Dual Segment Tree
(data_structure/dual_segment_tree.cpp)

• View this file on GitHub
• Last update: 2020-03-11 22:42:07+09:00
• Link: https://kimiyuki.net/blog/2019/02/21/dual-segment-tree/

Depends on

• other/bit_width.cpp
• other/countl_zero.cpp
• other/countr_zero.cpp
• other/int_alias.cpp

Verified with

• test/dual_segment_tree.test.cpp

Code

#include "other/bit_width.cpp"
#include "other/countr_zero.cpp"
#include "other/int_alias.cpp"

#include <cassert>
#include <cstddef>
#include <vector>

template <class M> class dual_segment_tree {
  using T = typename M::value_type;

public:
  using value_type = T;

private:
  static void add(T &x, const T y) { x = M::operation(x, y); }

  std::vector<T> tree;

  void push(const usize index) {
    add(tree[index * 2], tree[index]);
    add(tree[index * 2 + 1], tree[index]);
    tree[index] = M::identity;
  }
  void propagate(const usize index) {
    if (index == 0)
      return;
    const usize crz = countr_zero(index);
    for (usize h = bit_width(index) - 1; h != crz; h -= 1)
      push(index >> h);
  }

public:
  dual_segment_tree() = default;
  explicit dual_segment_tree(const usize n) : tree(n * 2, M::identity) {}

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

  T fold(usize index) const {
    assert(index < size());
    index += size();
    T ret = tree[index];
    while (index != 1) {
      index /= 2;
      add(ret, tree[index]);
    }
    return ret;
  }

  void update(usize first, usize last, const T x) {
    assert(first <= last);
    assert(last <= size());
    first += size();
    last += size();
    propagate(first);
    propagate(last);
    while (first != last) {
      if (first % 2 != 0) {
        add(tree[first], x);
        first += 1;
      }
      first /= 2;
      if (last % 2 != 0) {
        last -= 1;
        add(tree[last], x);
      }
      last /= 2;
    }
  }
};

/**
 * @brief Dual Segment Tree
 * @see https://kimiyuki.net/blog/2019/02/21/dual-segment-tree/
 */

#line 2 "other/bit_width.cpp"

#line 2 "other/countl_zero.cpp"

#line 2 "other/countr_zero.cpp"

#line 2 "other/int_alias.cpp"

#include <cstddef>
#include <cstdint>

using i32 = std::int32_t;
using i64 = std::int64_t;
using u32 = std::uint32_t;
using u64 = std::uint64_t;
using isize = std::ptrdiff_t;
using usize = std::size_t;
#line 4 "other/countr_zero.cpp"

#include <array>

usize countr_zero(u64 x) {
  if (x == 0)
    return 64;
#ifdef __GNUC__
  return __builtin_ctzll(x);
#else
  constexpr std::array<usize, 64> table = {
      0,  1,  2,  7,  3,  13, 8,  27, 4,  33, 14, 36, 9,  49, 28, 19,
      5,  25, 34, 17, 15, 53, 37, 55, 10, 46, 50, 39, 29, 42, 20, 57,
      63, 6,  12, 26, 32, 35, 48, 18, 24, 16, 52, 54, 45, 38, 41, 56,
      62, 11, 31, 47, 23, 51, 44, 40, 61, 30, 22, 43, 60, 21, 59, 58};
  return table[(x & ~x + 1) * 0x218A7A392DD9ABF >> 58 & 0x3F];
#endif
}
#line 5 "other/countl_zero.cpp"

usize countl_zero(u64 x) {
#ifdef __GNUC__
  return x == 0 ? 64 : __builtin_clzll(x);
#else
  x |= x >> 1;
  x |= x >> 2;
  x |= x >> 4;
  x |= x >> 8;
  x |= x >> 16;
  x |= x >> 32;
  return 64 - countr_zero(~x);
#endif
}
#line 5 "other/bit_width.cpp"

usize bit_width(const u64 x) { return 64 - countl_zero(x); }
#line 4 "data_structure/dual_segment_tree.cpp"

#include <cassert>
#line 7 "data_structure/dual_segment_tree.cpp"
#include <vector>

template <class M> class dual_segment_tree {
  using T = typename M::value_type;

public:
  using value_type = T;

private:
  static void add(T &x, const T y) { x = M::operation(x, y); }

  std::vector<T> tree;

  void push(const usize index) {
    add(tree[index * 2], tree[index]);
    add(tree[index * 2 + 1], tree[index]);
    tree[index] = M::identity;
  }
  void propagate(const usize index) {
    if (index == 0)
      return;
    const usize crz = countr_zero(index);
    for (usize h = bit_width(index) - 1; h != crz; h -= 1)
      push(index >> h);
  }

public:
  dual_segment_tree() = default;
  explicit dual_segment_tree(const usize n) : tree(n * 2, M::identity) {}

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

  T fold(usize index) const {
    assert(index < size());
    index += size();
    T ret = tree[index];
    while (index != 1) {
      index /= 2;
      add(ret, tree[index]);
    }
    return ret;
  }

  void update(usize first, usize last, const T x) {
    assert(first <= last);
    assert(last <= size());
    first += size();
    last += size();
    propagate(first);
    propagate(last);
    while (first != last) {
      if (first % 2 != 0) {
        add(tree[first], x);
        first += 1;
      }
      first /= 2;
      if (last % 2 != 0) {
        last -= 1;
        add(tree[last], x);
      }
      last /= 2;
    }
  }
};

/**
 * @brief Dual Segment Tree
 * @see https://kimiyuki.net/blog/2019/02/21/dual-segment-tree/
 */

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