tpl_union.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:
 
  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_UNION_H
# define TPL_UNION_H
 
# include <tpl_dynArray.H>
# include <tpl_dynSetTree.H>
 
# include <limits>
# include <stdexcept>
 
# include <ah-errors.H>
 
 
class Fixed_Relation
{
protected:
  DynArray<size_t> id;
  DynArray<size_t> sz;
  size_t num_blocks;
 
  void verify_index(const size_t i) const
  {
    ah_out_of_range_error_if(i >= id.size()) << "index out of range";
  }
 
  virtual size_t root(size_t i)
  {
    verify_index(i);
    while (i != id(i))
      {
        id(i) = id(id(i));
        i = id(i);
      }
 
    return i;
  }
 
  size_t depth(size_t i) const
  {
    verify_index(i);
    size_t d = 0;
    while (true)
      {
        ++d;
        const size_t parent = id(i);
        verify_index(parent);
        if (parent == i)
          return d;
        i = parent;
        if (d > id.size())
          ah_logic_error_if(d > id.size())
              << "cycle detected in union-find structure";
      }
  }
 
public:
  virtual ~Fixed_Relation() = default;
 
  Fixed_Relation(const size_t n = 0) : num_blocks(n)
  {
    if (num_blocks == 0)
      return;
 
    id.reserve(num_blocks);
    sz.reserve(num_blocks);
    for (size_t i = 0; i < num_blocks; ++i)
      {
        id(i) = i;
        sz(i) = 1;
      }
  }
 
  void set_n(size_t n)
  {
    id.empty();
    sz.empty();
    num_blocks = n;
    if (num_blocks == 0)
      return;
 
    id.reserve(num_blocks);
    sz.reserve(num_blocks);
    for (size_t i = 0; i < num_blocks; ++i)
      {
        id(i) = i;
        sz(i) = 1;
      }
  }
 
  size_t size() const noexcept { return id.size(); }
 
  [[nodiscard]] constexpr size_t get_num_blocks() const noexcept { return num_blocks; }
 
  bool are_connected(size_t i, size_t j)
  {
    return root(i) == root(j);
  }
 
  void join(size_t i, size_t j)
  {
    i = root(i);
    j = root(j);
    if (i == j)
      return;
 
    if (sz(i) < sz(j))
      {
        id(i) = j;
        sz(j) += sz(i);
      }
    else
      {
        id(j) = i;
        sz(i) += sz(j);
      }
    --num_blocks;
  }
};
 
 
class Relation : public Fixed_Relation
{
  void verify_if_add_new_points(const size_t n)
  {
    const size_t l = size();
    if (n < l)
      return;
 
    id.reserve(l, n);
    sz.reserve(l, n);
    for (size_t i = l; i <= n; ++i)
      {
        id(i) = i;
        sz(i) = 1;
      }
    num_blocks += n - l + 1;
  }
 
  size_t root(size_t i) override
  {
    verify_if_add_new_points(i);
    return Fixed_Relation::root(i);
  }
 
public:
  Relation(const size_t n = 0) : Fixed_Relation(n) {}
};
 
 
template <typename T, class Compare = Aleph::less<T>>
class Relation_T : public Relation
{
  struct Pair
  {
    T item;
    size_t i;
 
    Pair() noexcept {}
 
    Pair(const T & __item, size_t __i)
      : item(__item), i(__i)
    { /* empty */
    }
  };
 
  struct Cmp
  {
    bool operator ()(const Pair & p1, const Pair & p2) const noexcept
    {
      return Compare()(p1.item, p2.item);
    }
  };
 
  DynSetAvlTree<Pair, Cmp> items_tree;
 
  // returns the item ID; either because it is found or because it is inserted
  size_t test_and_insert_new_item(const T & item)
  {
    Pair p(item, std::numeric_limits<size_t>::max());
    Pair *ptr = items_tree.search_or_insert(p);
    if (ptr->i == std::numeric_limits<size_t>::max())
      {
        const size_t new_id = size();
        ptr->i = new_id;
        Relation::are_connected(new_id, new_id);
      }
    return ptr->i;
  }
 
public:
  bool are_connected(const T & p, const T & q)
  {
    const size_t i = test_and_insert_new_item(p);
    const size_t j = test_and_insert_new_item(q);
 
    return Relation::are_connected(i, j);
  }
 
  void join(const T & p, const T & q)
  {
    const size_t i = test_and_insert_new_item(p);
    const size_t j = test_and_insert_new_item(q);
    Relation::join(i, j);
  }
};
 
# endif // TPL_UNION_H