Wavelet Matrix Point Add Rectangle Sum (structure/wavelet/wavelet-matrix-point-add-rectangle-sum.hpp)

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Last update: 2026-08-10 15:44:16+00:00
Include: #include "structure/wavelet/wavelet-matrix-point-add-rectangle-sum.hpp"

点更新付きで、値範囲の重み総和を処理するデータ構造です。

WaveletMatrixPointAddRectangleSum< T, MAXLOG, D > は値配列 v の位置は固定したまま、重み配列に対して一点加算と範囲和クエリを処理します。

コンストラクタ

(1) WaveletMatrixPointAddRectangleSum()
(2) WaveletMatrixPointAddRectangleSum(const vector<T>& v, const vector<D>& d)

(2) は v[i] に重み d[i] を対応づけて構築します。

制約

v.size() == d.size()

計算量

(2) $O(|v| \cdot MAXLOG)$

rect_sum

(1) D rect_sum(int l, int r, T upper)
(2) D rect_sum(int l, int r, T lower, T upper)

(1) 区間 [l, r) で v[i] < upper を満たす要素の重み総和を返します。
(2) 区間 [l, r) で lower <= v[i] < upper を満たす要素の重み総和を返します。

制約

$0 \leq l \leq r \leq N$

計算量

$O(MAXLOG \log N)$

point_add

void point_add(int k, const D& x)

k 番目要素の重みに x を加算します。

制約

$0 \leq k < N$

計算量

$O(MAXLOG \log N)$

CompressedWaveletMatrixPointAddRectangleSum

座標圧縮を内部で行うラッパです。値が疎な場合はこちらを使うと扱いやすくなります。

コンストラクタ

CompressedWaveletMatrixPointAddRectangleSum(const vector<T>& v, const vector<D>& d)

配列 v を座標圧縮して構築します。

制約

v.size() == d.size()

計算量

$O(|v| \log |v| + |v| \cdot MAXLOG)$

rect_sum

(1) D rect_sum(int l, int r, T upper)
(2) D rect_sum(int l, int r, T lower, T upper)

(1) 区間 [l, r) で v[i] < upper を満たす要素の重み総和を返します。
(2) 区間 [l, r) で lower <= v[i] < upper を満たす要素の重み総和を返します。

制約

$0 \leq l \leq r \leq N$

計算量

$O(\log |v| + MAXLOG \log N)$

point_add

void point_add(int k, const D& x)

k 番目要素の重みに x を加算します。

制約

$0 \leq k < N$

計算量

$O(MAXLOG \log N)$

Depends on

Verified with

test/verify/yosupo-point-add-rectangle-sum.test.cpp

Code

#pragma once

#include <algorithm>
#include <cassert>
#include <cstddef>
#include <iterator>
#include <numeric>
#include <tuple>
#include <utility>
#include <vector>

#include "../others/binary-indexed-tree.hpp"
#include "succinct-indexable-dictionary.hpp"

/*
 * @brief Wavelet Matrix Point Add Rectangle Sum
 *
 */
template <typename T, int MAXLOG, typename D>
struct WaveletMatrixPointAddRectangleSum {
  std::size_t length;
  SuccinctIndexableDictionary matrix[MAXLOG];
  BinaryIndexedTree<D> ds[MAXLOG];
  std::vector<T> v;
  int mid[MAXLOG];

  WaveletMatrixPointAddRectangleSum() = default;

  WaveletMatrixPointAddRectangleSum(const std::vector<T>& v,
                                    const std::vector<D>& d)
      : length(v.size()), v(v) {
    assert(v.size() == d.size());
    std::vector<int> l(length), r(length), ord(length);
    std::iota(std::begin(ord), std::end(ord), 0);
    std::vector<D> dd(length);
    for (int level = MAXLOG - 1; level >= 0; level--) {
      matrix[level] = SuccinctIndexableDictionary(length + 1);
      int left = 0, right = 0;
      for (int i = 0; i < length; i++) {
        if (((v[ord[i]] >> level) & 1)) {
          matrix[level].set(i);
          r[right++] = ord[i];
        } else {
          l[left++] = ord[i];
        }
      }
      mid[level] = left;
      matrix[level].build();
      std::swap(ord, l);
      for (int i = 0; i < right; i++) {
        ord[left + i] = r[i];
      }
      for (int i = 0; i < length; i++) {
        dd[i] = d[ord[i]];
      }
      ds[level] = BinaryIndexedTree<D>(dd);
    }
  }

  std::pair<int, int> succ(bool f, int l, int r, int level) {
    return {matrix[level].rank(f, l) + mid[level] * f,
            matrix[level].rank(f, r) + mid[level] * f};
  }

  // count d[i] s.t. (l <= i < r) && (v[i] < upper)
  D rect_sum(int l, int r, T upper) {
    D ret = 0;
    for (int level = MAXLOG - 1; level >= 0; level--) {
      if (((upper >> level) & 1)) {
        auto nxt = succ(false, l, r, level);
        ret += ds[level].prod(nxt.first, nxt.second);
        l = l - nxt.first + mid[level];
        r = r - nxt.second + mid[level];
      } else {
        std::tie(l, r) = succ(false, l, r, level);
      }
    }
    return ret;
  }

  D rect_sum(int l, int r, T lower, T upper) {
    return rect_sum(l, r, upper) - rect_sum(l, r, lower);
  }

  void point_add(int k, const D& x) {
    auto& y = v[k];
    for (int level = MAXLOG - 1; level >= 0; level--) {
      bool f = ((y >> level) & 1);
      k = matrix[level].rank(f, k) + mid[level] * f;
      ds[level].apply(k, x);
    }
  }
};

template <typename T, int MAXLOG, typename D>
struct CompressedWaveletMatrixPointAddRectangleSum {
  WaveletMatrixPointAddRectangleSum<int, MAXLOG, D> mat;
  std::vector<T> ys;

  CompressedWaveletMatrixPointAddRectangleSum(const std::vector<T>& v,
                                              const std::vector<D>& d)
      : ys(v) {
    std::sort(std::begin(ys), std::end(ys));
    ys.erase(std::unique(std::begin(ys), std::end(ys)), std::end(ys));
    std::vector<int> t(v.size());
    for (int i = 0; i < v.size(); i++) t[i] = get(v[i]);
    mat = WaveletMatrixPointAddRectangleSum<int, MAXLOG, D>(t, d);
  }

  inline int get(const T& x) {
    return std::lower_bound(std::begin(ys), std::end(ys), x) - std::begin(ys);
  }

  D rect_sum(int l, int r, T upper) { return mat.rect_sum(l, r, get(upper)); }

  D rect_sum(int l, int r, T lower, T upper) {
    return mat.rect_sum(l, r, get(lower), get(upper));
  }

  void point_add(int k, const D& x) { mat.point_add(k, x); }
};

#line 2 "structure/wavelet/wavelet-matrix-point-add-rectangle-sum.hpp"

#include <algorithm>
#include <cassert>
#include <cstddef>
#include <iterator>
#include <numeric>
#include <tuple>
#include <utility>
#include <vector>

#line 2 "structure/others/binary-indexed-tree.hpp"

#line 5 "structure/others/binary-indexed-tree.hpp"

template <typename T>
struct BinaryIndexedTree {
 private:
  int n;
  std::vector<T> data;

 public:
  BinaryIndexedTree() = default;

  explicit BinaryIndexedTree(int n) : n(n) { data.assign(n + 1, T()); }

  explicit BinaryIndexedTree(const std::vector<T>& v)
      : BinaryIndexedTree((int)v.size()) {
    build(v);
  }

  void build(const std::vector<T>& v) {
    assert(n == (int)v.size());
    for (int i = 1; i <= n; i++) data[i] = v[i - 1];
    for (int i = 1; i <= n; i++) {
      int j = i + (i & -i);
      if (j <= n) data[j] += data[i];
    }
  }

  void apply(int k, const T& x) {
    for (++k; k <= n; k += k & -k) data[k] += x;
  }

  T prod(int r) const {
    T ret = T();
    for (; r > 0; r -= r & -r) ret += data[r];
    return ret;
  }

  T prod(int l, int r) const { return prod(r) - prod(l); }

  int lower_bound(T x) const {
    int i = 0;
    for (int k = 1 << (32 - __builtin_clz(n)); k > 0; k >>= 1) {
      if (i + k <= n && data[i + k] < x) {
        x -= data[i + k];
        i += k;
      }
    }
    return i;
  }

  int upper_bound(T x) const {
    int i = 0;
    for (int k = 1 << (32 - __builtin_clz(n)); k > 0; k >>= 1) {
      if (i + k <= n && data[i + k] <= x) {
        x -= data[i + k];
        i += k;
      }
    }
    return i;
  }
};
#line 2 "structure/wavelet/succinct-indexable-dictionary.hpp"

#line 5 "structure/wavelet/succinct-indexable-dictionary.hpp"

/**
 * @brief Succinct Indexable Dictionary(完備辞書)
 */
struct SuccinctIndexableDictionary {
  std::size_t length;
  std::size_t blocks;
  std::vector<unsigned> bit, sum;

  SuccinctIndexableDictionary() = default;

  SuccinctIndexableDictionary(std::size_t length)
      : length(length), blocks((length + 31) >> 5) {
    bit.assign(blocks, 0U);
    sum.assign(blocks, 0U);
  }

  void set(int k) { bit[k >> 5] |= 1U << (k & 31); }

  void build() {
    sum[0] = 0U;
    for (int i = 1; i < blocks; i++) {
      sum[i] = sum[i - 1] + __builtin_popcount(bit[i - 1]);
    }
  }

  bool operator[](int k) { return (bool((bit[k >> 5] >> (k & 31)) & 1)); }

  int rank(int k) {
    return (sum[k >> 5] +
            __builtin_popcount(bit[k >> 5] & ((1U << (k & 31)) - 1)));
  }

  int rank(bool val, int k) { return (val ? rank(k) : k - rank(k)); }
};
#line 14 "structure/wavelet/wavelet-matrix-point-add-rectangle-sum.hpp"

/*
 * @brief Wavelet Matrix Point Add Rectangle Sum
 *
 */
template <typename T, int MAXLOG, typename D>
struct WaveletMatrixPointAddRectangleSum {
  std::size_t length;
  SuccinctIndexableDictionary matrix[MAXLOG];
  BinaryIndexedTree<D> ds[MAXLOG];
  std::vector<T> v;
  int mid[MAXLOG];

  WaveletMatrixPointAddRectangleSum() = default;

  WaveletMatrixPointAddRectangleSum(const std::vector<T>& v,
                                    const std::vector<D>& d)
      : length(v.size()), v(v) {
    assert(v.size() == d.size());
    std::vector<int> l(length), r(length), ord(length);
    std::iota(std::begin(ord), std::end(ord), 0);
    std::vector<D> dd(length);
    for (int level = MAXLOG - 1; level >= 0; level--) {
      matrix[level] = SuccinctIndexableDictionary(length + 1);
      int left = 0, right = 0;
      for (int i = 0; i < length; i++) {
        if (((v[ord[i]] >> level) & 1)) {
          matrix[level].set(i);
          r[right++] = ord[i];
        } else {
          l[left++] = ord[i];
        }
      }
      mid[level] = left;
      matrix[level].build();
      std::swap(ord, l);
      for (int i = 0; i < right; i++) {
        ord[left + i] = r[i];
      }
      for (int i = 0; i < length; i++) {
        dd[i] = d[ord[i]];
      }
      ds[level] = BinaryIndexedTree<D>(dd);
    }
  }

  std::pair<int, int> succ(bool f, int l, int r, int level) {
    return {matrix[level].rank(f, l) + mid[level] * f,
            matrix[level].rank(f, r) + mid[level] * f};
  }

  // count d[i] s.t. (l <= i < r) && (v[i] < upper)
  D rect_sum(int l, int r, T upper) {
    D ret = 0;
    for (int level = MAXLOG - 1; level >= 0; level--) {
      if (((upper >> level) & 1)) {
        auto nxt = succ(false, l, r, level);
        ret += ds[level].prod(nxt.first, nxt.second);
        l = l - nxt.first + mid[level];
        r = r - nxt.second + mid[level];
      } else {
        std::tie(l, r) = succ(false, l, r, level);
      }
    }
    return ret;
  }

  D rect_sum(int l, int r, T lower, T upper) {
    return rect_sum(l, r, upper) - rect_sum(l, r, lower);
  }

  void point_add(int k, const D& x) {
    auto& y = v[k];
    for (int level = MAXLOG - 1; level >= 0; level--) {
      bool f = ((y >> level) & 1);
      k = matrix[level].rank(f, k) + mid[level] * f;
      ds[level].apply(k, x);
    }
  }
};

template <typename T, int MAXLOG, typename D>
struct CompressedWaveletMatrixPointAddRectangleSum {
  WaveletMatrixPointAddRectangleSum<int, MAXLOG, D> mat;
  std::vector<T> ys;

  CompressedWaveletMatrixPointAddRectangleSum(const std::vector<T>& v,
                                              const std::vector<D>& d)
      : ys(v) {
    std::sort(std::begin(ys), std::end(ys));
    ys.erase(std::unique(std::begin(ys), std::end(ys)), std::end(ys));
    std::vector<int> t(v.size());
    for (int i = 0; i < v.size(); i++) t[i] = get(v[i]);
    mat = WaveletMatrixPointAddRectangleSum<int, MAXLOG, D>(t, d);
  }

  inline int get(const T& x) {
    return std::lower_bound(std::begin(ys), std::end(ys), x) - std::begin(ys);
  }

  D rect_sum(int l, int r, T upper) { return mat.rect_sum(l, r, get(upper)); }

  D rect_sum(int l, int r, T lower, T upper) {
    return mat.rect_sum(l, r, get(lower), get(upper));
  }

  void point_add(int k, const D& x) { mat.point_add(k, x); }
};