data-structure/wavelet-matrix.hpp

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• Last update: 2023-03-13 02:01:43+09:00
• Include: #include "data-structure/wavelet-matrix.hpp"

Depends on

• data-structure/bitvector.hpp

Required by

• data-structure/wavelet-matrix-comp.hpp

Verified with

• test/yosupo/Data-Structure/Range-Kth-Smallest.test.cpp
• test/yosupo/Data-Structure/Static-Range-Frequency.test.cpp

Code

#include "bitvector.hpp"

//----- Wavelet Matrix -----


template <class T, int maxlog, bool USE_SUM = false>
struct WaveletMatrix {
  int len;
  BitVector matrix[maxlog];
  int mid[maxlog];
  vector<T> sum[maxlog];
  WaveletMatrix(){}
  WaveletMatrix(vector<T> v) : len(v.size()){
    vector<T> l(len), r(len);
		fill(matrix, matrix + maxlog, BitVector(len + 1));
    if(USE_SUM) fill(sum, sum + maxlog, vector<T>(len + 1));
    for(int level = maxlog - 1; level >= 0; level--){
      int left = 0, right = 0;
      for(int i = 0; i < len; i++){
        if(v[i] >> level & 1){
          matrix[level].set(i);
          r[right++] = v[i];
        }else{
          l[left++] = v[i];
        }
      }
      mid[level] = left;
      matrix[level].build();
      v.swap(l);
      copy(r.begin(), r.begin() + right, v.begin() + left);
      if(USE_SUM){
        sum[level][0] = 0;
        for(int i = 0; i < len; i++){
          sum[level][i + 1] = sum[level][i] + v[i];
        }
      }
    }
  }
  inline int succ(const int f, const int l, const int level) const{
    return matrix[level].rank(f, l) + mid[level] * f;
  }
  //find v[k]

  T access(int k) const{
    assert(0 <= k && k < len);
    T res = 0;
    for(int level = maxlog - 1; level >= 0; level--){
      const bool f = matrix[level][k];
      if(f) res |= T(1) << level;
      k = matrix[level].rank(f, k) + mid[level]*f;
    }
    return res;
  }
  T operator[](const int k) const{ return access(k); }
  // count i  (0 <= i < r) && v[i] == x

  int rank(const T x, int r) const{
    assert(0 <= r && r <= len);
    int l = 0;
    for(int level = maxlog - 1; level >= 0; level--){
      l = succ(x >> level & 1, l, level);
      r = succ(x >> level & 1, r, level);
    }
    return r - l;
  }
  //k-th value v[l,r)

  T kth_smallest(int l, int r, int k) const{
    assert(0 <= l && l <= r && r <= len);
    assert(0 <= k && k < r - l);
    T res = 0;
    for(int level = maxlog - 1; level >= 0; level--){
      int cnt = matrix[level].rank(0, r) - matrix[level].rank(0, l);
      bool f = cnt <= k;
      if(f){
        res |= T(1) << level;
        k -= cnt;
      }
      l = succ(f, l, level);
      r = succ(f, r, level);
    }
    return res;
  }
  T kth_largest(int l, int r, int k) const{
    return kth_smallest(l, r, r-l-k-1);
  }
  // sum of [0,k)th smallest elements([l, r))

  T kth_smallest_sum(int l, int r, int k) const{
    assert(0 <= l && l <= r && r <= len);
    assert(0 <= k && k <= r - l);
    assert(USE_SUM);
    T res = 0;
    for(int level = maxlog - 1; level >= 0; level--){
      const int l0 = matrix[level].rank(0, l);
      const int r0 = matrix[level].rank(0, r);
      if(k < r0 - l0){
        l = l0, r = r0;
      }else{
        k -= r0 - l0;
        res += sum[level][r0] - sum[level][l0];
        l += mid[level] - l0;
        r += mid[level] - r0;
      }
    }
    if(k) res += sum[0][l + k] - sum[0][l];
    return res;
  }
  // sum of [0,k)th largest elements([l, r))

  T kth_largest_sum(int l, int r, int k) const{
    assert(0 <= l && l <= r && r <= len);
    assert(0 <= k && k <= r - l);
    assert(USE_SUM);
    return  kth_smallest_sum(l, r, r - l) - kth_smallest_sum(l, r, r - l - k);
  }
  // count i  (l <= i < r), (v[i] < upper)

  int range_freq(int l, int r, const T upper) const{
    int res = 0;
    for(int level = maxlog - 1; level >= 0; level--){
      bool f = upper >> level & 1;
      if(f) res += matrix[level].rank(0, r) - matrix[level].rank(0, l);
      l = succ(f, l, level);
      r = succ(f, r, level);
    }
    return res;
  }
  // count i  (l <= i < r), (lower <= v[i] < upper)

  int range_freq(int l, int r, const T lower, const T upper) const{
    assert(0 <= l && l <= r && r <= len);
    return range_freq(l, r, upper) - range_freq(l, r, lower);
  }
  // max v[i]  (l <= i < r), (v[i] < upper)

  T prev_value(int l, int r, const T upper) const{
    assert(0 <= l && l <= r && r <= len);
    int cnt = range_freq(l, r, upper);
    return cnt == 0 ? -1 : kth_smallest(l, r, cnt - 1);
  }
  // min v[i]  (l <= i < r), (lower <= v[i])

  T next_value(int l, int r, const T lower) const{
    assert(0 <= l && l <= r && r <= len);
    int cnt = range_freq(l, r, lower);
    return cnt == r - l ? -1 : kth_smallest(l, r, cnt);
  }
};

#line 1 "data-structure/bitvector.hpp"
struct BitVector {
  using uint = unsigned int;
  static constexpr int w = 32;
  #define rem(k) ((k) & (w - 1))
  int len, blocks;
  vector<uint> bit, sum;
  BitVector(){}
  BitVector(const int len) : len(len), blocks((len+w-1)/w){
    bit.assign(blocks, 0);
    sum.assign(blocks, 0);
  }
  inline void set(const int k, const int b = 1) noexcept{
    if(b) bit[k / w] |= 1U << rem(k);
    else bit[k / w] &= ~(1U << rem(k));
  }
  void build(){
    sum[0] = 0;
    for(int i = 1; i < blocks; i++){
      sum[i] = sum[i - 1] + __builtin_popcount(bit[i - 1]);
    }
  }
  int operator[](const int k) const{
    return bit[k / w] >> rem(k) & 1;
  }
  inline int rank(const int k) const noexcept{
    return sum[k / w] + __builtin_popcount(bit[k / w] & ((1U << rem(k)) - 1));
  }
  inline int rank(const int val, const int k) const noexcept{
    return val ? rank(k) : k - rank(k);
  }
  #undef rem
};
#line 2 "data-structure/wavelet-matrix.hpp"

//----- Wavelet Matrix -----


template <class T, int maxlog, bool USE_SUM = false>
struct WaveletMatrix {
  int len;
  BitVector matrix[maxlog];
  int mid[maxlog];
  vector<T> sum[maxlog];
  WaveletMatrix(){}
  WaveletMatrix(vector<T> v) : len(v.size()){
    vector<T> l(len), r(len);
		fill(matrix, matrix + maxlog, BitVector(len + 1));
    if(USE_SUM) fill(sum, sum + maxlog, vector<T>(len + 1));
    for(int level = maxlog - 1; level >= 0; level--){
      int left = 0, right = 0;
      for(int i = 0; i < len; i++){
        if(v[i] >> level & 1){
          matrix[level].set(i);
          r[right++] = v[i];
        }else{
          l[left++] = v[i];
        }
      }
      mid[level] = left;
      matrix[level].build();
      v.swap(l);
      copy(r.begin(), r.begin() + right, v.begin() + left);
      if(USE_SUM){
        sum[level][0] = 0;
        for(int i = 0; i < len; i++){
          sum[level][i + 1] = sum[level][i] + v[i];
        }
      }
    }
  }
  inline int succ(const int f, const int l, const int level) const{
    return matrix[level].rank(f, l) + mid[level] * f;
  }
  //find v[k]

  T access(int k) const{
    assert(0 <= k && k < len);
    T res = 0;
    for(int level = maxlog - 1; level >= 0; level--){
      const bool f = matrix[level][k];
      if(f) res |= T(1) << level;
      k = matrix[level].rank(f, k) + mid[level]*f;
    }
    return res;
  }
  T operator[](const int k) const{ return access(k); }
  // count i  (0 <= i < r) && v[i] == x

  int rank(const T x, int r) const{
    assert(0 <= r && r <= len);
    int l = 0;
    for(int level = maxlog - 1; level >= 0; level--){
      l = succ(x >> level & 1, l, level);
      r = succ(x >> level & 1, r, level);
    }
    return r - l;
  }
  //k-th value v[l,r)

  T kth_smallest(int l, int r, int k) const{
    assert(0 <= l && l <= r && r <= len);
    assert(0 <= k && k < r - l);
    T res = 0;
    for(int level = maxlog - 1; level >= 0; level--){
      int cnt = matrix[level].rank(0, r) - matrix[level].rank(0, l);
      bool f = cnt <= k;
      if(f){
        res |= T(1) << level;
        k -= cnt;
      }
      l = succ(f, l, level);
      r = succ(f, r, level);
    }
    return res;
  }
  T kth_largest(int l, int r, int k) const{
    return kth_smallest(l, r, r-l-k-1);
  }
  // sum of [0,k)th smallest elements([l, r))

  T kth_smallest_sum(int l, int r, int k) const{
    assert(0 <= l && l <= r && r <= len);
    assert(0 <= k && k <= r - l);
    assert(USE_SUM);
    T res = 0;
    for(int level = maxlog - 1; level >= 0; level--){
      const int l0 = matrix[level].rank(0, l);
      const int r0 = matrix[level].rank(0, r);
      if(k < r0 - l0){
        l = l0, r = r0;
      }else{
        k -= r0 - l0;
        res += sum[level][r0] - sum[level][l0];
        l += mid[level] - l0;
        r += mid[level] - r0;
      }
    }
    if(k) res += sum[0][l + k] - sum[0][l];
    return res;
  }
  // sum of [0,k)th largest elements([l, r))

  T kth_largest_sum(int l, int r, int k) const{
    assert(0 <= l && l <= r && r <= len);
    assert(0 <= k && k <= r - l);
    assert(USE_SUM);
    return  kth_smallest_sum(l, r, r - l) - kth_smallest_sum(l, r, r - l - k);
  }
  // count i  (l <= i < r), (v[i] < upper)

  int range_freq(int l, int r, const T upper) const{
    int res = 0;
    for(int level = maxlog - 1; level >= 0; level--){
      bool f = upper >> level & 1;
      if(f) res += matrix[level].rank(0, r) - matrix[level].rank(0, l);
      l = succ(f, l, level);
      r = succ(f, r, level);
    }
    return res;
  }
  // count i  (l <= i < r), (lower <= v[i] < upper)

  int range_freq(int l, int r, const T lower, const T upper) const{
    assert(0 <= l && l <= r && r <= len);
    return range_freq(l, r, upper) - range_freq(l, r, lower);
  }
  // max v[i]  (l <= i < r), (v[i] < upper)

  T prev_value(int l, int r, const T upper) const{
    assert(0 <= l && l <= r && r <= len);
    int cnt = range_freq(l, r, upper);
    return cnt == 0 ? -1 : kth_smallest(l, r, cnt - 1);
  }
  // min v[i]  (l <= i < r), (lower <= v[i])

  T next_value(int l, int r, const T lower) const{
    assert(0 <= l && l <= r && r <= len);
    int cnt = range_freq(l, r, lower);
    return cnt == r - l ? -1 : kth_smallest(l, r, cnt);
  }
};

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