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// -*- C++ -*-
// Copyright (C) 2007, 2008, 2009 Free Software Foundation, Inc.
//
// This file is part of the GNU ISO C++ Library. This library is free
// software; you can redistribute it and/or modify it under the terms
// of the GNU General Public License as published by the Free Software
// Foundation; either version 3, or (at your option) any later
// version.
// This library is distributed in the hope that it will be useful, but
// WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
// General Public License for more details.
// Under Section 7 of GPL version 3, you are granted additional
// permissions described in the GCC Runtime Library Exception, version
// 3.1, as published by the Free Software Foundation.
// You should have received a copy of the GNU General Public License and
// a copy of the GCC Runtime Library Exception along with this program;
// see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
// <http://www.gnu.org/licenses/>.
/** @file parallel/multiseq_selection.h
* @brief Functions to find elements of a certain global rank in
* multiple sorted sequences. Also serves for splitting such
* sequence sets.
*
* The algorithm description can be found in
*
* P. J. Varman, S. D. Scheufler, B. R. Iyer, and G. R. Ricard.
* Merging Multiple Lists on Hierarchical-Memory Multiprocessors.
* Journal of Parallel and Distributed Computing, 12(2):171–177, 1991.
*
* This file is a GNU parallel extension to the Standard C++ Library.
*/
// Written by Johannes Singler.
#ifndef _GLIBCXX_PARALLEL_MULTISEQ_SELECTION_H
#define _GLIBCXX_PARALLEL_MULTISEQ_SELECTION_H 1
#include <vector>
#include <queue>
#include <bits/stl_algo.h>
#include <parallel/sort.h>
namespace __gnu_parallel
{
/** @brief Compare a pair of types lexicographically, ascending. */
template<typename T1, typename T2, typename Comparator>
class lexicographic
: public std::binary_function<std::pair<T1, T2>, std::pair<T1, T2>, bool>
{
private:
Comparator& comp;
public:
lexicographic(Comparator& _comp) : comp(_comp) { }
bool
operator()(const std::pair<T1, T2>& p1,
const std::pair<T1, T2>& p2) const
{
if (comp(p1.first, p2.first))
return true;
if (comp(p2.first, p1.first))
return false;
// Firsts are equal.
return p1.second < p2.second;
}
};
/** @brief Compare a pair of types lexicographically, descending. */
template<typename T1, typename T2, typename Comparator>
class lexicographic_reverse : public std::binary_function<T1, T2, bool>
{
private:
Comparator& comp;
public:
lexicographic_reverse(Comparator& _comp) : comp(_comp) { }
bool
operator()(const std::pair<T1, T2>& p1,
const std::pair<T1, T2>& p2) const
{
if (comp(p2.first, p1.first))
return true;
if (comp(p1.first, p2.first))
return false;
// Firsts are equal.
return p2.second < p1.second;
}
};
/**
* @brief Splits several sorted sequences at a certain global rank,
* resulting in a splitting point for each sequence.
* The sequences are passed via a sequence of random-access
* iterator pairs, none of the sequences may be empty. If there
* are several equal elements across the split, the ones on the
* left side will be chosen from sequences with smaller number.
* @param begin_seqs Begin of the sequence of iterator pairs.
* @param end_seqs End of the sequence of iterator pairs.
* @param rank The global rank to partition at.
* @param begin_offsets A random-access sequence begin where the
* result will be stored in. Each element of the sequence is an
* iterator that points to the first element on the greater part of
* the respective sequence.
* @param comp The ordering functor, defaults to std::less<T>.
*/
template<typename RanSeqs, typename RankType, typename RankIterator,
typename Comparator>
void
multiseq_partition(RanSeqs begin_seqs, RanSeqs end_seqs,
RankType rank,
RankIterator begin_offsets,
Comparator comp = std::less<
typename std::iterator_traits<typename
std::iterator_traits<RanSeqs>::value_type::
first_type>::value_type>()) // std::less<T>
{
_GLIBCXX_CALL(end_seqs - begin_seqs)
typedef typename std::iterator_traits<RanSeqs>::value_type::first_type
It;
typedef typename std::iterator_traits<It>::difference_type
difference_type;
typedef typename std::iterator_traits<It>::value_type value_type;
lexicographic<value_type, int, Comparator> lcomp(comp);
lexicographic_reverse<value_type, int, Comparator> lrcomp(comp);
// Number of sequences, number of elements in total (possibly
// including padding).
difference_type m = std::distance(begin_seqs, end_seqs), N = 0,
nmax, n, r;
for (int i = 0; i < m; i++)
{
N += std::distance(begin_seqs[i].first, begin_seqs[i].second);
_GLIBCXX_PARALLEL_ASSERT(
std::distance(begin_seqs[i].first, begin_seqs[i].second) > 0);
}
if (rank == N)
{
for (int i = 0; i < m; i++)
begin_offsets[i] = begin_seqs[i].second; // Very end.
// Return m - 1;
return;
}
_GLIBCXX_PARALLEL_ASSERT(m != 0);
_GLIBCXX_PARALLEL_ASSERT(N != 0);
_GLIBCXX_PARALLEL_ASSERT(rank >= 0);
_GLIBCXX_PARALLEL_ASSERT(rank < N);
difference_type* ns = new difference_type[m];
difference_type* a = new difference_type[m];
difference_type* b = new difference_type[m];
difference_type l;
ns[0] = std::distance(begin_seqs[0].first, begin_seqs[0].second);
nmax = ns[0];
for (int i = 0; i < m; i++)
{
ns[i] = std::distance(begin_seqs[i].first, begin_seqs[i].second);
nmax = std::max(nmax, ns[i]);
}
r = __log2(nmax) + 1;
// Pad all lists to this length, at least as long as any ns[i],
// equality iff nmax = 2^k - 1.
l = (1ULL << r) - 1;
for (int i = 0; i < m; i++)
{
a[i] = 0;
b[i] = l;
}
n = l / 2;
// Invariants:
// 0 <= a[i] <= ns[i], 0 <= b[i] <= l
#define S(i) (begin_seqs[i].first)
// Initial partition.
std::vector<std::pair<value_type, int> > sample;
for (int i = 0; i < m; i++)
if (n < ns[i]) //sequence long enough
sample.push_back(std::make_pair(S(i)[n], i));
__gnu_sequential::sort(sample.begin(), sample.end(), lcomp);
for (int i = 0; i < m; i++) //conceptual infinity
if (n >= ns[i]) //sequence too short, conceptual infinity
sample.push_back(std::make_pair(S(i)[0] /*dummy element*/, i));
difference_type localrank = rank / l;
int j;
for (j = 0; j < localrank && ((n + 1) <= ns[sample[j].second]); ++j)
a[sample[j].second] += n + 1;
for (; j < m; j++)
b[sample[j].second] -= n + 1;
// Further refinement.
while (n > 0)
{
n /= 2;
int lmax_seq = -1; // to avoid warning
const value_type* lmax = NULL; // impossible to avoid the warning?
for (int i = 0; i < m; i++)
{
if (a[i] > 0)
{
if (!lmax)
{
lmax = &(S(i)[a[i] - 1]);
lmax_seq = i;
}
else
{
// Max, favor rear sequences.
if (!comp(S(i)[a[i] - 1], *lmax))
{
lmax = &(S(i)[a[i] - 1]);
lmax_seq = i;
}
}
}
}
int i;
for (i = 0; i < m; i++)
{
difference_type middle = (b[i] + a[i]) / 2;
if (lmax && middle < ns[i] &&
lcomp(std::make_pair(S(i)[middle], i),
std::make_pair(*lmax, lmax_seq)))
a[i] = std::min(a[i] + n + 1, ns[i]);
else
b[i] -= n + 1;
}
difference_type leftsize = 0;
for (int i = 0; i < m; i++)
leftsize += a[i] / (n + 1);
difference_type skew = rank / (n + 1) - leftsize;
if (skew > 0)
{
// Move to the left, find smallest.
std::priority_queue<std::pair<value_type, int>,
std::vector<std::pair<value_type, int> >,
lexicographic_reverse<value_type, int, Comparator> >
pq(lrcomp);
for (int 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)
{
int 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<value_type, int>,
std::vector<std::pair<value_type, int> >,
lexicographic<value_type, int, Comparator> > pq(lcomp);
for (int i = 0; i < m; i++)
if (a[i] > 0)
pq.push(std::make_pair(S(i)[a[i] - 1], i));
for (; skew != 0; ++skew)
{
int 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.
value_type* maxleft = NULL;
value_type* minright = NULL;
for (int i = 0; i < m; i++)
{
if (a[i] > 0)
{
if (!maxleft)
maxleft = &(S(i)[a[i] - 1]);
else
{
// Max, favor rear sequences.
if (!comp(S(i)[a[i] - 1], *maxleft))
maxleft = &(S(i)[a[i] - 1]);
}
}
if (b[i] < ns[i])
{
if (!minright)
minright = &(S(i)[b[i]]);
else
{
// Min, favor fore sequences.
if (comp(S(i)[b[i]], *minright))
minright = &(S(i)[b[i]]);
}
}
}
int seq = 0;
for (int i = 0; i < m; i++)
begin_offsets[i] = S(i) + a[i];
delete[] ns;
delete[] a;
delete[] b;
}
/**
* @brief Selects the element at a certain global rank from several
* sorted sequences.
*
* The sequences are passed via a sequence of random-access
* iterator pairs, none of the sequences may be empty.
* @param begin_seqs Begin of the sequence of iterator pairs.
* @param end_seqs End of the sequence of iterator pairs.
* @param rank The global rank to partition at.
* @param offset The rank of the selected element in the global
* subsequence of elements equal to the selected element. If the
* selected element is unique, this number is 0.
* @param comp The ordering functor, defaults to std::less.
*/
template<typename T, typename RanSeqs, typename RankType,
typename Comparator>
T
multiseq_selection(RanSeqs begin_seqs, RanSeqs end_seqs, RankType rank,
RankType& offset, Comparator comp = std::less<T>())
{
_GLIBCXX_CALL(end_seqs - begin_seqs)
typedef typename std::iterator_traits<RanSeqs>::value_type::first_type
It;
typedef typename std::iterator_traits<It>::difference_type
difference_type;
lexicographic<T, int, Comparator> lcomp(comp);
lexicographic_reverse<T, int, Comparator> lrcomp(comp);
// Number of sequences, number of elements in total (possibly
// including padding).
difference_type m = std::distance(begin_seqs, end_seqs);
difference_type N = 0;
difference_type nmax, n, r;
for (int i = 0; i < m; i++)
N += std::distance(begin_seqs[i].first, begin_seqs[i].second);
if (m == 0 || N == 0 || rank < 0 || rank >= N)
{
// Result undefined when there is no data or rank is outside bounds.
throw std::exception();
}
difference_type* ns = new difference_type[m];
difference_type* a = new difference_type[m];
difference_type* b = new difference_type[m];
difference_type l;
ns[0] = std::distance(begin_seqs[0].first, begin_seqs[0].second);
nmax = ns[0];
for (int i = 0; i < m; ++i)
{
ns[i] = std::distance(begin_seqs[i].first, begin_seqs[i].second);
nmax = std::max(nmax, ns[i]);
}
r = __log2(nmax) + 1;
// Pad all lists to this length, at least as long as any ns[i],
// equality iff nmax = 2^k - 1
l = pow2(r) - 1;
for (int i = 0; i < m; ++i)
{
a[i] = 0;
b[i] = l;
}
n = l / 2;
// Invariants:
// 0 <= a[i] <= ns[i], 0 <= b[i] <= l
#define S(i) (begin_seqs[i].first)
// Initial partition.
std::vector<std::pair<T, int> > sample;
for (int i = 0; i < m; i++)
if (n < ns[i])
sample.push_back(std::make_pair(S(i)[n], i));
__gnu_sequential::sort(sample.begin(), sample.end(),
lcomp, sequential_tag());
// Conceptual infinity.
for (int i = 0; i < m; i++)
if (n >= ns[i])
sample.push_back(std::make_pair(S(i)[0] /*dummy element*/, i));
difference_type localrank = rank / l;
int j;
for (j = 0; j < localrank && ((n + 1) <= ns[sample[j].second]); ++j)
a[sample[j].second] += n + 1;
for (; j < m; ++j)
b[sample[j].second] -= n + 1;
// Further refinement.
while (n > 0)
{
n /= 2;
const T* lmax = NULL;
for (int 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]);
}
}
}
int i;
for (i = 0; i < m; i++)
{
difference_type 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;
}
difference_type leftsize = 0;
for (int i = 0; i < m; ++i)
leftsize += a[i] / (n + 1);
difference_type skew = rank / (n + 1) - leftsize;
if (skew > 0)
{
// Move to the left, find smallest.
std::priority_queue<std::pair<T, int>,
std::vector<std::pair<T, int> >,
lexicographic_reverse<T, int, Comparator> > pq(lrcomp);
for (int 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)
{
int 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<T, int>,
std::vector<std::pair<T, int> >,
lexicographic<T, int, Comparator> > pq(lcomp);
for (int i = 0; i < m; ++i)
if (a[i] > 0)
pq.push(std::make_pair(S(i)[a[i] - 1], i));
for (; skew != 0; ++skew)
{
int 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?
T maxleft, minright;
for (int 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 (int i = 0; i < m; ++i)
{
difference_type 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 */
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