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645 lines
22 KiB
C++
645 lines
22 KiB
C++
// -*- C++ -*-
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// Copyright (C) 2007-2019 Free Software Foundation, Inc.
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//
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// This file is part of the GNU ISO C++ Library. This library is free
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// software; you can redistribute it and/or modify it under the terms
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// of the GNU General Public License as published by the Free Software
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// Foundation; either version 3, or (at your option) any later
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// version.
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// This library is distributed in the hope that it will be useful, but
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// WITHOUT ANY WARRANTY; without even the implied warranty of
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// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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// General Public License for more details.
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// Under Section 7 of GPL version 3, you are granted additional
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// permissions described in the GCC Runtime Library Exception, version
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// 3.1, as published by the Free Software Foundation.
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// You should have received a copy of the GNU General Public License and
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// a copy of the GCC Runtime Library Exception along with this program;
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// see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
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// <http://www.gnu.org/licenses/>.
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/** @file parallel/multiseq_selection.h
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* @brief Functions to find elements of a certain global __rank in
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* multiple sorted sequences. Also serves for splitting such
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* sequence sets.
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*
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* The algorithm description can be found in
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*
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* P. J. Varman, S. D. Scheufler, B. R. Iyer, and G. R. Ricard.
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* Merging Multiple Lists on Hierarchical-Memory Multiprocessors.
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* Journal of Parallel and Distributed Computing, 12(2):171-177, 1991.
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*
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* This file is a GNU parallel extension to the Standard C++ Library.
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*/
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// Written by Johannes Singler.
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#ifndef _GLIBCXX_PARALLEL_MULTISEQ_SELECTION_H
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#define _GLIBCXX_PARALLEL_MULTISEQ_SELECTION_H 1
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#include <vector>
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#include <queue>
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#include <bits/stl_algo.h>
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namespace __gnu_parallel
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{
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/** @brief Compare __a pair of types lexicographically, ascending. */
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template<typename _T1, typename _T2, typename _Compare>
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class _Lexicographic
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: public std::binary_function<std::pair<_T1, _T2>,
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std::pair<_T1, _T2>, bool>
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{
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private:
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_Compare& _M_comp;
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public:
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_Lexicographic(_Compare& __comp) : _M_comp(__comp) { }
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bool
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operator()(const std::pair<_T1, _T2>& __p1,
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const std::pair<_T1, _T2>& __p2) const
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{
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if (_M_comp(__p1.first, __p2.first))
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return true;
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if (_M_comp(__p2.first, __p1.first))
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return false;
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// Firsts are equal.
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return __p1.second < __p2.second;
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}
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};
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/** @brief Compare __a pair of types lexicographically, descending. */
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template<typename _T1, typename _T2, typename _Compare>
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class _LexicographicReverse : public std::binary_function<_T1, _T2, bool>
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{
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private:
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_Compare& _M_comp;
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public:
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_LexicographicReverse(_Compare& __comp) : _M_comp(__comp) { }
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bool
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operator()(const std::pair<_T1, _T2>& __p1,
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const std::pair<_T1, _T2>& __p2) const
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{
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if (_M_comp(__p2.first, __p1.first))
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return true;
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if (_M_comp(__p1.first, __p2.first))
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return false;
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// Firsts are equal.
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return __p2.second < __p1.second;
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}
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};
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/**
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* @brief Splits several sorted sequences at a certain global __rank,
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* resulting in a splitting point for each sequence.
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* The sequences are passed via a sequence of random-access
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* iterator pairs, none of the sequences may be empty. If there
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* are several equal elements across the split, the ones on the
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* __left side will be chosen from sequences with smaller number.
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* @param __begin_seqs Begin of the sequence of iterator pairs.
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* @param __end_seqs End of the sequence of iterator pairs.
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* @param __rank The global rank to partition at.
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* @param __begin_offsets A random-access __sequence __begin where the
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* __result will be stored in. Each element of the sequence is an
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* iterator that points to the first element on the greater part of
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* the respective __sequence.
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* @param __comp The ordering functor, defaults to std::less<_Tp>.
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*/
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template<typename _RanSeqs, typename _RankType, typename _RankIterator,
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typename _Compare>
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void
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multiseq_partition(_RanSeqs __begin_seqs, _RanSeqs __end_seqs,
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_RankType __rank,
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_RankIterator __begin_offsets,
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_Compare __comp = std::less<
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typename std::iterator_traits<typename
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std::iterator_traits<_RanSeqs>::value_type::
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first_type>::value_type>()) // std::less<_Tp>
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{
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_GLIBCXX_CALL(__end_seqs - __begin_seqs)
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typedef typename std::iterator_traits<_RanSeqs>::value_type::first_type
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_It;
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typedef typename std::iterator_traits<_RanSeqs>::difference_type
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_SeqNumber;
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typedef typename std::iterator_traits<_It>::difference_type
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_DifferenceType;
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typedef typename std::iterator_traits<_It>::value_type _ValueType;
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_Lexicographic<_ValueType, _SeqNumber, _Compare> __lcomp(__comp);
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_LexicographicReverse<_ValueType, _SeqNumber, _Compare> __lrcomp(__comp);
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// Number of sequences, number of elements in total (possibly
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// including padding).
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_DifferenceType __m = std::distance(__begin_seqs, __end_seqs), __nn = 0,
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__nmax, __n, __r;
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for (_SeqNumber __i = 0; __i < __m; __i++)
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{
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__nn += std::distance(__begin_seqs[__i].first,
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__begin_seqs[__i].second);
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_GLIBCXX_PARALLEL_ASSERT(
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std::distance(__begin_seqs[__i].first,
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__begin_seqs[__i].second) > 0);
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}
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if (__rank == __nn)
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{
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for (_SeqNumber __i = 0; __i < __m; __i++)
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__begin_offsets[__i] = __begin_seqs[__i].second; // Very end.
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// Return __m - 1;
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return;
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}
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_GLIBCXX_PARALLEL_ASSERT(__m != 0);
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_GLIBCXX_PARALLEL_ASSERT(__nn != 0);
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_GLIBCXX_PARALLEL_ASSERT(__rank >= 0);
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_GLIBCXX_PARALLEL_ASSERT(__rank < __nn);
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_DifferenceType* __ns = new _DifferenceType[__m];
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_DifferenceType* __a = new _DifferenceType[__m];
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_DifferenceType* __b = new _DifferenceType[__m];
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_DifferenceType __l;
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__ns[0] = std::distance(__begin_seqs[0].first, __begin_seqs[0].second);
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__nmax = __ns[0];
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for (_SeqNumber __i = 0; __i < __m; __i++)
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{
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__ns[__i] = std::distance(__begin_seqs[__i].first,
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__begin_seqs[__i].second);
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__nmax = std::max(__nmax, __ns[__i]);
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}
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__r = __rd_log2(__nmax) + 1;
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// Pad all lists to this length, at least as long as any ns[__i],
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// equality iff __nmax = 2^__k - 1.
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__l = (1ULL << __r) - 1;
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for (_SeqNumber __i = 0; __i < __m; __i++)
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{
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__a[__i] = 0;
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__b[__i] = __l;
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}
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__n = __l / 2;
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// Invariants:
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// 0 <= __a[__i] <= __ns[__i], 0 <= __b[__i] <= __l
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#define __S(__i) (__begin_seqs[__i].first)
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// Initial partition.
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std::vector<std::pair<_ValueType, _SeqNumber> > __sample;
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for (_SeqNumber __i = 0; __i < __m; __i++)
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if (__n < __ns[__i]) //__sequence long enough
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__sample.push_back(std::make_pair(__S(__i)[__n], __i));
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__gnu_sequential::sort(__sample.begin(), __sample.end(), __lcomp);
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for (_SeqNumber __i = 0; __i < __m; __i++) //conceptual infinity
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if (__n >= __ns[__i]) //__sequence too short, conceptual infinity
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__sample.push_back(
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std::make_pair(__S(__i)[0] /*__dummy element*/, __i));
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_DifferenceType __localrank = __rank / __l;
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_SeqNumber __j;
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for (__j = 0;
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__j < __localrank && ((__n + 1) <= __ns[__sample[__j].second]);
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++__j)
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__a[__sample[__j].second] += __n + 1;
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for (; __j < __m; __j++)
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__b[__sample[__j].second] -= __n + 1;
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// Further refinement.
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while (__n > 0)
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{
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__n /= 2;
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_SeqNumber __lmax_seq = -1; // to avoid warning
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const _ValueType* __lmax = 0; // impossible to avoid the warning?
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for (_SeqNumber __i = 0; __i < __m; __i++)
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{
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if (__a[__i] > 0)
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{
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if (!__lmax)
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{
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__lmax = &(__S(__i)[__a[__i] - 1]);
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__lmax_seq = __i;
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}
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else
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{
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// Max, favor rear sequences.
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if (!__comp(__S(__i)[__a[__i] - 1], *__lmax))
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{
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__lmax = &(__S(__i)[__a[__i] - 1]);
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__lmax_seq = __i;
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}
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}
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}
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}
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_SeqNumber __i;
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for (__i = 0; __i < __m; __i++)
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{
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_DifferenceType __middle = (__b[__i] + __a[__i]) / 2;
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if (__lmax && __middle < __ns[__i] &&
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__lcomp(std::make_pair(__S(__i)[__middle], __i),
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std::make_pair(*__lmax, __lmax_seq)))
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__a[__i] = std::min(__a[__i] + __n + 1, __ns[__i]);
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else
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__b[__i] -= __n + 1;
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}
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_DifferenceType __leftsize = 0;
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for (_SeqNumber __i = 0; __i < __m; __i++)
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__leftsize += __a[__i] / (__n + 1);
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_DifferenceType __skew = __rank / (__n + 1) - __leftsize;
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if (__skew > 0)
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{
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// Move to the left, find smallest.
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std::priority_queue<std::pair<_ValueType, _SeqNumber>,
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std::vector<std::pair<_ValueType, _SeqNumber> >,
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_LexicographicReverse<_ValueType, _SeqNumber, _Compare> >
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__pq(__lrcomp);
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for (_SeqNumber __i = 0; __i < __m; __i++)
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if (__b[__i] < __ns[__i])
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__pq.push(std::make_pair(__S(__i)[__b[__i]], __i));
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for (; __skew != 0 && !__pq.empty(); --__skew)
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{
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_SeqNumber __source = __pq.top().second;
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__pq.pop();
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__a[__source]
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= std::min(__a[__source] + __n + 1, __ns[__source]);
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__b[__source] += __n + 1;
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if (__b[__source] < __ns[__source])
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__pq.push(
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std::make_pair(__S(__source)[__b[__source]], __source));
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}
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}
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else if (__skew < 0)
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{
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// Move to the right, find greatest.
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std::priority_queue<std::pair<_ValueType, _SeqNumber>,
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std::vector<std::pair<_ValueType, _SeqNumber> >,
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_Lexicographic<_ValueType, _SeqNumber, _Compare> >
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__pq(__lcomp);
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for (_SeqNumber __i = 0; __i < __m; __i++)
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if (__a[__i] > 0)
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__pq.push(std::make_pair(__S(__i)[__a[__i] - 1], __i));
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for (; __skew != 0; ++__skew)
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{
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_SeqNumber __source = __pq.top().second;
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__pq.pop();
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__a[__source] -= __n + 1;
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__b[__source] -= __n + 1;
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if (__a[__source] > 0)
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__pq.push(std::make_pair(
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__S(__source)[__a[__source] - 1], __source));
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}
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}
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}
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// Postconditions:
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// __a[__i] == __b[__i] in most cases, except when __a[__i] has been
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// clamped because of having reached the boundary
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// Now return the result, calculate the offset.
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// Compare the keys on both edges of the border.
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// Maximum of left edge, minimum of right edge.
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_ValueType* __maxleft = 0;
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_ValueType* __minright = 0;
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for (_SeqNumber __i = 0; __i < __m; __i++)
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{
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if (__a[__i] > 0)
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{
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if (!__maxleft)
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__maxleft = &(__S(__i)[__a[__i] - 1]);
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else
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{
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// Max, favor rear sequences.
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if (!__comp(__S(__i)[__a[__i] - 1], *__maxleft))
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__maxleft = &(__S(__i)[__a[__i] - 1]);
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}
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}
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if (__b[__i] < __ns[__i])
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{
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if (!__minright)
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__minright = &(__S(__i)[__b[__i]]);
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else
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{
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// Min, favor fore sequences.
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if (__comp(__S(__i)[__b[__i]], *__minright))
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__minright = &(__S(__i)[__b[__i]]);
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}
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}
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}
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_SeqNumber __seq = 0;
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for (_SeqNumber __i = 0; __i < __m; __i++)
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__begin_offsets[__i] = __S(__i) + __a[__i];
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delete[] __ns;
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delete[] __a;
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delete[] __b;
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}
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/**
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* @brief Selects the element at a certain global __rank from several
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* sorted sequences.
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*
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* The sequences are passed via a sequence of random-access
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* iterator pairs, none of the sequences may be empty.
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* @param __begin_seqs Begin of the sequence of iterator pairs.
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* @param __end_seqs End of the sequence of iterator pairs.
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* @param __rank The global rank to partition at.
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* @param __offset The rank of the selected element in the global
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* subsequence of elements equal to the selected element. If the
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* selected element is unique, this number is 0.
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* @param __comp The ordering functor, defaults to std::less.
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*/
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template<typename _Tp, typename _RanSeqs, typename _RankType,
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typename _Compare>
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_Tp
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multiseq_selection(_RanSeqs __begin_seqs, _RanSeqs __end_seqs,
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_RankType __rank,
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_RankType& __offset, _Compare __comp = std::less<_Tp>())
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{
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_GLIBCXX_CALL(__end_seqs - __begin_seqs)
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typedef typename std::iterator_traits<_RanSeqs>::value_type::first_type
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_It;
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typedef typename std::iterator_traits<_RanSeqs>::difference_type
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_SeqNumber;
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typedef typename std::iterator_traits<_It>::difference_type
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_DifferenceType;
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_Lexicographic<_Tp, _SeqNumber, _Compare> __lcomp(__comp);
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_LexicographicReverse<_Tp, _SeqNumber, _Compare> __lrcomp(__comp);
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// Number of sequences, number of elements in total (possibly
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// including padding).
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_DifferenceType __m = std::distance(__begin_seqs, __end_seqs);
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_DifferenceType __nn = 0;
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_DifferenceType __nmax, __n, __r;
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for (_SeqNumber __i = 0; __i < __m; __i++)
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__nn += std::distance(__begin_seqs[__i].first,
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__begin_seqs[__i].second);
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if (__m == 0 || __nn == 0 || __rank < 0 || __rank >= __nn)
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{
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// result undefined if there is no data or __rank is outside bounds
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throw std::exception();
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}
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_DifferenceType* __ns = new _DifferenceType[__m];
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_DifferenceType* __a = new _DifferenceType[__m];
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_DifferenceType* __b = new _DifferenceType[__m];
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_DifferenceType __l;
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__ns[0] = std::distance(__begin_seqs[0].first, __begin_seqs[0].second);
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__nmax = __ns[0];
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for (_SeqNumber __i = 0; __i < __m; ++__i)
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{
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__ns[__i] = std::distance(__begin_seqs[__i].first,
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__begin_seqs[__i].second);
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__nmax = std::max(__nmax, __ns[__i]);
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}
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__r = __rd_log2(__nmax) + 1;
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// Pad all lists to this length, at least as long as any ns[__i],
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// equality iff __nmax = 2^__k - 1
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__l = __round_up_to_pow2(__r) - 1;
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for (_SeqNumber __i = 0; __i < __m; ++__i)
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{
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__a[__i] = 0;
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__b[__i] = __l;
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}
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__n = __l / 2;
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// Invariants:
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// 0 <= __a[__i] <= __ns[__i], 0 <= __b[__i] <= __l
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#define __S(__i) (__begin_seqs[__i].first)
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// Initial partition.
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std::vector<std::pair<_Tp, _SeqNumber> > __sample;
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for (_SeqNumber __i = 0; __i < __m; __i++)
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if (__n < __ns[__i])
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__sample.push_back(std::make_pair(__S(__i)[__n], __i));
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__gnu_sequential::sort(__sample.begin(), __sample.end(),
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__lcomp, sequential_tag());
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// Conceptual infinity.
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for (_SeqNumber __i = 0; __i < __m; __i++)
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if (__n >= __ns[__i])
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__sample.push_back(
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std::make_pair(__S(__i)[0] /*__dummy element*/, __i));
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_DifferenceType __localrank = __rank / __l;
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_SeqNumber __j;
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for (__j = 0;
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__j < __localrank && ((__n + 1) <= __ns[__sample[__j].second]);
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++__j)
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__a[__sample[__j].second] += __n + 1;
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for (; __j < __m; ++__j)
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__b[__sample[__j].second] -= __n + 1;
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// Further refinement.
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while (__n > 0)
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{
|
|
__n /= 2;
|
|
|
|
const _Tp* __lmax = 0;
|
|
for (_SeqNumber __i = 0; __i < __m; ++__i)
|
|
{
|
|
if (__a[__i] > 0)
|
|
{
|
|
if (!__lmax)
|
|
__lmax = &(__S(__i)[__a[__i] - 1]);
|
|
else
|
|
{
|
|
if (__comp(*__lmax, __S(__i)[__a[__i] - 1])) //max
|
|
__lmax = &(__S(__i)[__a[__i] - 1]);
|
|
}
|
|
}
|
|
}
|
|
|
|
_SeqNumber __i;
|
|
for (__i = 0; __i < __m; __i++)
|
|
{
|
|
_DifferenceType __middle = (__b[__i] + __a[__i]) / 2;
|
|
if (__lmax && __middle < __ns[__i]
|
|
&& __comp(__S(__i)[__middle], *__lmax))
|
|
__a[__i] = std::min(__a[__i] + __n + 1, __ns[__i]);
|
|
else
|
|
__b[__i] -= __n + 1;
|
|
}
|
|
|
|
_DifferenceType __leftsize = 0;
|
|
for (_SeqNumber __i = 0; __i < __m; ++__i)
|
|
__leftsize += __a[__i] / (__n + 1);
|
|
|
|
_DifferenceType __skew = __rank / (__n + 1) - __leftsize;
|
|
|
|
if (__skew > 0)
|
|
{
|
|
// Move to the left, find smallest.
|
|
std::priority_queue<std::pair<_Tp, _SeqNumber>,
|
|
std::vector<std::pair<_Tp, _SeqNumber> >,
|
|
_LexicographicReverse<_Tp, _SeqNumber, _Compare> >
|
|
__pq(__lrcomp);
|
|
|
|
for (_SeqNumber __i = 0; __i < __m; ++__i)
|
|
if (__b[__i] < __ns[__i])
|
|
__pq.push(std::make_pair(__S(__i)[__b[__i]], __i));
|
|
|
|
for (; __skew != 0 && !__pq.empty(); --__skew)
|
|
{
|
|
_SeqNumber __source = __pq.top().second;
|
|
__pq.pop();
|
|
|
|
__a[__source]
|
|
= std::min(__a[__source] + __n + 1, __ns[__source]);
|
|
__b[__source] += __n + 1;
|
|
|
|
if (__b[__source] < __ns[__source])
|
|
__pq.push(
|
|
std::make_pair(__S(__source)[__b[__source]], __source));
|
|
}
|
|
}
|
|
else if (__skew < 0)
|
|
{
|
|
// Move to the right, find greatest.
|
|
std::priority_queue<std::pair<_Tp, _SeqNumber>,
|
|
std::vector<std::pair<_Tp, _SeqNumber> >,
|
|
_Lexicographic<_Tp, _SeqNumber, _Compare> > __pq(__lcomp);
|
|
|
|
for (_SeqNumber __i = 0; __i < __m; ++__i)
|
|
if (__a[__i] > 0)
|
|
__pq.push(std::make_pair(__S(__i)[__a[__i] - 1], __i));
|
|
|
|
for (; __skew != 0; ++__skew)
|
|
{
|
|
_SeqNumber __source = __pq.top().second;
|
|
__pq.pop();
|
|
|
|
__a[__source] -= __n + 1;
|
|
__b[__source] -= __n + 1;
|
|
|
|
if (__a[__source] > 0)
|
|
__pq.push(std::make_pair(
|
|
__S(__source)[__a[__source] - 1], __source));
|
|
}
|
|
}
|
|
}
|
|
|
|
// Postconditions:
|
|
// __a[__i] == __b[__i] in most cases, except when __a[__i] has been
|
|
// clamped because of having reached the boundary
|
|
|
|
// Now return the result, calculate the offset.
|
|
|
|
// Compare the keys on both edges of the border.
|
|
|
|
// Maximum of left edge, minimum of right edge.
|
|
bool __maxleftset = false, __minrightset = false;
|
|
|
|
// Impossible to avoid the warning?
|
|
_Tp __maxleft, __minright;
|
|
for (_SeqNumber __i = 0; __i < __m; ++__i)
|
|
{
|
|
if (__a[__i] > 0)
|
|
{
|
|
if (!__maxleftset)
|
|
{
|
|
__maxleft = __S(__i)[__a[__i] - 1];
|
|
__maxleftset = true;
|
|
}
|
|
else
|
|
{
|
|
// Max.
|
|
if (__comp(__maxleft, __S(__i)[__a[__i] - 1]))
|
|
__maxleft = __S(__i)[__a[__i] - 1];
|
|
}
|
|
}
|
|
if (__b[__i] < __ns[__i])
|
|
{
|
|
if (!__minrightset)
|
|
{
|
|
__minright = __S(__i)[__b[__i]];
|
|
__minrightset = true;
|
|
}
|
|
else
|
|
{
|
|
// Min.
|
|
if (__comp(__S(__i)[__b[__i]], __minright))
|
|
__minright = __S(__i)[__b[__i]];
|
|
}
|
|
}
|
|
}
|
|
|
|
// Minright is the __splitter, in any case.
|
|
|
|
if (!__maxleftset || __comp(__minright, __maxleft))
|
|
{
|
|
// Good luck, everything is split unambiguously.
|
|
__offset = 0;
|
|
}
|
|
else
|
|
{
|
|
// We have to calculate an offset.
|
|
__offset = 0;
|
|
|
|
for (_SeqNumber __i = 0; __i < __m; ++__i)
|
|
{
|
|
_DifferenceType lb
|
|
= std::lower_bound(__S(__i), __S(__i) + __ns[__i],
|
|
__minright,
|
|
__comp) - __S(__i);
|
|
__offset += __a[__i] - lb;
|
|
}
|
|
}
|
|
|
|
delete[] __ns;
|
|
delete[] __a;
|
|
delete[] __b;
|
|
|
|
return __minright;
|
|
}
|
|
}
|
|
|
|
#undef __S
|
|
|
|
#endif /* _GLIBCXX_PARALLEL_MULTISEQ_SELECTION_H */
|