = -li_chao_tree.query(p[i]);
      if (ans == LINF) {
        std::cout << "INFINITY\n";
      } else {
        std::cout << ans << '\n';
      }
    }
  }
  return 0;
}
#line 1 "test/dynamic_programming/li_chao_tree.2.test.cpp"
/*
 * @title 動的計画法/Li Chao tree（最大値）
 *
 * verification-helper: PROBLEM https://judge.yosupo.jp/problem/segment_add_get_min
 */

#include <iostream>
#include <vector>

#line 1 "include/emthrm/dynamic_programming/li_chao_tree.hpp"



#include <algorithm>
#include <bit>
#include <cassert>
#include <iterator>
#include <numeric>
#include <utility>
#line 11 "include/emthrm/dynamic_programming/li_chao_tree.hpp"

namespace emthrm {

template <typename T, bool IS_MINIMIZED = true>
struct LiChaoTree {
  struct Line {
    T a, b;
    explicit Line(const T a, const T b) : a(a), b(b) {}
    T f(const T x) const { return a * x + b; }
  };

  explicit LiChaoTree(const std::vector<T>& xs_, const T inf) : n(1), xs(xs_) {
    std::sort(xs.begin(), xs.end());
    xs.erase(std::unique(xs.begin(), xs.end()), xs.end());
    assert(xs.size() > 0);
    n = std::bit_ceil(xs.size());
    const T xs_back = xs.back();
    xs.resize(n, xs_back);
    dat.assign(n << 1, Line(0, inf));
  }

  void add(T a, T b) {
    if constexpr (!IS_MINIMIZED) {
      a = -a;
      b = -b;
    }
    Line line(a, b);
    add(&line, 1, 0, n);
  }

  void add(T a, T b, T left, T right) {
    if constexpr (!IS_MINIMIZED) {
      a = -a;
      b = -b;
    }
    for (int len = 1,
             node_l = std::distance(
                 xs.begin(), std::lower_bound(xs.begin(), xs.end(), left)),
             node_r = std::distance(
                 xs.begin(), std::lower_bound(xs.begin(), xs.end(), right)),
             l = node_l + n, r = node_r + n;
         l < r;
         l >>= 1, r >>= 1, len <<= 1) {
      if (l & 1) {
        Line line(a, b);
        add(&line, l++, node_l, node_l + len);
        node_l += len;
      }
      if (r & 1) {
        Line line(a, b);
        node_r -= len;
        add(&line, --r, node_r, node_r + len);
      }
    }
  }

  T query(const T x) const {
    int node = n + std::distance(xs.begin(),
                                 std::lower_bound(xs.begin(), xs.end(), x));
    T res = dat[node].f(x);
    while (node >>= 1) {
      if (dat[node].f(x) < res) res = dat[node].f(x);
    }
    return IS_MINIMIZED ? res : -res;
  }

 private:
  int n;
  std::vector<T> xs;
  std::vector<Line> dat;

  void add(Line* line, int node, int left, int right) {
    const bool flag_l = dat[node].f(xs[left]) <= line->f(xs[left]);
    const bool flag_r = dat[node].f(xs[right - 1]) <= line->f(xs[right - 1]);
    if (flag_l && flag_r) return;
    if (!flag_l && !flag_r) {
      std::swap(dat[node], *line);
      return;
    }
    const int mid = std::midpoint(left, right);
    if (line->f(xs[mid]) < dat[node].f(xs[mid])) std::swap(dat[node], *line);
    if (line->f(xs[left]) <= dat[node].f(xs[left])) {
      add(line, node << 1, left, mid);
    } else {
      add(line, (node << 1) + 1, mid, right);
    }
  }
};

}  // namespace emthrm


#line 11 "test/dynamic_programming/li_chao_tree.2.test.cpp"

int main() {
  constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL;
  int n, q;
  std::cin >> n >> q;
  std::vector<int> query(q), l(n + q), r(n + q), a(n + q), p(q);
  std::vector<long long> b(n + q), xs;
  for (int i = 0; i < n; ++i) {
    std::cin >> l[i] >> r[i] >> a[i] >> b[i];
  }
  for (int i = 0; i < q; ++i) {
    std::cin >> query[i];
    if (query[i] == 0) {
      std::cin >> l[n + i] >> r[n + i] >> a[n + i] >> b[n + i];
    } else if (query[i] == 1) {
      std::cin >> p[i];
      xs.emplace_back(p[i]);
    }
  }
  if (xs.empty()) return 0;
  emthrm::LiChaoTree<long long, false> li_chao_tree(xs, LINF);
  for (int i = 0; i < n; ++i) {
    li_chao_tree.add(-a[i], -b[i], l[i], r[i]);
  }
  for (int i = 0; i < q; ++i) {
    if (query[i] == 0) {
      li_chao_tree.add(-a[n + i], -b[n + i], l[n + i], r[n + i]);
    } else if (query[i] == 1) {
      const long long ans = -li_chao_tree.query(p[i]);
      if (ans == LINF) {
        std::cout << "INFINITY\n";
      } else {
        std::cout << ans << '\n';
      }
    }
  }
  return 0;
}
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