461 lines
13 KiB
C++
Executable File
461 lines
13 KiB
C++
Executable File
// Copyright (c) 2003
|
|
// Utrecht University (The Netherlands),
|
|
// ETH Zurich (Switzerland),
|
|
// INRIA Sophia-Antipolis (France),
|
|
// Max-Planck-Institute Saarbruecken (Germany),
|
|
// and Tel-Aviv University (Israel). All rights reserved.
|
|
//
|
|
// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
|
|
// modify it under the terms of the GNU Lesser General Public License as
|
|
// published by the Free Software Foundation; either version 3 of the License,
|
|
// or (at your option) any later version.
|
|
//
|
|
// Licensees holding a valid commercial license may use this file in
|
|
// accordance with the commercial license agreement provided with the software.
|
|
//
|
|
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
|
|
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
|
|
//
|
|
// $URL$
|
|
// $Id$
|
|
// SPDX-License-Identifier: LGPL-3.0+
|
|
//
|
|
//
|
|
// Author(s) : Michael Hoffmann <hoffmann@inf.ethz.ch>
|
|
// Lutz Kettner <kettner@mpi-sb.mpg.de>
|
|
// Sylvain Pion
|
|
|
|
#ifndef CGAL_ALGORITHM_H
|
|
#define CGAL_ALGORITHM_H
|
|
|
|
#include <CGAL/config.h>
|
|
#include <CGAL/utils.h>
|
|
#include <CGAL/enum.h>
|
|
#include <algorithm>
|
|
#include <iosfwd>
|
|
#include <iostream>
|
|
|
|
#include <boost/random/random_number_generator.hpp>
|
|
#include <boost/random.hpp>
|
|
#include <boost/random/linear_congruential.hpp>
|
|
|
|
#ifdef CGAL_CFG_NO_CPP0X_NEXT_PREV
|
|
# include <boost/next_prior.hpp>
|
|
#endif
|
|
|
|
namespace CGAL {
|
|
|
|
namespace cpp11 {
|
|
#ifndef CGAL_CFG_NO_CPP0X_NEXT_PREV
|
|
using std::next;
|
|
using std::prev;
|
|
#else
|
|
using boost::next;
|
|
|
|
// boost provides prior, we go with the standard declaration as
|
|
// described in $24.4.4 and forward it to boost prior
|
|
template<typename BidirectionalIterator>
|
|
BidirectionalIterator prev( BidirectionalIterator x,
|
|
typename std::iterator_traits<BidirectionalIterator>::difference_type n = 1)
|
|
{
|
|
return boost::prior(x, n);
|
|
}
|
|
#endif
|
|
} // namespace cpp11
|
|
|
|
namespace cpp0x = cpp11;
|
|
|
|
// copy_n is usually in the STL as well, but not in the official
|
|
// standard. We provide our own copy_n. It is planned for C++0x.
|
|
// Our own version is declared deprecated, if std::copy_n is
|
|
// available.
|
|
|
|
#ifndef CGAL_CFG_NO_CPP0X_COPY_N
|
|
#ifndef CGAL_NO_DEPRECATED_CODE
|
|
template <class InputIterator, class Size, class OutputIterator>
|
|
CGAL_DEPRECATED OutputIterator copy_n( InputIterator first, Size n, OutputIterator result )
|
|
{
|
|
// copies the first `n' items from `first' to `result'. Returns
|
|
// the value of `result' after inserting the `n' items.
|
|
while( n--) {
|
|
*result = *first;
|
|
first++;
|
|
result++;
|
|
}
|
|
return result;
|
|
}
|
|
#endif // no CGAL_NO_DEPRECATED_CODE
|
|
#else // CGAL_CFG_NO_CPP0X_COPY_N
|
|
template <class InputIterator, class Size, class OutputIterator>
|
|
OutputIterator copy_n( InputIterator first, Size n, OutputIterator result )
|
|
{
|
|
// copies the first `n' items from `first' to `result'. Returns
|
|
// the value of `result' after inserting the `n' items.
|
|
while( n--) {
|
|
*result = *first;
|
|
first++;
|
|
result++;
|
|
}
|
|
return result;
|
|
}
|
|
#endif // CGAL_CFG_NO_CPP0X_COPY_N
|
|
|
|
namespace cpp11 {
|
|
#ifndef CGAL_CFG_NO_CPP0X_COPY_N
|
|
using std::copy_n;
|
|
#else
|
|
using CGAL::copy_n;
|
|
#endif
|
|
} // cpp11
|
|
|
|
namespace cpp0x = cpp11;
|
|
|
|
|
|
// Not documented
|
|
template <class T> inline
|
|
bool
|
|
are_sorted(const T & a, const T & b, const T & c)
|
|
{
|
|
return a <= b && b <= c;
|
|
}
|
|
|
|
// Not documented
|
|
template <class T, class Compare> inline
|
|
bool
|
|
are_sorted(const T & a, const T & b, const T & c, Compare cmp)
|
|
{
|
|
return !cmp(b, a) && !cmp(c, b);
|
|
}
|
|
|
|
// Not documented
|
|
template <class T> inline
|
|
bool
|
|
are_strictly_sorted(const T & a, const T & b, const T & c)
|
|
{
|
|
return a < b && b < c;
|
|
}
|
|
|
|
// Not documented
|
|
template <class T, class Compare> inline
|
|
bool
|
|
are_strictly_sorted(const T & a, const T & b, const T & c, Compare cmp)
|
|
{
|
|
return cmp(a, b) && cmp(b, c);
|
|
}
|
|
|
|
// Not documented
|
|
// Checks that b is in the interval [min(a, c) , max(a, c)].
|
|
template <class T> inline
|
|
bool
|
|
are_ordered(const T & a, const T & b, const T & c)
|
|
{
|
|
const T& min = (CGAL::min)(a, c);
|
|
const T& max = (CGAL::max)(a, c);
|
|
return min <= b && b <= max;
|
|
}
|
|
|
|
// Not documented
|
|
// Checks that b is in the interval [min(a, c) , max(a, c)].
|
|
template <class T, class Compare> inline
|
|
bool
|
|
are_ordered(const T & a, const T & b, const T & c, Compare cmp)
|
|
{
|
|
const T& min = (std::min)(a, c, cmp);
|
|
const T& max = (std::max)(a, c, cmp);
|
|
return !cmp(b, min) && !cmp(max, b);
|
|
}
|
|
|
|
// Not documented
|
|
// Checks that b is in the interval ]min(a, c) , max(a, c)[.
|
|
template <class T> inline
|
|
bool
|
|
are_strictly_ordered(const T & a, const T & b, const T & c)
|
|
{
|
|
const T& min = (CGAL::min)(a, c);
|
|
const T& max = (CGAL::max)(a, c);
|
|
return min < b && b < max;
|
|
}
|
|
|
|
// Not documented
|
|
// Checks that b is in the interval ]min(a, c) , max(a, c)[.
|
|
template <class T, class Compare> inline
|
|
bool
|
|
are_strictly_ordered(const T & a, const T & b, const T & c, Compare cmp)
|
|
{
|
|
const T& min = (std::min)(a, c, cmp);
|
|
const T& max = (std::max)(a, c, cmp);
|
|
return cmp(min, b) && cmp(b, max);
|
|
}
|
|
|
|
|
|
#ifndef CGAL_NO_DEPRECATED_CODE
|
|
template <class ForwardIterator>
|
|
inline
|
|
CGAL_DEPRECATED
|
|
ForwardIterator
|
|
successor( ForwardIterator it )
|
|
{
|
|
return ++it;
|
|
}
|
|
|
|
template <class BidirectionalIterator>
|
|
inline
|
|
CGAL_DEPRECATED
|
|
BidirectionalIterator
|
|
predecessor( BidirectionalIterator it )
|
|
{
|
|
return --it;
|
|
}
|
|
#endif // CGAL_NO_DEPRECATED_CODE
|
|
|
|
template < class ForwardIterator >
|
|
std::pair< ForwardIterator, ForwardIterator >
|
|
min_max_element(ForwardIterator first, ForwardIterator last)
|
|
{
|
|
typedef std::pair< ForwardIterator, ForwardIterator > FP;
|
|
FP result(first, first);
|
|
if (first != last)
|
|
while (++first != last) {
|
|
if (*first < *result.first)
|
|
result.first = first;
|
|
if (*result.second < *first)
|
|
result.second = first;
|
|
}
|
|
return result;
|
|
}
|
|
|
|
template < class ForwardIterator, class CompareMin, class CompareMax >
|
|
std::pair< ForwardIterator, ForwardIterator >
|
|
min_max_element(ForwardIterator first,
|
|
ForwardIterator last,
|
|
CompareMin comp_min,
|
|
CompareMax comp_max)
|
|
{
|
|
typedef std::pair< ForwardIterator, ForwardIterator > FP;
|
|
FP result(first, first);
|
|
if (first != last)
|
|
while (++first != last) {
|
|
if (comp_min(*first, *result.first))
|
|
result.first = first;
|
|
if (comp_max(*result.second, *first))
|
|
result.second = first;
|
|
}
|
|
return result;
|
|
}
|
|
|
|
template < class ForwardIterator, class Predicate >
|
|
ForwardIterator
|
|
min_element_if(ForwardIterator first,
|
|
ForwardIterator last,
|
|
Predicate pred)
|
|
{
|
|
ForwardIterator result = first = std::find_if(first, last, pred);
|
|
if (first != last)
|
|
while (++first != last)
|
|
if (*first < *result && pred(*first))
|
|
result = first;
|
|
return result;
|
|
}
|
|
|
|
template < class ForwardIterator, class Compare, class Predicate >
|
|
ForwardIterator
|
|
min_element_if(ForwardIterator first,
|
|
ForwardIterator last,
|
|
Compare comp,
|
|
Predicate pred)
|
|
{
|
|
ForwardIterator result = first = std::find_if(first, last, pred);
|
|
if (first != last)
|
|
while (++first != last)
|
|
if (comp(*first, *result) && pred(*first))
|
|
result = first;
|
|
return result;
|
|
}
|
|
|
|
template < class ForwardIterator, class Predicate >
|
|
ForwardIterator
|
|
max_element_if(ForwardIterator first,
|
|
ForwardIterator last,
|
|
Predicate pred)
|
|
{
|
|
ForwardIterator result = first = std::find_if(first, last, pred);
|
|
if (first != last)
|
|
while (++first != last)
|
|
if (*result < *first && pred(*first))
|
|
result = first;
|
|
return result;
|
|
}
|
|
|
|
template < class ForwardIterator, class Compare, class Predicate >
|
|
ForwardIterator
|
|
max_element_if(ForwardIterator first,
|
|
ForwardIterator last,
|
|
Compare comp,
|
|
Predicate pred)
|
|
{
|
|
ForwardIterator result = first = std::find_if(first, last, pred);
|
|
if (first != last)
|
|
while (++first != last)
|
|
if (comp(*result, *first) && pred(*first))
|
|
result = first;
|
|
return result;
|
|
}
|
|
|
|
|
|
|
|
/*! \brief lexicographic comparison of the two ranges using the \a cmp
|
|
function object.
|
|
|
|
Compares the two ranges \c [first1,last1) and \c [first2,last2)
|
|
lexicographically and returns one of the \c CGAL::Comparison_result enum
|
|
values respectively:
|
|
- \c CGAL::SMALLER
|
|
- \c CGAL::EQUAL
|
|
- \c CGAL::LARGER
|
|
|
|
\pre The \c value_type of \a InputIterator1 must be convertible
|
|
to the \c first_argument_type of \c BinaryFunction.
|
|
The \c value_type of \a InputIterator2 must be convertible
|
|
to the \c second_argument_type of \c BinaryFunction.
|
|
The \c result_type of \c BinaryFunction must be convertible to
|
|
\c CGAL::Comparison_result.
|
|
*/
|
|
|
|
template <class InputIterator1, class InputIterator2, class BinaryFunction>
|
|
CGAL::Comparison_result
|
|
lexicographical_compare_three_valued( InputIterator1 first1, InputIterator1 last1,
|
|
InputIterator2 first2, InputIterator2 last2,
|
|
BinaryFunction cmp) {
|
|
while ( first1 != last1 && first2 != last2) {
|
|
CGAL::Comparison_result result = cmp( *first1, *first2);
|
|
if ( result != CGAL::EQUAL)
|
|
return result;
|
|
++first1;
|
|
++first2;
|
|
}
|
|
if ( first1 != last1)
|
|
return CGAL::LARGER;
|
|
if ( first2 != last2)
|
|
return CGAL::SMALLER;
|
|
return CGAL::EQUAL;
|
|
}
|
|
|
|
/*! \brief output iterator range to a stream, with separators
|
|
|
|
The iterator range \c [first,beyond) is written
|
|
to \c os (obeying CGAL I/O modes). Each element is bracketed by
|
|
\c pre and \c post (default: empty string). Adjacent values are
|
|
spearated by \c sep (default: ", ", i.e. comma space).
|
|
The stream \c os is returned in its new state after output.
|
|
|
|
Example:
|
|
<PRE>
|
|
int a[] = {1, 2, 3};
|
|
output_range(std::cout, a, a+3, ":", "(", ")");
|
|
</PRE>
|
|
produces \c (1):(2):(3)
|
|
*/
|
|
template <class InputIterator>
|
|
std::ostream&
|
|
output_range(std::ostream& os,
|
|
InputIterator first, InputIterator beyond,
|
|
const char* sep = ", ", const char* pre = "", const char* post = "")
|
|
{
|
|
InputIterator it = first;
|
|
if (it != beyond) {
|
|
os << pre << oformat(*it) << post;
|
|
while (++it != beyond) os << sep << pre << oformat(*it) << post;
|
|
}
|
|
return os;
|
|
}
|
|
|
|
|
|
namespace cpp98 {
|
|
|
|
// Reimplementation of std::random_shuffle, for the use of Spatial_sorting.
|
|
// We want an implementation of random_shuffle that produces the same
|
|
// result on all platforms, for a given seeded random generator.
|
|
template <class RandomAccessIterator,
|
|
class RandomGenerator>
|
|
void
|
|
random_shuffle(RandomAccessIterator begin, RandomAccessIterator end,
|
|
RandomGenerator& random)
|
|
{
|
|
if(begin == end) return;
|
|
for(RandomAccessIterator it = begin + 1; it != end; ++it)
|
|
{
|
|
std::iter_swap( it, begin + random( (it - begin) + 1 ) );
|
|
// The +1 inside random is because random(N) gives numbers in the open
|
|
// interval [0, N[
|
|
}
|
|
}
|
|
|
|
|
|
template <class RandomAccessIterator>
|
|
void
|
|
random_shuffle(RandomAccessIterator begin, RandomAccessIterator end)
|
|
{
|
|
typedef std::iterator_traits<RandomAccessIterator> Iterator_traits;
|
|
typedef typename Iterator_traits::difference_type Diff_t;
|
|
boost::rand48 random;
|
|
boost::random_number_generator<boost::rand48, Diff_t> rng(random);
|
|
CGAL::cpp98::random_shuffle(begin,end, rng);
|
|
}
|
|
|
|
} // namespace cpp98
|
|
|
|
namespace internal {
|
|
namespace algorithm {
|
|
|
|
// Implementation of the algorithm described here:
|
|
// http://en.wikipedia.org/w/index.php?title=Selection_algorithm&oldid=480099620#Partition-based_general_selection_algorithm
|
|
template <class RandomAccessIterator, class Compare>
|
|
RandomAccessIterator
|
|
partition(RandomAccessIterator left,
|
|
RandomAccessIterator right, // points to the last element of the sequence
|
|
RandomAccessIterator pivot_it,
|
|
Compare& compare)
|
|
{
|
|
std::iter_swap(pivot_it, right); // move pivot to the right
|
|
RandomAccessIterator result = left;
|
|
for(RandomAccessIterator it = left; it != right; ++it) {
|
|
if(compare(*it, *right)) {
|
|
std::iter_swap(result, it);
|
|
++result;
|
|
}
|
|
}
|
|
std::iter_swap(right, result);
|
|
return result;
|
|
}
|
|
|
|
} // end namespace algorithm
|
|
} // end namespace internal
|
|
|
|
// Reimplementation of std::nth_element, for the use of Spatial_sorting.
|
|
// We want an implementation of nth_element that produces the same result
|
|
// on all platforms.
|
|
template <class RandomAccessIterator, class Compare>
|
|
void nth_element(RandomAccessIterator left,
|
|
RandomAccessIterator nth,
|
|
RandomAccessIterator right,
|
|
Compare& comp)
|
|
{
|
|
if(left == right) return;
|
|
--right; // 'right' points to the last element of the sequence
|
|
if(left == right) return; // exit if there is only one element
|
|
while(true) {
|
|
RandomAccessIterator pivot_it = left + ((right - left) / 2);
|
|
RandomAccessIterator new_pivot_it =
|
|
internal::algorithm::partition(left, right, pivot_it, comp);
|
|
if(new_pivot_it == nth) return;
|
|
if(nth < new_pivot_it)
|
|
right = new_pivot_it - 1;
|
|
else
|
|
left = new_pivot_it + 1;
|
|
} // end while(true)
|
|
}
|
|
|
|
} //namespace CGAL
|
|
|
|
#endif // CGAL_ALGORITHM_H
|