GetFEM++  5.3
bgeot_permutations.h
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4  Copyright (C) 2004-2017 Julien Pommier
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30 ===========================================================================*/
31 #include <vector>
32 #include "bgeot_config.h"
33 
34 namespace bgeot {
35  /**
36  generation of permutations, and ranking/unranking of these.
37 
38  based on algorithms detailed in "Ranking and Unranking Permutations in linear time", W. Myrvold, F. Ruskey
39  ( http://www.csr.uvic.ca/~fruskey/Publications/RankPerm.html )
40  note that this is not lexigraphical order, and to_rank(0) != {0,1,2,3,...} (it is {1,2,3,...,n,0})
41 
42  however, the reset(), finished(), and ++ operator are based on the lexicagraphical ordering
43  */
44  class permutation : public std::vector<dim_type> {
45  size_type remaining;
46  public:
47  permutation(size_type n) : std::vector<dim_type>(n) { reset(); }
48  size_type nb_permutations() { return permutation::nb_permutations(size()); }
49  static size_type nb_permutations(size_type n)
50  { size_type f=1; for (; n>1; --n) f *= n; return f; }
51  void reset() {
52  remaining = 1;
53  for (size_type i=0; i < size(); ++i)
54  { (*this)[i] = dim_type(i); remaining *= (i+1); }
55  }
56  permutation& to_rank(size_type r);
57  permutation inversed() const {
58  permutation pinv(*this);
59  for (size_type i=0; i < size(); ++i) pinv[(*this)[i]] = dim_type(i);
60  return pinv;
61  }
62  size_type rank() const;
63  bool finished() const { return remaining == 0; }
64  /* increment in lexicographical order (not the best, but it is simple) */
65  const permutation &operator ++();
66  template < typename CONT1, typename CONT2 > void apply_to(const CONT1& src, CONT2& dest)
67  { for (size_type i=0; i < size(); ++i) dest[i] = src[(*this)[i]]; }
68  };
69  inline permutation& permutation::to_rank(size_type r) {
70  reset();
71  for (size_type n = size(); n; --n) {
72  std::swap((*this)[n-1], (*this)[r % n]);
73  r /= n;
74  }
75  return (*this);
76  }
77  inline size_type permutation::rank() const {
78  permutation p(*this);
79  permutation pinv(p.inversed());
80  size_type mul=1, r=0;
81  for (size_type n=size(); n>1; --n) {
82  dim_type s = p[n-1];
83  std::swap(p[n-1], p[pinv[n-1]]);
84  std::swap(pinv[s],pinv[n-1]);
85  r += s*mul; mul*=n;
86  }
87  return r;
88  }
89  inline const permutation &permutation::operator ++() {
90  if (--remaining == 0) return (*this);
91  size_type i = size()-2, j=size()-1;
92  while ((*this)[i] > (*this)[i+1]) i--;
93  while ((*this)[i] > (*this)[j]) j--;
94  std::swap((*this)[i], (*this)[j]);
95  for (size_type r = size()-1, s=i+1; r>s; --r, ++s) std::swap((*this)[r],(*this)[s]);
96  return (*this);
97  }
98 }
generation of permutations, and ranking/unranking of these.
size_t size_type
used as the common size type in the library
Definition: bgeot_poly.h:49
Basic Geometric Tools.
defines and typedefs for namespace bgeot