tpl_sparse_table.H

Go to the documentation of this file.

 
/*
                          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:
 
  The above copyright notice and this permission notice shall be included in all
  copies or substantial portions of the Software.
 
  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
  IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
  AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
  LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
  OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
  SOFTWARE.
*/
 
 
# ifndef TPL_SPARSE_TABLE_H
# define TPL_SPARSE_TABLE_H
 
# include <bit>
# include <cassert>
# include <cstdlib>
# include <concepts>
# include <functional>
# include <initializer_list>
# include <type_traits>
# include <vector>
# include <utility>
# include <algorithm>
# include <ah-concepts.H>
# include <tpl_array.H>
# include <tpl_dynList.H>
# include <ahFunction.H>
# include <ah-errors.H>
 
namespace Aleph
{
  namespace sparse_table_detail
  {
    // Arithmetic functors: never idempotent over numbers other than bool.
    template <typename F>
    inline constexpr bool is_arithmetic_functor = false;
 
    template <typename U>
    inline constexpr bool is_arithmetic_functor<std::plus<U>> = true;
    template <typename U>
    inline constexpr bool is_arithmetic_functor<std::minus<U>> = true;
    template <typename U>
    inline constexpr bool is_arithmetic_functor<std::multiplies<U>> = true;
    template <typename U>
    inline constexpr bool is_arithmetic_functor<std::divides<U>> = true;
    template <typename U>
    inline constexpr bool is_arithmetic_functor<std::modulus<U>> = true;
    template <typename U>
    inline constexpr bool is_arithmetic_functor<std::bit_xor<U>> = true;
    template <typename U>
    inline constexpr bool is_arithmetic_functor<Aleph::plus<U>> = true;
    template <typename U>
    inline constexpr bool is_arithmetic_functor<Aleph::minus<U>> = true;
    template <typename U>
    inline constexpr bool is_arithmetic_functor<Aleph::multiplies<U>> = true;
    template <typename U>
    inline constexpr bool is_arithmetic_functor<Aleph::divides<U>> = true;
    template <typename U>
    inline constexpr bool is_arithmetic_functor<Aleph::modulus<U>> = true;
  } // namespace sparse_table_detail
 
  template <typename F, typename T>
  inline constexpr bool is_known_non_idempotent_op =
      sparse_table_detail::is_arithmetic_functor<std::remove_cvref_t<F>> and
      std::is_arithmetic_v<std::remove_cv_t<T>> and
      not std::is_same_v<std::remove_cv_t<T>, bool>;
 
  template <typename F, typename T>
  concept IdempotentOp =
      Aleph::ClosedBinaryOp<F, T> and not is_known_non_idempotent_op<F, T>;
 
  template <typename F, typename T>
  concept SparseTableOp = IdempotentOp<F, T>;
 
  template <std::totally_ordered T>
  struct Min_Op
  {
    constexpr T operator()(const T & a, const T & b) const noexcept
    {
      return a <= b ? a : b;
    }
  };
 
  template <std::totally_ordered T>
  struct Max_Op
  {
    constexpr T operator()(const T & a, const T & b) const noexcept
    {
      return a >= b ? a : b;
    }
  };
 
  template <typename T, class Op>
    requires SparseTableOp<Op, T>
  class Gen_Sparse_Table
  {
    Array<T> table;        // flattened 2D: table[k * n + i]
    Array<size_t> log_tbl; // log_tbl[len] = floor(log2(len)) for len in [1..n]
    size_t n = 0;          // number of logical elements
    size_t levels = 0;     // number of levels = floor(log2(n)) + 1
 
    Op op;
 
    T & at(const size_t k, const size_t i) { return table(k * n + i); }
    const T & at(const size_t k, const size_t i) const { return table(k * n + i); }
 
    static constexpr size_t compute_levels(const size_t nn) noexcept
    {
      return nn == 0 ? 0 : static_cast<size_t>(std::bit_width(nn));
    }
 
    static constexpr size_t compute_cells(const size_t nn) noexcept
    {
      return nn == 0 ? 1 : compute_levels(nn) * nn;
    }
 
    void build_log_table()
    {
      if (n == 0)
        return;
 
      log_tbl = Array<size_t>::create(n + 1);
      log_tbl(0) = 0;
      log_tbl(1) = 0;
      for (size_t i = 2; i <= n; ++i)
        log_tbl(i) = log_tbl(i / 2) + 1;
    }
 
    void build_upper_levels()
    {
      // table[k][i] = Op(table[k-1][i], table[k-1][i + 2^(k-1)])
      for (size_t k = 1; k < levels; ++k)
        {
          const size_t half = size_t{1} << (k - 1);
          const size_t limit = n - (size_t{1} << k) + 1;
          for (size_t i = 0; i < limit; ++i)
            at(k, i) = op(at(k - 1, i), at(k - 1, i + half));
        }
    }
 
    template <class Getter>
    void fill_and_build(Getter getter)
    {
      // Level 0: intervals of length 1
      for (size_t i = 0; i < n; ++i)
        at(0, i) = getter(i);
 
      build_upper_levels();
    }
 
    template <class AlephIt>
    void fill_from_aleph_it(AlephIt it)
    {
      size_t i = 0;
      for (; it.has_curr(); it.next_ne())
        at(0, i++) = it.get_curr();
 
      build_upper_levels();
    }
 
  public:
    using Item_Type = T;
 
    Gen_Sparse_Table(const size_t num, const T & init_val,
                     Op oper = Op())
      : table(Array<T>::create(compute_cells(num))),
        n(num), levels(compute_levels(num)), op(oper)
    {
      build_log_table();
      if (n > 0)
        fill_and_build([&init_val](size_t) { return init_val; });
    }
 
    Gen_Sparse_Table(std::initializer_list<T> il, Op oper = Op())
      : table(Array<T>::create(compute_cells(il.size()))),
        n(il.size()), levels(compute_levels(il.size())), op(oper)
    {
      build_log_table();
      if (n > 0)
        {
          auto it = il.begin();
          fill_and_build([&it](size_t) { return *it++; });
        }
    }
 
    Gen_Sparse_Table(const Array<T> & values, Op oper = Op())
      : table(Array<T>::create(compute_cells(values.size()))),
        n(values.size()), levels(compute_levels(values.size())), op(oper)
    {
      build_log_table();
      if (n > 0)
        fill_and_build([&values](size_t i) { return values(i); });
    }
 
    Gen_Sparse_Table(const std::vector<T> & values, Op oper = Op())
      : table(Array<T>::create(compute_cells(values.size()))),
        n(values.size()), levels(compute_levels(values.size())), op(oper)
    {
      build_log_table();
      if (n > 0)
        fill_and_build([&values](size_t i) { return values[i]; });
    }
 
    Gen_Sparse_Table(const DynList<T> & values, Op oper = Op())
      : table(Array<T>::create(compute_cells(values.size()))),
        n(values.size()), levels(compute_levels(values.size())), op(oper)
    {
      build_log_table();
      if (n > 0)
        fill_from_aleph_it(values.get_it());
    }
 
    Gen_Sparse_Table(const Gen_Sparse_Table &) = default;
 
    Gen_Sparse_Table(Gen_Sparse_Table &&) noexcept(
      std::is_nothrow_move_constructible_v<Array<T>> &&
      std::is_nothrow_move_constructible_v<Op>) = default;
 
    Gen_Sparse_Table & operator=(const Gen_Sparse_Table &) = default;
 
    Gen_Sparse_Table & operator=(Gen_Sparse_Table &&) noexcept(
      std::is_nothrow_move_assignable_v<Array<T>> &&
      std::is_nothrow_move_assignable_v<Op>) = default;
 
    T query(const size_t l, const size_t r) const
    {
      ah_out_of_range_error_if(r >= n)
        << "Gen_Sparse_Table::query: r=" << r << " >= n=" << n;
      ah_out_of_range_error_if(l > r)
        << "Gen_Sparse_Table::query: l=" << l << " > r=" << r;
 
      const size_t k = log_tbl(r - l + 1);
      return op(at(k, l), at(k, r - (size_t{1} << k) + 1));
    }
 
    T get(const size_t i) const
    {
      ah_out_of_range_error_if(i >= n)
        << "Gen_Sparse_Table::get: index " << i << " >= size " << n;
 
      return at(0, i);
    }
 
    [[nodiscard]] constexpr size_t size() const noexcept { return n; }
 
    [[nodiscard]] constexpr bool is_empty() const noexcept { return n == 0; }
 
    [[nodiscard]] constexpr size_t num_levels() const noexcept
    {
      return levels;
    }
 
    Array<T> values() const
    {
      auto ret = Array<T>::create(n);
      for (size_t i = 0; i < n; ++i)
        ret(i) = at(0, i);
      return ret;
    }
 
    void swap(Gen_Sparse_Table & other) noexcept
    {
      table.swap(other.table);
      log_tbl.swap(other.log_tbl);
      std::swap(n, other.n);
      std::swap(levels, other.levels);
      std::swap(op, other.op);
    }
  };
 
 
  template <std::totally_ordered T>
  struct Sparse_Table
      : public Gen_Sparse_Table<T, Min_Op<T>>
  {
    using Base = Gen_Sparse_Table<T, Min_Op<T>>;
    using Base::Base; // inherit all constructors
  };
 
  template <std::totally_ordered T>
  struct Max_Sparse_Table
      : public Gen_Sparse_Table<T, Max_Op<T>>
  {
    using Base = Gen_Sparse_Table<T, Max_Op<T>>;
    using Base::Base; // inherit all constructors
  };
 
} // end namespace Aleph
 
# endif /* TPL_SPARSE_TABLE_H */