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(src/data-structure/segment-tree/point-mapping-range-fold-segment-tree.hpp)

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Last update: 2023-07-30 00:54:52+09:00
Include: #include "src/data-structure/segment-tree/point-mapping-range-fold-segment-tree.hpp"

Appendix

コンストラクタ

PointMappingRangeFoldSegmentTree のエイリアスとして SegmentTree を提供している。

(1) SegmentTree< V >(usize n)
(2) SegmentTree< V >(usize n, VT v)
(3) SegmentTree< V >(vector< VT > vs)

列 $a$ を長さ $n$ の列で初期化する。各要素の初期値は V::identity() となる。
列 $a$ を長さ $n$ の列で初期化する。各要素の初期値は v となる。
列 $a$ を vs で初期化する。

制約

$0 \leq n$

計算量

$O(n)$

build

void build(vector< VT > vs)

列 $(a_0, a_1, \dots, a_{n-1})$ を vs で初期化して再構築する。

制約

$n$ と vs.size() が一致すること。

計算量

$O(n)$

size

usize size() const

扱っている列 $(a_0, a_1, \dots, a_{n - 1})$ の長さ $n$ を返す。

計算量

$O(1)$

set

void set(usize i, VT x)

$a_i \leftarrow x$ で更新する。

計算量

$O(\log(n))$

fold

(1) VT fold(usize i) const
(2) VT fold(usize l, usize r) const
(3) VT fold_all() const

$a_i$ を返す。
$a_l \cdot a_{l+1} \cdot \dotsm \cdot a_{r-1}$ を返す。$l = r$ のとき V::identity() が返る。
$a_0 \cdot a_1 \cdot \dotsm \cdot a_{n-1}$ を返す。

制約

$0 \leq i < n$
$0 \leq l \leq r \leq n$

計算量

(1): $O(1)$
(2):
- $O(\log(n))$
- $d = r - l$ として $O(\log(d))$
(3): $O(1)$

max_right

気が向いたらそのうち実装する

min_left

気が向いたらそのうち実装する2

Depends on

Required by

Verified with

Code

#pragma once

#include "src/cpp-template/header/rep.hpp"
#include "src/cpp-template/header/size-alias.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/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

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)