permutation.hpp

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// (C) Copyright Jeremy Siek 2001.
// Distributed under the Boost Software License, Version 1.0. (See
// accompanying file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)

#ifndef BOOST_PERMUTATION_HPP
#define BOOST_PERMUTATION_HPP

#include <vector>
#include <memory>
#include <functional>
#include <algorithm>
#include <boost/graph/detail/shadow_iterator.hpp>

namespace boost {

template <class Iter1, class Iter2>
void permute_serial(Iter1 permuter, Iter1 last, Iter2 result)
{
#ifdef BOOST_NO_STD_ITERATOR_TRAITS
  typedef std::ptrdiff_t D:
#else
  typedef typename std::iterator_traits<Iter1>::difference_type D;
#endif

  D n = 0;
  while (permuter != last) {
    std::swap(result[n], result[*permuter]);
    ++n;
    ++permuter;
  }
}

template <class InIter, class RandIterP, class RandIterR>
void permute_copy(InIter first, InIter last, RandIterP p, RandIterR result)
{
#ifdef BOOST_NO_STD_ITERATOR_TRAITS
  typedef std::ptrdiff_t i = 0;
#else
  typename std::iterator_traits<RandIterP>::difference_type i = 0;
#endif
  for (; first != last; ++first, ++i)
    result[p[i]] = *first;
}

namespace detail {

template <class RandIter, class RandIterPerm, class D, class T>
void permute_helper(RandIter first, RandIter last, RandIterPerm p, D, T)
{
  D i = 0, pi, n = last - first, cycle_start;
  T tmp;
  std::vector<int> visited(n, false);

  while (i != n) { // continue until all elements have been processed
    cycle_start = i;
    tmp = first[i];
    do { // walk around a cycle
      pi = p[i];
      visited[pi] = true;
      std::swap(tmp, first[pi]);
      i = pi;
    } while (i != cycle_start);
    
    // find the next cycle
    for (i = 0; i < n; ++i)
      if (visited[i] == false)
        break;
  }
}

} // namespace detail

template <class RandIter, class RandIterPerm>
void permute(RandIter first, RandIter last, RandIterPerm p)
{
  detail::permute_helper(first, last, p, last - first, *first);
}


// Knuth 1.3.3, Vol. 1 p 176
// modified for zero-based arrays
// time complexity?
//
// WARNING: T must be a signed integer!
template <class PermIter>
void invert_permutation(PermIter X, PermIter Xend)
{
#ifdef BOOST_NO_STD_ITERATOR_TRAITS
  typedef std::ptrdiff_t T:
#else
  typedef typename std::iterator_traits<PermIter>::value_type T;
#endif
  T n = Xend - X;
  T m = n;
  T j = -1;

  while (m > 0) {
    T i = X[m-1] + 1;
    if (i > 0) {
      do {
        X[m-1] = j - 1;
        j = -m;
        m = i;
        i = X[m-1] + 1;
      } while (i > 0);
      i = j;
    }
    X[m-1] = -i - 1;
    --m;
  }
}

// Takes a "normal" permutation array (and its inverse), and turns it
// into a BLAS-style permutation array (which can be thought of as a
// serialized permutation).
template <class Iter1, class Iter2, class Iter3>
inline void serialize_permutation(Iter1 q, Iter1 q_end, Iter2 q_inv, Iter3 p)
{
#ifdef BOOST_NO_STD_ITERATOR_TRAITS
  typedef std::ptrdiff_t P1;
  typedef std::ptrdiff_t P2;
  typedef std::ptrdiff_t D;
#else
  typedef typename std::iterator_traits<Iter1>::value_type P1;
  typedef typename std::iterator_traits<Iter2>::value_type P2;
  typedef typename std::iterator_traits<Iter1>::difference_type D;
#endif
  D n = q_end - q;
  for (D i = 0; i < n; ++i) {
    P1 qi = q[i];
    P2 qii = q_inv[i];
    *p++ = qii;
    std::swap(q[i], q[qii]);
    std::swap(q_inv[i], q_inv[qi]);
  }
}

// Not used anymore, leaving it here for future reference.
template <typename Iter, typename Compare>
void merge_sort(Iter first, Iter last, Compare cmp)
{
  if (first + 1 < last) {
    Iter mid = first + (last - first)/2;
    merge_sort(first, mid, cmp);
    merge_sort(mid, last, cmp);
    std::inplace_merge(first, mid, last, cmp);
  }
}


// time: N log N + 3N + ?
// space: 2N
template <class Iter, class IterP, class Cmp, class Alloc>
inline void sortp(Iter first, Iter last, IterP p, Cmp cmp, Alloc alloc)
{
  typedef typename std::iterator_traits<IterP>::value_type P;
  typedef typename std::iterator_traits<IterP>::difference_type D;
  D n = last - first;
  std::vector<P, Alloc> q(n);
  for (D i = 0; i < n; ++i) 
    q[i] = i;
  std::sort(make_shadow_iter(first, q.begin()),
            make_shadow_iter(last, q.end()),
            shadow_cmp<Cmp>(cmp));
  invert_permutation(q.begin(), q.end());
  std::copy(q.begin(), q.end(), p);
}

template <class Iter, class IterP, class Cmp>
inline void sortp(Iter first, Iter last, IterP p, Cmp cmp)
{
  typedef typename std::iterator_traits<IterP>::value_type P;  
  sortp(first, last, p, cmp, std::allocator<P>());
}

template <class Iter, class IterP>
inline void sortp(Iter first, Iter last, IterP p)
{
  typedef typename std::iterator_traits<Iter>::value_type T;  
  typedef typename std::iterator_traits<IterP>::value_type P;  
  sortp(first, last, p, std::less<T>(), std::allocator<P>());
}

template <class Iter, class IterP, class Cmp, class Alloc>
inline void sortv(Iter first, Iter last, IterP p, Cmp cmp, Alloc alloc)
{
  typedef typename std::iterator_traits<IterP>::value_type P;
  typedef typename std::iterator_traits<IterP>::difference_type D;
  D n = last - first;
  std::vector<P, Alloc> q(n), q_inv(n);
  for (D i = 0; i < n; ++i) 
    q_inv[i] = i;
  std::sort(make_shadow_iter(first, q_inv.begin()), 
            make_shadow_iter(last, q_inv.end()), 
            shadow_cmp<Cmp>(cmp));
  std::copy(q_inv, q_inv.end(), q.begin());
  invert_permutation(q.begin(), q.end());
  serialize_permutation(q.begin(), q.end(), q_inv.end(), p);
}


} // namespace boost

#endif // BOOST_PERMUTATION_HPP