一点更新 + 区間最大クエリ solver (Range Maximum Query Solver)
(src/data-structure/segment-tree/presets/range-maximum-query-solver.hpp)

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• Last update: 2023-07-30 00:54:52+09:00
• Include: #include "src/data-structure/segment-tree/presets/range-maximum-query-solver.hpp"

数列に対する一点更新クエリと区間最大クエリを処理するデータ構造。

内部ではセグメント木を用いているため、詳細な仕様などはそちらのドキュメントに追従する。

コンストラクタ

(1) RangeMaximumQuerySolver< T >(usize n)
(2) RangeMaximumQuerySolver< T >(usize n, T v)
(3) RangeMaximumQuerySolver< T >(std::vector< T > vs)

Depends on

• rep 構造体 (src/cpp-template/header/rep.hpp)
• size alias (src/cpp-template/header/size-alias.hpp)
• 一点更新+区間取得 セグメント木 (src/data-structure/segment-tree/point-mapping-range-fold-segment-tree.hpp)
• src/data-structure/segment-tree/presets/monoid/value-structure-maximum.hpp

Verified with

• test/atcoder/abc298_f.test.cpp

Code

#pragma once

#include "src/data-structure/segment-tree/point-mapping-range-fold-segment-tree.hpp"
#include "src/data-structure/segment-tree/presets/monoid/value-structure-maximum.hpp"

namespace luz {

  template < typename T >
  using RangeMaximumQuerySolver =
      SegmentTree< monoid::RangeMaximumQueryMonoid< T > >;

} // namespace luz

#line 2 "src/data-structure/segment-tree/presets/range-maximum-query-solver.hpp"

#line 2 "src/data-structure/segment-tree/point-mapping-range-fold-segment-tree.hpp"

#line 2 "src/cpp-template/header/rep.hpp"

#line 2 "src/cpp-template/header/size-alias.hpp"

#include <cstddef>

namespace luz {

  using isize = std::ptrdiff_t;
  using usize = std::size_t;

} // namespace luz
#line 4 "src/cpp-template/header/rep.hpp"

#include <algorithm>

namespace luz {

  struct rep {
    struct itr {
      usize i;
      constexpr itr(const usize i) noexcept: i(i) {}
      void operator++() noexcept {
        ++i;
      }
      constexpr usize operator*() const noexcept {
        return i;
      }
      constexpr bool operator!=(const itr x) const noexcept {
        return i != x.i;
      }
    };
    const itr f, l;
    constexpr rep(const usize f, const usize l) noexcept
        : f(std::min(f, l)),
          l(l) {}
    constexpr auto begin() const noexcept {
      return f;
    }
    constexpr auto end() const noexcept {
      return l;
    }
  };

  struct rrep {
    struct itr {
      usize i;
      constexpr itr(const usize i) noexcept: i(i) {}
      void operator++() noexcept {
        --i;
      }
      constexpr usize operator*() const noexcept {
        return i;
      }
      constexpr bool operator!=(const itr x) const noexcept {
        return i != x.i;
      }
    };
    const itr f, l;
    constexpr rrep(const usize f, const usize l) noexcept
        : f(l - 1),
          l(std::min(f, l) - 1) {}
    constexpr auto begin() const noexcept {
      return f;
    }
    constexpr auto end() const noexcept {
      return l;
    }
  };

} // namespace luz
#line 5 "src/data-structure/segment-tree/point-mapping-range-fold-segment-tree.hpp"

#include <cassert>
#include <vector>

namespace luz {

  template < class value_structure >
  class PointMappingRangeFoldSegmentTree {
    using V  = value_structure;
    using VT = typename V::value_type;

    std::vector< VT > tree;

    void evaluate(usize index) {
      tree[index] =
          V::operation(tree[index << 1 | 0], tree[index << 1 | 1]);
    }

   public:
    using value_type = VT;

    PointMappingRangeFoldSegmentTree() = default;

    explicit PointMappingRangeFoldSegmentTree(const usize n)
        : tree(n * 2, V::identity()) {}

    explicit PointMappingRangeFoldSegmentTree(const usize n, VT v)
        : PointMappingRangeFoldSegmentTree(n) {
      build(std::vector< VT >(n, v));
    }

    explicit PointMappingRangeFoldSegmentTree(
        const std::vector< VT > &vs)
        : PointMappingRangeFoldSegmentTree(vs.size()) {
      build(vs);
    }

    void build(const std::vector< VT > &vs) {
      usize n = vs.size();
      assert(2 * n == tree.size());
      std::copy(vs.begin(), vs.end(), tree.begin() + n);
      for (usize index: rrep(1, n)) {
        evaluate(index);
      }
    }

    usize size() const {
      return tree.size() / 2;
    }

    void set(usize index, const VT x) {
      assert(index < size());
      index += size();
      tree[index] = x;

      while (index != 1) {
        index >>= 1;
        evaluate(index);
      }
    }

    VT fold(usize index) const {
      assert(index < size());

      return tree[index + size()];
    }

    VT fold(usize first, usize last) const {
      assert(first <= last);
      assert(last <= size());

      first += size();
      last += size();

      VT fold_l = V::identity();
      VT fold_r = V::identity();

      while (first != last) {
        if (first & 1) {
          fold_l = V::operation(fold_l, tree[first]);
          first += 1;
        }
        first >>= 1;

        if (last & 1) {
          last -= 1;
          fold_r = V::operation(tree[last], fold_r);
        }
        last >>= 1;
      }

      return V::operation(fold_l, fold_r);
    }

    VT fold_all() const {
      return (size() ? tree[1] : V::identity());
    }
  };

  template < class value_structure >
  using SegmentTree =
      PointMappingRangeFoldSegmentTree< value_structure >;

} // namespace luz
#line 2 "src/data-structure/segment-tree/presets/monoid/value-structure-maximum.hpp"

#line 4 "src/data-structure/segment-tree/presets/monoid/value-structure-maximum.hpp"
#include <limits>

namespace luz::monoid {

  template < typename T >
  class RangeMaximumQueryMonoid {

    static constexpr T identity_{std::numeric_limits< T >::min()};

   public:
    using value_type = T;

    static constexpr T operation(T a, T b) {
      return std::max(a, b);
    }

    static constexpr T identity() {
      return identity_;
    }
  };

} // namespace luz::monoid
#line 5 "src/data-structure/segment-tree/presets/range-maximum-query-solver.hpp"

namespace luz {

  template < typename T >
  using RangeMaximumQuerySolver =
      SegmentTree< monoid::RangeMaximumQueryMonoid< T > >;

} // namespace luz

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