modular_combinatorics.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
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  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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*/
 
# ifndef MODULAR_COMBINATORICS_H
# define MODULAR_COMBINATORICS_H
 
# include <cstdint>
# include <ah-errors.H>
# include <tpl_array.H>
# include <modular_arithmetic.H>
# include <primality.H>
 
namespace Aleph
{
  class ModularCombinatorics
  {
    uint64_t mod_;            
    Array<uint64_t> fact_;    
    Array<uint64_t> invFact_; 
 
  public:
    ModularCombinatorics(size_t max_n, const uint64_t p) : mod_(p)
    {
      ah_invalid_argument_if(not miller_rabin(mod_))
        << "ModularCombinatorics: modulus " << mod_ << " must be prime";
 
      if (max_n >= mod_)
        max_n = static_cast<size_t>(mod_ - 1);
 
      fact_.reserve(max_n + 1);
      invFact_.reserve(max_n + 1);
 
      fact_.append(1);
      for (size_t i = 1; i <= max_n; i++)
        fact_.append(mod_mul(fact_[i - 1], i, mod_));
 
      invFact_.putn(max_n + 1);
      invFact_(max_n) = mod_inv(fact_[max_n], mod_);
      for (size_t i = max_n; i > 0; i--)
        invFact_(i - 1) = mod_mul(invFact_[i], i, mod_);
    }
 
    [[nodiscard]] uint64_t nCk(const uint64_t n, const uint64_t k) const
    {
      if (k > n) return 0;
      ah_out_of_range_error_if(n >= fact_.size())
          << "ModularCombinatorics::nCk: n=" << n << " exceeds precomputed range "
          << fact_.size() - 1;
 
      const uint64_t num = fact_[n];
      const uint64_t den = mod_mul(invFact_[k], invFact_[n - k], mod_);
      return mod_mul(num, den, mod_);
    }
 
    [[nodiscard]] uint64_t lucas_nCk(const uint64_t n, const uint64_t k) const
    {
      if (k > n) return 0;
      if (k == 0) return 1;
 
      const uint64_t ni = n % mod_;
      const uint64_t ki = k % mod_;
 
      if (ki > ni) return 0;
 
      return mod_mul(nCk(ni, ki), lucas_nCk(n / mod_, k / mod_), mod_);
    }
  };
} // namespace Aleph
 
# endif // MODULAR_COMBINATORICS_H