tpl_mo_algorithm.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_MO_ALGORITHM_H
# define TPL_MO_ALGORITHM_H
 
# include <algorithm>
# include <cmath>
# include <concepts>
# include <type_traits>
# include <utility>
# include <tpl_array.H>
# include <tpl_dynMapOhash.H>
# include <tpl_dynList.H>
# include <ah-errors.H>
 
namespace Aleph
{
  struct Mo_Query
  {
    size_t l; 
    size_t r; 
    size_t id; 
  };
 
  template <typename P, typename T>
  concept MoPolicy = requires(P & p, const Array<T> & data,
                              size_t idx, size_t n)
    {
      typename P::answer_type;
      { p.init(data, n) };
      { p.add(data, idx) };
      { p.remove(data, idx) };
      { p.answer() } -> std::convertible_to<typename P::answer_type>;
    };
 
  // ================================================================
  // Gen_Mo_Algorithm — Offline range queries via Mo's algorithm
  // ================================================================
 
  template <typename T, class Policy>
    requires MoPolicy<Policy, T>
  class Gen_Mo_Algorithm
  {
    Array<T> data_;
    mutable Policy pol_;
 
  public:
    using Item_Type = T;
    using answer_type = typename Policy::answer_type;
 
    Gen_Mo_Algorithm(std::initializer_list<T> il, Policy p = Policy())
      : data_(il), pol_(std::move(p))
    {}
 
    Gen_Mo_Algorithm(const Array<T> & arr, Policy p = Policy())
      : data_(arr), pol_(std::move(p))
    {}
 
    Gen_Mo_Algorithm(Array<T> and arr, Policy p = Policy())
      : data_(std::move(arr)), pol_(std::move(p))
    {}
 
    Gen_Mo_Algorithm(const DynList<T> & lst, Policy p = Policy())
      : data_(Array<T>::create(lst.size())), pol_(std::move(p))
    {
      size_t i = 0;
      for (auto it = lst.get_it(); it.has_curr(); it.next_ne())
        data_(i++) = it.get_curr();
    }
 
    Gen_Mo_Algorithm(const Gen_Mo_Algorithm &) = default;
 
    Gen_Mo_Algorithm(Gen_Mo_Algorithm &&) noexcept(
      std::is_nothrow_move_constructible_v<Array<T>> and
      std::is_nothrow_move_constructible_v<Policy>) = default;
 
    Gen_Mo_Algorithm &operator=(const Gen_Mo_Algorithm &) = default;
 
    Gen_Mo_Algorithm &operator=(Gen_Mo_Algorithm &&) noexcept(
      std::is_nothrow_move_assignable_v<Array<T>> and
      std::is_nothrow_move_assignable_v<Policy>) = default;
 
    [[nodiscard]] constexpr size_t size() const noexcept
    {
      return data_.size();
    }
 
    [[nodiscard]] constexpr bool is_empty() const noexcept
    {
      return data_.size() == 0;
    }
 
    void swap(Gen_Mo_Algorithm & other) noexcept(
      noexcept(std::swap(std::declval<Policy &>(), std::declval<Policy &>())))
    {
      data_.swap(other.data_);
      std::swap(pol_, other.pol_);
    }
 
    Array<answer_type> solve(const Array<std::pair<size_t, size_t>> & ranges) const
    {
      auto queries = Array<Mo_Query>::create(ranges.size());
      for (size_t i = 0; i < ranges.size(); ++i)
        queries(i) = {ranges(i).first, ranges(i).second, i};
      return solve(queries);
    }
 
    Array<answer_type> solve(const std::initializer_list<std::pair<size_t, size_t>> il) const
    {
      const Array<std::pair<size_t, size_t>> ranges(il);
      return solve(ranges);
    }
 
    Array<answer_type> solve(Array<Mo_Query> queries) const
    {
      const size_t n = data_.size();
      const size_t q = queries.size();
 
      if (q == 0)
        return Array<answer_type>();
 
      // Validate all queries
      for (size_t i = 0; i < q; ++i)
        {
          ah_out_of_range_error_if(queries(i).r >= n)
            << "Gen_Mo_Algorithm::solve: query " << i
            << " r=" << queries(i).r << " >= n=" << n;
          ah_out_of_range_error_if(queries(i).l > queries(i).r)
            << "Gen_Mo_Algorithm::solve: query " << i
            << " l=" << queries(i).l << " > r=" << queries(i).r;
          ah_out_of_range_error_if(queries(i).id >= q)
            << "Gen_Mo_Algorithm::solve: query " << i
            << " id=" << queries(i).id << " >= q=" << q;
        }
 
      const size_t block = std::max<size_t>(1, static_cast<size_t>(std::sqrt(static_cast<double>(n))));
 
      // Snake sort: primary by l/block, secondary alternating by r
      std::sort(&queries(0), &queries(0) + q,
                [block](const Mo_Query & a, const Mo_Query & b)
                  {
                    const size_t ba = a.l / block;
                    const size_t bb = b.l / block;
                    if (ba != bb)
                      return ba < bb;
                    // Even blocks: r ascending; odd blocks: r descending
                    return (ba & 1) ? (a.r > b.r) : (a.r < b.r);
                  });
 
      pol_.init(data_, n);
 
      auto answers = Array<answer_type>::create(q);
 
      // Initialise a window to the first query
      size_t cur_l = queries(0).l;
      size_t cur_r = queries(0).l;
      pol_.add(data_, cur_l);
 
      // Expand to the first query's right endpoint
      while (cur_r < queries(0).r)
        pol_.add(data_, ++cur_r);
 
      answers(queries(0).id) = pol_.answer();
 
      // Sweep remaining queries
      for (size_t i = 1; i < q; ++i)
        {
          const size_t ql = queries(i).l;
          const size_t qr = queries(i).r;
 
          // Expand right
          while (cur_r < qr)
            pol_.add(data_, ++cur_r);
 
          // Expand left
          while (cur_l > ql)
            pol_.add(data_, --cur_l);
 
          // Shrink right
          while (cur_r > qr)
            pol_.remove(data_, cur_r--);
 
          // Shrink left
          while (cur_l < ql)
            pol_.remove(data_, cur_l++);
 
          answers(queries(i).id) = pol_.answer();
        }
 
      return answers;
    }
  };
 
  // ================================================================
  // Built-in policies
  // ================================================================
 
  template <typename T>
  struct Distinct_Count_Policy
  {
    using answer_type = size_t;
 
    MapOLhash<T, size_t> freq;
    size_t distinct = 0;
 
    void init(const Array<T> &, size_t)
    {
      MapOLhash<T, size_t> tmp;
      freq.swap(tmp);
      distinct = 0;
    }
 
    void add(const Array<T> & data, size_t idx)
    {
      if (++freq[data(idx)] == 1)
        ++distinct;
    }
 
    void remove(const Array<T> & data, size_t idx)
    {
      if (--freq[data(idx)] == 0)
        --distinct;
    }
 
    [[nodiscard]] answer_type answer() const { return distinct; }
  };
 
  template <typename T>
  struct Powerful_Array_Policy
  {
    using answer_type = long long;
 
    MapOLhash<T, long long> cnt;
    long long sum = 0;
 
    void init(const Array<T> &, size_t)
    {
      MapOLhash<T, long long> tmp;
      cnt.swap(tmp);
      sum = 0;
    }
 
    void add(const Array<T> & data, size_t idx)
    {
      const auto x = static_cast<long long>(data(idx));
      sum += (2 * cnt[data(idx)] + 1) * x;
      ++cnt[data(idx)];
    }
 
    void remove(const Array<T> & data, size_t idx)
    {
      const auto x = static_cast<long long>(data(idx));
      --cnt[data(idx)];
      sum -= (2 * cnt[data(idx)] + 1) * x;
    }
 
    [[nodiscard]] answer_type answer() const { return sum; }
  };
 
  template <typename T>
  struct Range_Mode_Policy
  {
    using answer_type = std::pair<size_t, T>;
 
    MapOLhash<T, size_t> freq;
    MapOLhash<size_t, size_t> cnt_of_cnt;
    size_t max_freq = 0;
    T mode_val = T();
 
    void init(const Array<T> &, size_t)
    {
      MapOLhash<T, size_t> tmp_freq;
      MapOLhash<size_t, size_t> tmp_cnt;
      freq.swap(tmp_freq);
      cnt_of_cnt.swap(tmp_cnt);
      max_freq = 0;
      mode_val = T();
    }
 
    void add(const Array<T> & data, size_t idx)
    {
      const T & x = data(idx);
      const size_t old_f = freq[x];
      if (old_f > 0)
        --cnt_of_cnt[old_f];
      ++freq[x];
      ++cnt_of_cnt[old_f + 1];
      if (old_f + 1 > max_freq)
        {
          max_freq = old_f + 1;
          mode_val = x;
        }
    }
 
    void remove(const Array<T> & data, size_t idx)
    {
      const T & x = data(idx);
      const size_t old_f = freq[x];
      --cnt_of_cnt[old_f];
      if (old_f > 1)
        ++cnt_of_cnt[old_f - 1];
      --freq[x];
      if (old_f == max_freq and cnt_of_cnt[old_f] == 0)
        {
          --max_freq;
          // Find a value with the new max frequency; if max_freq is 0,
          // the window is empty.
          if (max_freq > 0)
            {
              for (typename MapOLhash<T, size_t>::Iterator it(freq);
                   it.has_curr(); it.next_ne())
                if (it.get_curr().second == max_freq)
                  {
                    mode_val = it.get_curr().first;
                    break;
                  }
            }
        }
      else if (old_f == max_freq and x == mode_val)
        {
          // x was the mode, but other elements still share max_freq;
          // pick any one of them.
          for (typename MapOLhash<T, size_t>::Iterator it(freq);
               it.has_curr(); it.next_ne())
            if (it.get_curr().second == max_freq)
              {
                mode_val = it.get_curr().first;
                break;
              }
        }
    }
 
    answer_type answer() const { return {max_freq, mode_val}; }
  };
 
  // ================================================================
  // Convenient typedefs
  // ================================================================
 
  template <typename T>
  using Distinct_Count_Mo = Gen_Mo_Algorithm<T, Distinct_Count_Policy<T>>;
 
  template <typename T>
  using Powerful_Array_Mo = Gen_Mo_Algorithm<T, Powerful_Array_Policy<T>>;
 
  template <typename T>
  using Range_Mode_Mo = Gen_Mo_Algorithm<T, Range_Mode_Policy<T>>;
} // namespace Aleph
 
# endif // TPL_MO_ALGORITHM_H