データ構造/セグメント木 (range minimum query)
(test/data_structure/range_minimum_query.test.cpp)

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• Last update: 2023-05-15 12:41:41+09:00
• Problem: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DSL_2_A

Depends on

• セグメント木 (segment tree) (include/emthrm/data_structure/segment_tree.hpp)

Code

/*
 * @title データ構造/セグメント木 (range minimum query)
 *
 * verification-helper: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DSL_2_A
 */

#include <iostream>

#include "emthrm/data_structure/segment_tree.hpp"

int main() {
  int n, q;
  std::cin >> n >> q;
  emthrm::SegmentTree<emthrm::monoid::RangeMinimumQuery<int>> rmq(n);
  while (q--) {
    int com, x, y;
    std::cin >> com >> x >> y;
    if (com == 0) {
      rmq.set(x, y);
    } else if (com == 1) {
      std::cout << rmq.get(x, y + 1) << '\n';
    }
  }
  return 0;
}

#line 1 "test/data_structure/range_minimum_query.test.cpp"
/*
 * @title データ構造/セグメント木 (range minimum query)
 *
 * verification-helper: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DSL_2_A
 */

#include <iostream>

#line 1 "include/emthrm/data_structure/segment_tree.hpp"



#include <algorithm>
#include <bit>
#include <limits>
#include <type_traits>
#include <vector>

namespace emthrm {

template <typename T>
requires requires {
  typename T::Monoid;
  {T::id()} -> std::same_as<typename T::Monoid>;
  {T::merge(std::declval<typename T::Monoid>(),
            std::declval<typename T::Monoid>())}
      -> std::same_as<typename T::Monoid>;
}
struct SegmentTree {
  using Monoid = typename T::Monoid;

  explicit SegmentTree(const int n)
      : SegmentTree(std::vector<Monoid>(n, T::id())) {}

  explicit SegmentTree(const std::vector<Monoid>& a)
      : n(a.size()), p2(std::bit_ceil(a.size())) {
    dat.assign(p2 << 1, T::id());
    std::copy(a.begin(), a.end(), dat.begin() + p2);
    for (int i = p2 - 1; i > 0; --i) {
      dat[i] = T::merge(dat[i << 1], dat[(i << 1) + 1]);
    }
  }

  void set(int idx, const Monoid val) {
    idx += p2;
    dat[idx] = val;
    while (idx >>= 1) dat[idx] = T::merge(dat[idx << 1], dat[(idx << 1) + 1]);
  }

  Monoid get(int left, int right) const {
    Monoid res_l = T::id(), res_r = T::id();
    for (left += p2, right += p2; left < right; left >>= 1, right >>= 1) {
      if (left & 1) res_l = T::merge(res_l, dat[left++]);
      if (right & 1) res_r = T::merge(dat[--right], res_r);
    }
    return T::merge(res_l, res_r);
  }

  Monoid operator[](const int idx) const { return dat[idx + p2]; }

  template <typename G>
  int find_right(int left, const G g) const {
    if (left >= n) [[unlikely]] return n;
    Monoid val = T::id();
    left += p2;
    do {
      while (!(left & 1)) left >>= 1;
      Monoid nxt = T::merge(val, dat[left]);
      if (!g(nxt)) {
        while (left < p2) {
          left <<= 1;
          nxt = T::merge(val, dat[left]);
          if (g(nxt)) {
            val = nxt;
            ++left;
          }
        }
        return left - p2;
      }
      val = nxt;
      ++left;
    } while (!std::has_single_bit(static_cast<unsigned int>(left)));
    return n;
  }

  template <typename G>
  int find_left(int right, const G g) const {
    if (right <= 0) [[unlikely]] return -1;
    Monoid val = T::id();
    right += p2;
    do {
      --right;
      while (right > 1 && (right & 1)) right >>= 1;
      Monoid nxt = T::merge(dat[right], val);
      if (!g(nxt)) {
        while (right < p2) {
          right = (right << 1) + 1;
          nxt = T::merge(dat[right], val);
          if (g(nxt)) {
            val = nxt;
            --right;
          }
        }
        return right - p2;
      }
      val = nxt;
    } while (!std::has_single_bit(static_cast<unsigned int>(right)));
    return -1;
  }

 private:
  const int n, p2;
  std::vector<Monoid> dat;
};

namespace monoid {

template <typename T>
struct RangeMinimumQuery {
  using Monoid = T;
  static constexpr Monoid id() { return std::numeric_limits<Monoid>::max(); }
  static Monoid merge(const Monoid& a, const Monoid& b) {
    return std::min(a, b);
  }
};

template <typename T>
struct RangeMaximumQuery {
  using Monoid = T;
  static constexpr Monoid id() { return std::numeric_limits<Monoid>::lowest(); }
  static Monoid merge(const Monoid& a, const Monoid& b) {
    return std::max(a, b);
  }
};

template <typename T>
struct RangeSumQuery {
  using Monoid = T;
  static constexpr Monoid id() { return 0; }
  static Monoid merge(const Monoid& a, const Monoid& b) { return a + b; }
};

}  // namespace monoid

}  // namespace emthrm


#line 10 "test/data_structure/range_minimum_query.test.cpp"

int main() {
  int n, q;
  std::cin >> n >> q;
  emthrm::SegmentTree<emthrm::monoid::RangeMinimumQuery<int>> rmq(n);
  while (q--) {
    int com, x, y;
    std::cin >> com >> x >> y;
    if (com == 0) {
      rmq.set(x, y);
    } else if (com == 1) {
      std::cout << rmq.get(x, y + 1) << '\n';
    }
  }
  return 0;
}

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