ah-comb.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 COMB_H
# define COMB_H
 
# include <algorithm>
# include <bit>
# include <cstdint>
# include <limits>
# include <numeric>
 
# include <htlist.H>
# include <tpl_dynDlist.H>
# include <tpl_dynArray.H>
# include <tpl_array.H>
# include <tpl_dynSetTree.H>
# include <ahFunction.H>
# include <ahSort.H>
 
namespace Aleph
{
  namespace comb_detail
  {
    template <typename T>
    [[nodiscard]] inline
    DynList<DynList<T>> transpose_impl(DynList<DynList<T>> & l)
    {
      if (l.is_empty())
        return {};
 
      Array<Array<Snodenc<T> *>> mat;
 
      size_t ncol = 0; {
        const HTList & lrow = l.get_first();
        Array<Snodenc<T> *> row;
        for (HTList::Iterator it(lrow); it.has_curr(); it.next_ne(), ++ncol)
          row.append(static_cast<Snodenc<T> *>(it.get_curr()));
        mat.append(std::move(row));
      }
 
      size_t nrow = 1;
      for (auto row_it = l.get_it(1); row_it.has_curr(); row_it.next_ne(), ++nrow)
        {
          const HTList & lrow = row_it.get_curr();
          Array<Snodenc<T> *> row;
          row.reserve(ncol);
          size_t col = 0;
          for (HTList::Iterator it(lrow); it.has_curr(); it.next_ne(), ++col)
            row.append(static_cast<Snodenc<T> *>(it.get_curr()));
 
          assert(col == ncol);
 
          mat.append(std::move(row));
        }
 
      DynList<DynList<T>> ret;
      for (size_t j = 0; j < ncol; ++j)
        {
          DynList<T> row;
          for (size_t i = 0; i < nrow; ++i)
            row.append(mat(i)(j)->get_data());
 
          ret.append(std::move(row));
        }
 
      return ret;
    }
 
    template <class ArrayLike>
    inline void reverse_range(ArrayLike & a,
                              size_t left, size_t right) noexcept
    {
      while (left < right)
        {
          std::swap(a(left), a(right));
          ++left;
          --right;
        }
    }
 
    template <class IndexArray>
    inline void validate_combination_indices(const IndexArray & idx,
                                             const size_t n)
    {
      const size_t k = idx.size();
      ah_domain_error_if(k > n)
        << "next_combination_indices: k=" << k << " cannot exceed n=" << n;
 
      for (size_t i = 0; i < k; ++i)
        {
          ah_out_of_range_error_if(idx(i) >= n)
            << "next_combination_indices: index " << idx(i)
            << " at position " << i << " is outside [0, " << n << ")";
 
          if (i > 0)
            ah_domain_error_if(idx(i - 1) >= idx(i))
              << "next_combination_indices: indices must be strictly increasing";
        }
    }
 
    template <class ArrayLike, class Compare>
    [[nodiscard]] inline bool next_permutation_impl(ArrayLike & a,
                                                    Compare cmp,
                                                    const bool reset_on_last)
    {
      const size_t n = a.size();
      if (n < 2)
        return false;
 
      size_t pivot = n;
      for (size_t i = n - 1; i > 0; --i)
        if (cmp(a(i - 1), a(i)))
          {
            pivot = i - 1;
            break;
          }
 
      if (pivot == n)
        {
          if (reset_on_last)
            reverse_range(a, 0, n - 1);
          return false;
        }
 
      size_t succ = n - 1;
      while (not cmp(a(pivot), a(succ)))
        --succ;
 
      std::swap(a(pivot), a(succ));
      reverse_range(a, pivot + 1, n - 1);
      return true;
    }
 
    template <class IndexArray>
    [[nodiscard]] inline bool next_combination_indices_impl(IndexArray & idx,
                                                            const size_t n,
                                                            const bool reset_on_last)
    {
      validate_combination_indices(idx, n);
 
      const size_t k = idx.size();
      if (k == 0)
        return false;
 
      for (size_t pos = k; pos > 0; --pos)
        {
          const size_t i = pos - 1;
          const size_t max_here = n - (k - i);
          if (idx(i) < max_here)
            {
              ++idx(i);
              for (size_t j = i + 1; j < k; ++j)
                idx(j) = idx(j - 1) + 1;
              return true;
            }
        }
 
      if (reset_on_last)
        for (size_t i = 0; i < k; ++i)
          idx(i) = i;
 
      return false;
    }
  } // namespace comb_detail
 
  template <typename T>
  [[nodiscard]] inline
  DynList<DynList<T>> transpose(const DynList<DynList<T>> & l)
  {
    if (l.is_empty())
      return {};
 
    Array<Array<T>> mat;
 
    for (auto it = l.get_it(); it.has_curr(); it.next_ne())
      mat.append(it.get_curr());
 
    const size_t nrow = mat.size();
    const size_t ncol = mat[0].size();
 
    for (size_t i = 1; i < nrow; ++i)
      assert(mat[i].size() == ncol);
 
    DynList<DynList<T>> ret;
 
    for (size_t j = 0; j < ncol; ++j)
      {
        DynList<T> row;
        for (size_t i = 0; i < nrow; ++i)
          row.append(mat(i)(j));
 
        ret.append(std::move(row));
      }
 
    return ret;
  }
 
 
  template <template <typename> class C, typename T>
  inline
  void in_place_transpose(C<C<T>> & l)
  {
    C<C<T>> mat;
 
    const size_t nrow = l.size();
    if (nrow == 0)
      return;
 
    const size_t ncol = l.get_first().size();
 
    for (size_t i = 0; i < nrow; ++i)
      assert(l(i).size() == ncol);
 
    for (size_t j = 0; j < ncol; ++j)
      {
        C<T> row;
        for (size_t i = 0; i < nrow; ++i)
          row.append(std::move(l(i)(j)));
        mat.append(std::move(row));
      }
    l.swap(mat);
  }
 
  template <typename T>
  inline
  void in_place_transpose(DynList<DynList<T>> & l)
  {
    if (l.is_empty())
      return;
 
    Array<Array<Slinknc *>> mat;
 
    size_t ncol = 0; {
      DynList<T> lrow = l.remove_first();
      Array<Slinknc *> row;
      for (; not lrow.is_empty(); ++ncol)
        row.append(lrow.remove_head());
      mat.append(std::move(row));
    }
 
    size_t nrow = 1;
    for (; not l.is_empty(); ++nrow)
      {
        DynList<T> lrow = l.remove_first();
        Array<Slinknc *> row;
        row.reserve(ncol);
        size_t col = 0;
        while (not lrow.is_empty())
          {
            row.append(lrow.remove_head());
            ++col;
          }
 
        assert(col == ncol);
 
        mat.append(std::move(row));
      }
 
    assert(l.is_empty());
 
    for (size_t j = 0; j < ncol; ++j)
      {
        DynList<T> row;
        for (size_t i = 0; i < nrow; ++i)
          {
            Slinknc *node_ptr = mat(i)(j);
            row.HTList::append(static_cast<Snodenc<T> *>(node_ptr));
          }
        l.append(std::move(row));
      }
  }
 
 
  template <typename T, class Op>
  static inline
  bool traverse_perm_impl(DynList<T> & sample,
                          DynList<typename DynList<T>::Iterator> & its, Op & op)
  {
    if (its.is_empty())
      return op(sample.template maps<T>([](const T & i) { return i; }));
 
    auto itor = its.remove_first();
    for (auto it = itor; it.has_curr(); it.next_ne())
      {
        auto item = it.get_curr();
        sample.insert(item);
        if (not traverse_perm_impl(sample, its, op))
          {
            sample.remove_first();
            its.insert(itor);
            return false;
          }
        sample.remove_first();
      }
    its.insert(itor);
 
    return true;
  }
 
 
  template <typename T, class Op>
  inline
  bool traverse_perm(const DynList<DynList<T>> & l, Op & op)
  {
    using IT = typename DynList<T>::Iterator;
    DynList<IT> its;
 
    { // This block allows getting a constant copy of l and then reverse
      // it. At the end of block lcpy memory is freed
      const DynList<IT> lcpy =
          l.template maps<IT>([](const auto & l) { return l.get_it(); });
      its = lcpy.rev();
    }
 
    DynList<T> ll;
    return traverse_perm_impl(ll, its, op);
  }
 
  template <typename T, class Op>
  inline
  bool traverse_perm(const DynList<DynList<T>> & l, Op && op)
  {
    return traverse_perm(l, op);
  }
 
  template <typename T, class Op>
  inline
  void for_each_perm(const DynList<DynList<T>> & l, Op & op)
  {
    traverse_perm(l, [&op](const auto & row)
                    {
                      op(row);
                      return true;
                    });
  }
 
  template <typename T, class Op>
  inline
  void for_each_perm(const DynList<DynList<T>> & l, Op && op)
  {
    return for_each_perm(l, op);
  }
 
  template <typename T>
  [[nodiscard]]
  DynList<DynList<T>> build_perms(const DynList<DynList<T>> & l)
  {
    DynList<DynList<T>> ret;
    for_each_perm(l, [&ret](const DynList<T> & perm) { ret.append(perm); });
    return ret;
  }
 
  template <typename T>
  [[nodiscard]]
  DynList<DynList<T>> build_combs(const DynList<DynList<T>> & l)
  {
    DynSetTree<DynList<T>, Avl_Tree, CmpContainer<DynList<T>, T>> combs;
 
    for_each_perm(l, [&combs](const DynList<T> & perm)
                    {
                      DynList<T> comb = sort(perm);
                      combs.insert(std::move(comb));
                    });
 
    return combs.
        template maps<DynList<T>>([](const DynList<T> & comb) { return comb; });
  }
 
  template <typename T, typename Tc, class Op = Dft_Fold_Op<Tc, T>>
  [[nodiscard]]
  T fold_perm(const T & init, const DynList<DynList<Tc>> & l, Op & op)
  {
    T acu = init;
    traverse_perm(l, [&op, &acu](const auto & l)
                    {
                      acu = op(acu, l);
                      return true;
                    });
    return acu;
  }
 
  template <typename T, typename Tc, class Op = Dft_Fold_Op<Tc, T>>
  [[nodiscard]]
  T fold_perm(const T & init, const DynList<DynList<Tc>> & l, Op && op)
  {
    return fold_perm(init, l, op);
  }
 
  template <typename T>
  [[nodiscard]]
  size_t perm_count(const DynList<DynList<T>> & l)
  {
    size_t count = 1;
    for (auto it = l.get_it(); it.has_curr(); it.next_ne())
      {
        const size_t sz = it.get_curr().size();
        if (sz == 0)
          return 0; // Any empty list results in no permutations
        count *= sz;
      }
    return count;
  }
 
  template <typename T, class Pred>
  [[nodiscard]]
  bool exists_perm(const DynList<DynList<T>> & l, Pred & pred)
  {
    bool found = false;
    traverse_perm(l, [&pred, &found](const DynList<T> & perm)
                    {
                      if (pred(perm))
                        {
                          found = true;
                          return false; // stop
                        }
                      return true;
                    });
    return found;
  }
 
  template <typename T, class Pred>
  [[nodiscard]]
  bool exists_perm(const DynList<DynList<T>> & l, Pred && pred)
  {
    return exists_perm(l, pred);
  }
 
  template <typename T, class Pred>
  [[nodiscard]]
  bool all_perm(const DynList<DynList<T>> & l, Pred & pred)
  {
    return traverse_perm(l, pred);
  }
 
  template <typename T, class Pred>
  [[nodiscard]]
  bool all_perm(const DynList<DynList<T>> & l, Pred && pred)
  {
    return all_perm(l, pred);
  }
 
  template <typename T, class Pred>
  [[nodiscard]]
  bool none_perm(const DynList<DynList<T>> & l, Pred & pred)
  {
    return not exists_perm(l, pred);
  }
 
  template <typename T, class Pred>
  [[nodiscard]]
  bool none_perm(const DynList<DynList<T>> & l, Pred && pred)
  {
    return none_perm(l, pred);
  }
 
  template <typename T, class Pred>
  [[nodiscard]]
  DynList<DynList<T>> filter_perm(const DynList<DynList<T>> & l, Pred & pred)
  {
    DynList<DynList<T>> ret;
    for_each_perm(l, [&ret, &pred](const DynList<T> & perm)
                    {
                      if (pred(perm))
                        ret.append(perm);
                    });
    return ret;
  }
 
  template <typename T, class Pred>
  [[nodiscard]]
  DynList<DynList<T>> filter_perm(const DynList<DynList<T>> & l, Pred && pred)
  {
    return filter_perm(l, pred);
  }
 
  template <typename R, typename T, class Op>
  [[nodiscard]]
  DynList<R> map_perm(const DynList<DynList<T>> & l, Op & op)
  {
    DynList<R> ret;
    for_each_perm(l, [&ret, &op](const DynList<T> & perm)
                    {
                      ret.append(op(perm));
                    });
    return ret;
  }
 
  template <typename R, typename T, class Op>
  [[nodiscard]]
  DynList<R> map_perm(const DynList<DynList<T>> & l, Op && op)
  {
    return map_perm<R>(l, op);
  }
 
  template <typename T, class Compare = Aleph::less<T>>
  [[nodiscard]] inline bool
  next_permutation(Array<T> & a,
                   Compare cmp = Compare(),
                   const bool reset_on_last = true)
  {
    return comb_detail::next_permutation_impl(a, cmp, reset_on_last);
  }
 
  template <typename T, class Compare = Aleph::less<T>>
  [[nodiscard]] inline bool
  next_permutation(DynArray<T> & a,
                   Compare cmp = Compare(),
                   const bool reset_on_last = true)
  {
    return comb_detail::next_permutation_impl(a, cmp, reset_on_last);
  }
 
  [[nodiscard]] inline size_t combination_count(size_t n, size_t k)
  {
    if (k > n)
      return 0;
 
    k = std::min(k, n - k);
    if (k == 0)
      return 1;
 
    size_t result = 1;
    for (size_t i = 1; i <= k; ++i)
      {
        size_t num = n - k + i;
        size_t den = i;
 
        size_t g = std::gcd(num, den);
        num /= g;
        den /= g;
 
        g = std::gcd(result, den);
        result /= g;
        den /= g;
 
        g = std::gcd(num, den);
        num /= g;
        den /= g;
 
        ah_runtime_error_if(den != 1)
          << "combination_count: internal reduction failure for C("
          << n << ", " << k << ")";
 
        ah_runtime_error_if(result > std::numeric_limits<size_t>::max() / num)
          << "combination_count: overflow for C(" << n << ", " << k << ")";
        result *= num;
      }
 
    return result;
  }
 
  [[nodiscard]] inline bool
  next_combination_indices(Array<size_t> & idx,
                           const size_t n,
                           const bool reset_on_last = true)
  {
    return comb_detail::next_combination_indices_impl(idx, n, reset_on_last);
  }
 
  [[nodiscard]] inline bool
  next_combination_indices(DynArray<size_t> & idx,
                           const size_t n,
                           const bool reset_on_last = true)
  {
    return comb_detail::next_combination_indices_impl(idx, n, reset_on_last);
  }
 
  [[nodiscard]] inline uint64_t first_combination_mask(const size_t k)
  {
    ah_out_of_range_error_if(k > 64)
      << "first_combination_mask: k=" << k << " cannot exceed 64";
 
    if (k == 0)
      return 0;
    if (k == 64)
      return std::numeric_limits<uint64_t>::max();
    return (uint64_t(1) << k) - 1;
  }
 
  [[nodiscard]] inline bool
  next_combination_mask(uint64_t & mask,
                        const size_t n,
                        const bool reset_on_last = true)
  {
    ah_out_of_range_error_if(n > 64)
      << "next_combination_mask: n=" << n << " cannot exceed 64";
 
    if (n == 0)
      {
        ah_domain_error_if(mask != 0)
          << "next_combination_mask: for n=0, mask must be 0";
        return false;
      }
 
    const uint64_t domain_mask =
      n == 64 ? std::numeric_limits<uint64_t>::max() : ((uint64_t(1) << n) - 1);
 
    ah_domain_error_if(mask & ~domain_mask)
      << "next_combination_mask: mask has bits outside the low n bits";
 
    const size_t k = std::popcount(mask);
    if (k == 0)
      {
        if (reset_on_last)
          mask = 0;
        return false;
      }
 
    const uint64_t c = mask & (~mask + 1); // isolate least significant set bit
    const uint64_t r = mask + c;
 
    if (r == 0)
      {
        if (reset_on_last)
          mask = first_combination_mask(k);
        return false;
      }
 
    const uint64_t next = (((r ^ mask) >> 2) / c) | r;
    if (next & ~domain_mask)
      {
        if (reset_on_last)
          mask = first_combination_mask(k);
        return false;
      }
 
    mask = next;
    return true;
  }
 
  template <class ValuesArray, class Op>
  [[nodiscard]] static inline bool
  for_each_combination_impl(const ValuesArray & values,
                            const size_t k,
                            Op && op)
  {
    const size_t n = values.size();
    ah_domain_error_if(k > n)
      << "for_each_combination: k=" << k << " cannot exceed n=" << n;
 
    if (k == 0)
      return op(Array<typename ValuesArray::Item_Type>());
 
    Array<size_t> idx = Array<size_t>::create(k);
    for (size_t i = 0; i < k; ++i)
      idx(i) = i;
 
    while (true)
      {
        Array<typename ValuesArray::Item_Type> comb = Array<typename ValuesArray::Item_Type>::create(k);
        for (size_t i = 0; i < k; ++i)
          comb(i) = values(idx(i));
 
        if (not op(comb))
          return false;
 
        if (not next_combination_indices(idx, n, false))
          break;
      }
 
    return true;
  }
 
  template <typename T, class Op>
  [[nodiscard]] inline bool
  for_each_combination(const Array<T> & values, const size_t k, Op && op)
  {
    return for_each_combination_impl(values, k, std::forward<Op>(op));
  }
 
  template <typename T, class Op>
  [[nodiscard]] inline bool
  for_each_combination(const DynArray<T> & values, const size_t k, Op && op)
  {
    return for_each_combination_impl(values, k, std::forward<Op>(op));
  }
 
  template <typename T>
  [[nodiscard]] inline Array<Array<T>>
  build_combinations(const Array<T> & values, const size_t k)
  {
    Array<Array<T>> ret;
    (void) for_each_combination(values, k, [&ret](const Array<T> & comb)
    {
      ret.append(comb);
      return true;
    });
    return ret;
  }
 
  template <typename T>
  [[nodiscard]] inline Array<Array<T>>
  build_combinations(const DynArray<T> & values, const size_t k)
  {
    Array<Array<T>> ret;
    (void) for_each_combination(values, k, [&ret](const Array<T> & comb)
    {
      ret.append(comb);
      return true;
    });
    return ret;
  }
 
 
  template <std::unsigned_integral T>
  [[nodiscard]] constexpr T bin_to_gray(const T n) noexcept
  {
    return n ^ (n >> 1);
  }
 
 
  template <std::unsigned_integral T>
  [[nodiscard]] constexpr T gray_to_bin(T g) noexcept
  {
    for (size_t shift = 1; shift < sizeof(T) * 8; shift <<= 1)
      g ^= (g >> shift);
    return g;
  }
 
 
  [[nodiscard]] inline Array<uint32_t> build_gray_code(const size_t n)
  {
    ah_domain_error_if(n > 31)
      << "build_gray_code: n=" << n << " exceeds 31-bit limit for Array";
 
    const size_t count = size_t(1) << n;
    Array<uint32_t> ret;
    ret.reserve(count);
    for (size_t i = 0; i < count; ++i)
      ret.append(bin_to_gray(static_cast<uint32_t>(i)));
 
    return ret;
  }
}
 
# endif // COMB_H