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
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  copies of the Software, and to permit persons to whom the Software is
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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 <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 =
      requires(const F& f, const T& a, const T& b)
        {
          { f(a, b) } -> std::convertible_to<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 */