bgeot_permutations.h

/* -*- c++ -*- (enables emacs c++ mode) */
/*===========================================================================
 
 Copyright (C) 2004-2020 Julien Pommier
 
 This file is a part of GetFEM
 
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 As a special exception, you  may use  this file  as it is a part of a free
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===========================================================================*/
#include <vector>
#include "bgeot_config.h"
 
namespace bgeot {
  /**
     generation of permutations, and ranking/unranking of these.
 
     based on algorithms detailed in "Ranking and Unranking Permutations in linear time", W. Myrvold, F. Ruskey 
     ( http://www.csr.uvic.ca/~fruskey/Publications/RankPerm.html )
     note that this is not lexigraphical order, and to_rank(0) != {0,1,2,3,...} (it is {1,2,3,...,n,0})
 
     however, the reset(), finished(), and ++ operator are based on the lexicagraphical ordering
   */
  class permutation : public std::vector<dim_type> {
    size_type remaining;
  public:
    permutation(size_type n) : std::vector<dim_type>(n) { reset(); }
    size_type nb_permutations() { return permutation::nb_permutations(size()); }
    static size_type nb_permutations(size_type n)
    { size_type f=1; for (; n>1; --n) f *= n; return f; }
    void reset() {
      remaining = 1;
      for (size_type i=0; i < size(); ++i)
        { (*this)[i] = dim_type(i); remaining *= (i+1); }
    }
    permutation& to_rank(size_type r);
    permutation inversed() const {
      permutation pinv(*this);
      for (size_type i=0; i < size(); ++i) pinv[(*this)[i]] = dim_type(i);
      return pinv;
    }
    size_type rank() const;
    bool finished() const { return remaining == 0; }
    /* increment in lexicographical order (not the best, but it is simple) */
    const permutation &operator ++();
    template < typename CONT1, typename CONT2 > void apply_to(const CONT1& src, CONT2& dest) 
    { for (size_type i=0; i < size(); ++i) dest[i] = src[(*this)[i]]; }
  };
  inline permutation& permutation::to_rank(size_type r) {
    reset();
    for (size_type n = size(); n; --n) {
      std::swap((*this)[n-1], (*this)[r % n]);
      r /= n;
    }
    return (*this);
  }
  inline size_type permutation::rank() const { 
    permutation p(*this);
    permutation pinv(p.inversed());
    size_type mul=1, r=0;
    for (size_type n=size(); n>1; --n) {
      dim_type s = p[n-1];
      std::swap(p[n-1], p[pinv[n-1]]);
      std::swap(pinv[s],pinv[n-1]);
      r += s*mul; mul*=n;
    }
    return r;
  }  
  inline const permutation &permutation::operator ++() {
    if (--remaining == 0) return (*this);
    size_type i = size()-2, j=size()-1;
    while ((*this)[i] > (*this)[i+1]) i--;      
    while ((*this)[i] > (*this)[j]) j--;
    std::swap((*this)[i], (*this)[j]);
    for (size_type r = size()-1, s=i+1; r>s; --r, ++s) std::swap((*this)[r],(*this)[s]);
    return (*this);
  }
}