tpl_fenwick_tree.H

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/*
                          Aleph_w
 
  Data structures & Algorithms
  version 2.0.0b
  https://github.com/lrleon/Aleph-w
 
  This file is part of Aleph-w library
 
  Copyright (c) 2002-2026 Leandro Rabindranath Leon
 
  Permission is hereby granted, free of charge, to any person obtaining a copy
  of this software and associated documentation files (the "Software"), to deal
  in the Software without restriction, including without limitation the rights
  to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
  copies of the Software, and to permit persons to whom the Software is
  furnished to do so, subject to the following conditions:
 
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  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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*/
 
 
# ifndef TPL_FENWICK_TREE_H
# define TPL_FENWICK_TREE_H
 
# include <bit>
# include <cassert>
# include <concepts>
# include <initializer_list>
# include <type_traits>
# include <vector>
# include <utility>
# include <ah-concepts.H>
# include <tpl_array.H>
# include <tpl_dynList.H>
# include <ahFunction.H>
# include <ah-errors.H>
 
namespace Aleph
{
  template <typename T>
  concept FenwickArithmetic =
      std::is_arithmetic_v<T> &&
      std::totally_ordered<T> &&
      std::is_signed_v<T> &&
      !std::same_as<T, bool>;
 
  template <typename F, typename T>
  concept FenwickBinaryOp = Aleph::ClosedBinaryOp<F, T>;
 
  template <typename T,
            class Plus = Aleph::plus<T>,
            class Minus = Aleph::minus<T>>
    requires (FenwickBinaryOp<Plus, T> && FenwickBinaryOp<Minus, T>)
  class Gen_Fenwick_Tree
  {
  protected:
    Array<T> tree; // 1-indexed internal storage (position 0 unused)
    size_t n = 0; // number of logical elements (0-indexed: 0..n-1)
 
    Plus plus_op;
    Minus minus_op;
 
    static constexpr size_t lowbit(size_t x) noexcept
    {
      return x & (~x + 1);
    }
 
    void build()
    {
      for (size_t i = 1; i <= n; ++i)
        if (const size_t parent = i + lowbit(i); parent <= n)
          tree(parent) = plus_op(tree(parent), tree(i));
    }
 
    template <class F>
    void fill_from_indexed(F getter)
    {
      for (size_t i = 0; i < n; ++i)
        tree(i + 1) = getter(i);
      build();
    }
 
    template <class StdIt>
    void fill_from_std_iter(StdIt first, StdIt last)
    {
      size_t i = 1;
      for (; first != last; ++first)
        tree(i++) = *first;
      build();
    }
 
    template <class AlephIt>
    void fill_from_aleph_it(AlephIt it)
    {
      size_t i = 1;
      for (; it.has_curr(); it.next_ne())
        tree(i++) = it.get_curr();
      build();
    }
 
  public:
    using Item_Type = T;
 
    Gen_Fenwick_Tree(const size_t num,
                     Plus pop = Plus(), Minus mop = Minus())
      : tree(num + 1, T()), n(num),
        plus_op(pop), minus_op(mop)
    {
      // empty — all elements are identity
    }
 
    Gen_Fenwick_Tree(std::initializer_list<T> il,
                     Plus pop = Plus(), Minus mop = Minus())
      : tree(il.size() + 1, T()), n(il.size()),
        plus_op(pop), minus_op(mop)
    {
      fill_from_std_iter(il.begin(), il.end());
    }
 
    Gen_Fenwick_Tree(const Array<T> & values,
                     Plus pop = Plus(), Minus mop = Minus())
      : tree(values.size() + 1, T()), n(values.size()),
        plus_op(pop), minus_op(mop)
    {
      fill_from_indexed([&values](size_t i) { return values(i); });
    }
 
    Gen_Fenwick_Tree(const std::vector<T> & values,
                     Plus pop = Plus(), Minus mop = Minus())
      : tree(values.size() + 1, T()), n(values.size()),
        plus_op(pop), minus_op(mop)
    {
      fill_from_indexed([&values](size_t i) { return values[i]; });
    }
 
    Gen_Fenwick_Tree(const DynList<T> & values,
                     Plus pop = Plus(), Minus mop = Minus())
      : tree(values.size() + 1, T()), n(values.size()),
        plus_op(pop), minus_op(mop)
    {
      fill_from_aleph_it(values.get_it());
    }
 
    Gen_Fenwick_Tree(const Gen_Fenwick_Tree &) = default;
 
    Gen_Fenwick_Tree(Gen_Fenwick_Tree &&) noexcept = default;
 
    Gen_Fenwick_Tree &operator=(const Gen_Fenwick_Tree &) = default;
 
    Gen_Fenwick_Tree &operator=(Gen_Fenwick_Tree &&) noexcept = default;
 
    void update(size_t i, const T & delta)
    {
      ah_out_of_range_error_if(i >= n)
        << "Gen_Fenwick_Tree::update: index " << i << " >= size " << n;
 
      for (++i; i <= n; i += i & (-i))
        tree(i) = plus_op(tree(i), delta);
    }
 
    T prefix(size_t i) const
    {
      ah_out_of_range_error_if(i >= n)
        << "Gen_Fenwick_Tree::prefix: index " << i << " >= size " << n;
 
      T s = T();
      for (++i; i > 0; i -= i & (-i))
        s = plus_op(s, tree(i));
      return s;
    }
 
    T query(const size_t l, const size_t r) const
    {
      ah_out_of_range_error_if(r >= n)
        << "Gen_Fenwick_Tree::query: r=" << r << " >= n=" << n;
      ah_out_of_range_error_if(l > r)
        << "Gen_Fenwick_Tree::query: l=" << l << " > r=" << r;
 
      return l > 0 ? minus_op(prefix(r), prefix(l - 1)) : prefix(r);
    }
 
    T get(const size_t i) const
    {
      return query(i, i);
    }
 
    void set(const size_t i, const T & value)
    {
      update(i, minus_op(value, get(i)));
    }
 
    [[nodiscard]] constexpr size_t size() const noexcept { return n; }
 
    [[nodiscard]] constexpr bool is_empty() const noexcept { return n == 0; }
 
    Array<T> values() const
    {
      auto ret = Array<T>::create(n);
      for (size_t i = 0; i < n; ++i)
        ret(i) = get(i);
      return ret;
    }
 
    void swap(Gen_Fenwick_Tree & other) noexcept
    {
      tree.swap(other.tree);
      std::swap(n, other.n);
      std::swap(plus_op, other.plus_op);
      std::swap(minus_op, other.minus_op);
    }
  };
 
 
  template <FenwickArithmetic T>
  struct Fenwick_Tree
      : public Gen_Fenwick_Tree<T, Aleph::plus<T>, Aleph::minus<T>>
  {
    using Base = Gen_Fenwick_Tree<T, Aleph::plus<T>, Aleph::minus<T>>;
    using Base::Base; // inherit all constructors
 
    size_t find_kth(T k) const requires std::integral<T>
    {
      const size_t nn = this->n;
      if (nn == 0)
        return 0;
 
      size_t pos = 0;
      // highest power of 2 that is <= nn
      size_t bit_mask = std::bit_floor(nn);
 
      while (bit_mask > 0)
        {
          if (const size_t next = pos + bit_mask; next <= nn && this->tree(next) < k)
            {
              k -= this->tree(next);
              pos = next;
            }
          bit_mask >>= 1;
        }
 
      return pos < nn ? pos : nn;
    }
  };
 
  template <FenwickArithmetic T>
  class Range_Fenwick_Tree
  {
   Gen_Fenwick_Tree<T> b1; // stores differences d[i]
   Gen_Fenwick_Tree<T> b2; // stores d[i] * i
   size_t n = 0;
 
    T prefix_sum(size_t i) const
    {
      return static_cast<T>(i + 1) * b1.prefix(i) - b2.prefix(i);
    }
 
    void build_from_diffs(const Array<T> & d)
    {
      auto d2 = Array<T>::create(n);
      d2(0) = T();
      for (size_t i = 1; i < n; ++i)
        d2(i) = d(i) * static_cast<T>(i);
 
      Gen_Fenwick_Tree<T> new_b1(d);
      Gen_Fenwick_Tree<T> new_b2(d2);
      b1.swap(new_b1);
      b2.swap(new_b2);
    }
 
  public:
    using Item_Type = T;
 
    Range_Fenwick_Tree(const size_t num)
      : b1(num), b2(num), n(num)
    {
      // empty — all elements are identity
    }
 
    Range_Fenwick_Tree(std::initializer_list<T> il)
      : b1(il.size()), b2(il.size()), n(il.size())
    {
      if (n == 0)
        return;
 
      auto d = Array<T>::create(n);
      auto it = il.begin();
      d(0) = *it;
      T prev = *it++;
      for (size_t i = 1; i < n; ++i, ++it)
        {
          d(i) = *it - prev;
          prev = *it;
        }
      build_from_diffs(d);
    }
 
    Range_Fenwick_Tree(const Array<T> & values)
      : b1(values.size()), b2(values.size()), n(values.size())
    {
      if (n == 0)
        return;
 
      auto d = Array<T>::create(n);
      d(0) = values(0);
      for (size_t i = 1; i < n; ++i)
        d(i) = values(i) - values(i - 1);
      build_from_diffs(d);
    }
 
    Range_Fenwick_Tree(const Range_Fenwick_Tree &) = default;
 
    Range_Fenwick_Tree(Range_Fenwick_Tree &&) noexcept = default;
 
    Range_Fenwick_Tree &operator=(const Range_Fenwick_Tree &) = default;
 
    Range_Fenwick_Tree &operator=(Range_Fenwick_Tree &&) noexcept = default;
 
    void update(size_t l, const size_t r, const T & delta)
    {
      ah_out_of_range_error_if(l > r)
        << "Range_Fenwick_Tree::update: l=" << l << " > r=" << r;
      ah_out_of_range_error_if(r >= n)
        << "Range_Fenwick_Tree::update: r=" << r << " >= size " << n;
 
      b1.update(l, delta);
      b2.update(l, delta * static_cast<T>(l));
 
      if (r + 1 < n)
        {
          T neg = -delta;
          b1.update(r + 1, neg);
          b2.update(r + 1, neg * static_cast<T>(r + 1));
        }
    }
 
    void point_update(const size_t i, const T & delta)
    {
      update(i, i, delta);
    }
 
    T prefix(const size_t i) const
    {
      ah_out_of_range_error_if(i >= n)
        << "Range_Fenwick_Tree::prefix: index " << i << " >= size " << n;
 
      return prefix_sum(i);
    }
 
    T query(const size_t l, const size_t r) const
    {
      ah_out_of_range_error_if(r >= n)
        << "Range_Fenwick_Tree::query: r=" << r << " >= n=" << n;
      ah_out_of_range_error_if(l > r)
        << "Range_Fenwick_Tree::query: l=" << l << " > r=" << r;
 
      return l > 0 ? prefix_sum(r) - prefix_sum(l - 1) : prefix_sum(r);
    }
 
    T get(const size_t i) const
    {
      return query(i, i);
    }
 
    void set(const size_t i, const T & value)
    {
      point_update(i, value - get(i));
    }
 
    [[nodiscard]] constexpr size_t size() const noexcept { return n; }
 
    [[nodiscard]] constexpr bool is_empty() const noexcept { return n == 0; }
 
    Array<T> values() const
    {
      auto ret = Array<T>::create(n);
      for (size_t i = 0; i < n; ++i)
        ret(i) = get(i);
      return ret;
    }
 
    void swap(Range_Fenwick_Tree & other) noexcept
    {
      b1.swap(other.b1);
      b2.swap(other.b2);
      std::swap(n, other.n);
    }
  };
} // end namespace Aleph
 
# endif /* TPL_FENWICK_TREE_H */