pq_losertree.h

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/***************************************************************************
 * include/stxxl/bits/containers/pq_losertree.h
 *
 * Part of the STXXL. See http://stxxl.sourceforge.net
 *
 * Copyright (C) 1999 Peter Sanders <[email protected]>
 * Copyright (C) 2003, 2004, 2007 Roman Dementiev <[email protected]>
 * Copyright (C) 2007-2009 Johannes Singler <[email protected]>
 * Copyright (C) 2007, 2008 Andreas Beckmann <[email protected]>
 *
 * 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 STXXL_CONTAINERS_PQ_LOSERTREE_HEADER
#define STXXL_CONTAINERS_PQ_LOSERTREE_HEADER

#include <stxxl/bits/containers/pq_helpers.h>

STXXL_BEGIN_NAMESPACE

//! \addtogroup stlcontinternals
//!
//! \{

/*! \internal
 */
namespace priority_queue_local {

//////////////////////////////////////////////////////////////////////
// The data structure from Knuth, "Sorting and Searching", Section 5.4.1
/*!
 * Loser tree from Knuth, "Sorting and Searching", Section 5.4.1
 * \param MaxArity maximum arity of loser tree, has to be a power of two
 */
template <class ValueType, class CompareType, unsigned MaxArity>
class loser_tree : private noncopyable
{
public:
 typedef ValueType value_type;
 typedef CompareType comparator_type;
 typedef value_type Element;
 enum { max_arity = MaxArity };

private:
#if STXXL_PQ_INTERNAL_LOSER_TREE
 struct Entry
 {
 value_type key; // Key of Loser element (winner for 0)
 unsigned_type index; // number of losing segment
 };
#endif //STXXL_PQ_INTERNAL_LOSER_TREE

 comparator_type cmp;
 // stack of free segment indices
 internal_bounded_stack<unsigned_type, MaxArity> free_slots;

 unsigned_type size_; // total number of elements stored
 unsigned_type logK; // log of current tree size
 unsigned_type k; // invariant (k == 1 << logK), always a power of two

 Element sentinel; // target of free segment pointers

#if STXXL_PQ_INTERNAL_LOSER_TREE
 // upper levels of loser trees
 // entry[0] contains the winner info
 Entry entry[MaxArity];
#endif //STXXL_PQ_INTERNAL_LOSER_TREE

 // leaf information
 // note that Knuth uses indices k..k-1
 // while we use 0..k-1
 Element* current[MaxArity]; // pointer to current element
 Element* current_end[MaxArity]; // pointer to end of block for current element
 Element* segment[MaxArity]; // start of Segments
 unsigned_type segment_size[MaxArity]; // just to count the internal memory consumption, in bytes

 unsigned_type mem_cons_;

 // private member functions
 unsigned_type initWinner(unsigned_type root);
 void update_on_insert(unsigned_type node, const Element& newKey, unsigned_type newIndex,
 Element* winnerKey, unsigned_type* winnerIndex, unsigned_type* mask);
 void deallocate_segment(unsigned_type slot);
 void doubleK();
 void compactTree();
 void rebuildLoserTree();
 bool is_segment_empty(unsigned_type slot);
 void multi_merge_k(Element* target, unsigned_type length);

#if STXXL_PQ_INTERNAL_LOSER_TREE
 template <int LogK>
 void multi_merge_f(Element* target, unsigned_type length)
 {
 //Entry *currentPos;
 //Element currentKey;
 //int currentIndex; // leaf pointed to by current entry
 Element* done = target + length;
 Entry* regEntry = entry;
 Element** regStates = current;
 unsigned_type winnerIndex = regEntry[0].index;
 Element winnerKey = regEntry[0].key;
 Element* winnerPos;
 //Element sup = sentinel; // supremum

 assert(logK >= LogK);
 while (target != done)
 {
 winnerPos = regStates[winnerIndex];

 // write result
 *target = winnerKey;

 // advance winner segment
 ++winnerPos;
 regStates[winnerIndex] = winnerPos;
 winnerKey = *winnerPos;

 // remove winner segment if empty now
 if (is_sentinel(winnerKey))
 {
 deallocate_segment(winnerIndex);
 }
 ++target;

 // update loser tree
#define TreeStep(L) \
 if (1 << LogK >= 1 << L) { \
 Entry* pos ## L = regEntry + ((winnerIndex + (1 << LogK)) >> ((LogK - L + 1 >= 0) ? (LogK - L + 1) : 0)); \
 Element key ## L = pos ## L->key; \
 if (cmp(winnerKey, key ## L)) { \
 unsigned_type index ## L = pos ## L->index; \
 pos ## L->key = winnerKey; \
 pos ## L->index = winnerIndex; \
 winnerKey = key ## L; \
 winnerIndex = index ## L; \
 } \
 }
 TreeStep(10);
 TreeStep(9);
 TreeStep(8);
 TreeStep(7);
 TreeStep(6);
 TreeStep(5);
 TreeStep(4);
 TreeStep(3);
 TreeStep(2);
 TreeStep(1);
#undef TreeStep
 }
 regEntry[0].index = winnerIndex;
 regEntry[0].key = winnerKey;
 }
#endif //STXXL_PQ_INTERNAL_LOSER_TREE

public:
 bool is_sentinel(const Element& a)
 {
 return !(cmp(cmp.min_value(), a));
 }
 bool not_sentinel(const Element& a)
 {
 return cmp(cmp.min_value(), a);
 }

public:
 loser_tree();
 ~loser_tree();
 void init();

 void swap(loser_tree& obj)
 {
 std::swap(cmp, obj.cmp);
 std::swap(free_slots, obj.free_slots);
 std::swap(size_, obj.size_);
 std::swap(logK, obj.logK);
 std::swap(k, obj.k);
 std::swap(sentinel, obj.sentinel);
#if STXXL_PQ_INTERNAL_LOSER_TREE
 swap_1D_arrays(entry, obj.entry, MaxArity);
#endif //STXXL_PQ_INTERNAL_LOSER_TREE
 swap_1D_arrays(current, obj.current, MaxArity);
 swap_1D_arrays(current_end, obj.current_end, MaxArity);
 swap_1D_arrays(segment, obj.segment, MaxArity);
 swap_1D_arrays(segment_size, obj.segment_size, MaxArity);
 std::swap(mem_cons_, obj.mem_cons_);
 }

 void multi_merge(Element* begin, Element* end)
 {
 multi_merge(begin, end - begin);
 }
 void multi_merge(Element*, unsigned_type length);

 unsigned_type mem_cons() const { return mem_cons_; }

 bool is_space_available() const // for new segment
 {
 return (k < MaxArity) || !free_slots.empty();
 }

 //! insert segment beginning at target
 void insert_segment(Element * target, unsigned_type length);

 unsigned_type size() const { return size_; }
};

///////////////////////// LoserTree ///////////////////////////////////
template <class ValueType, class CompareType, unsigned MaxArity>
loser_tree<ValueType, CompareType, MaxArity>::loser_tree()
 : size_(0), logK(0), k(1), mem_cons_(0)
{
 free_slots.push(0);
 segment[0] = NULL;
 current[0] = &sentinel;
 current_end[0] = &sentinel;
 // entry and sentinel are initialized by init
 // since they need the value of supremum
 init();
}

template <class ValueType, class CompareType, unsigned MaxArity>
void loser_tree<ValueType, CompareType, MaxArity>::init()
{
 assert(!cmp(cmp.min_value(), cmp.min_value())); // verify strict weak ordering
 sentinel = cmp.min_value();
 rebuildLoserTree();
#if STXXL_PQ_INTERNAL_LOSER_TREE
 assert(current[entry[0].index] == &sentinel);
#endif //STXXL_PQ_INTERNAL_LOSER_TREE
}

// rebuild loser tree information from the values in current
template <class ValueType, class CompareType, unsigned MaxArity>
void loser_tree<ValueType, CompareType, MaxArity>::rebuildLoserTree()
{
#if STXXL_PQ_INTERNAL_LOSER_TREE
 // MaxArity needs to be a power of two
 assert(LOG2<MaxArity>::floor == LOG2<MaxArity>::ceil);
 unsigned_type winner = initWinner(1);
 entry[0].index = winner;
 entry[0].key = *(current[winner]);
#endif //STXXL_PQ_INTERNAL_LOSER_TREE
}

#if STXXL_PQ_INTERNAL_LOSER_TREE
// given any values in the leaves this
// routing recomputes upper levels of the tree
// from scratch in linear time
// initialize entry[root].index and the subtree rooted there
// return winner index
template <class ValueType, class CompareType, unsigned MaxArity>
unsigned_type loser_tree<ValueType, CompareType, MaxArity>::initWinner(unsigned_type root)
{
 if (root >= k) { // leaf reached
 return root - k;
 }
 else {
 unsigned_type left = initWinner(2 * root);
 unsigned_type right = initWinner(2 * root + 1);
 Element lk = *(current[left]);
 Element rk = *(current[right]);
 if (!(cmp(lk, rk))) { // right subtree loses
 entry[root].index = right;
 entry[root].key = rk;
 return left;
 }
 else {
 entry[root].index = left;
 entry[root].key = lk;
 return right;
 }
 }
}

// first go up the tree all the way to the root
// hand down old winner for the respective subtree
// based on new value, and old winner and loser
// update each node on the path to the root top down.
// This is implemented recursively
template <class ValueType, class CompareType, unsigned MaxArity>
void loser_tree<ValueType, CompareType, MaxArity>::update_on_insert(
 unsigned_type node,
 const Element& newKey,
 unsigned_type newIndex,
 Element* winnerKey,
 unsigned_type* winnerIndex, // old winner
 unsigned_type* mask) // 1 << (ceil(log KNK) - dist-from-root)
{
 if (node == 0) { // winner part of root
 *mask = (unsigned_type)(1) << (logK - 1);
 *winnerKey = entry[0].key;
 *winnerIndex = entry[0].index;
 if (cmp(entry[node].key, newKey))
 {
 entry[node].key = newKey;
 entry[node].index = newIndex;
 }
 }
 else {
 update_on_insert(node >> 1, newKey, newIndex, winnerKey, winnerIndex, mask);
 Element loserKey = entry[node].key;
 unsigned_type loserIndex = entry[node].index;
 if ((*winnerIndex & *mask) != (newIndex & *mask)) { // different subtrees
 if (cmp(loserKey, newKey)) { // newKey will have influence here
 if (cmp(*winnerKey, newKey)) { // old winner loses here
 entry[node].key = *winnerKey;
 entry[node].index = *winnerIndex;
 }
 else { // new entry loses here
 entry[node].key = newKey;
 entry[node].index = newIndex;
 }
 }
 *winnerKey = loserKey;
 *winnerIndex = loserIndex;
 }
 // note that nothing needs to be done if
 // the winner came from the same subtree
 // a) newKey <= winnerKey => even more reason for the other tree to lose
 // b) newKey > winnerKey => the old winner will beat the new
 // entry further down the tree
 // also the same old winner is handed down the tree

 *mask >>= 1; // next level
 }
}
#endif //STXXL_PQ_INTERNAL_LOSER_TREE

// make the tree two times as wide
template <class ValueType, class CompareType, unsigned MaxArity>
void loser_tree<ValueType, CompareType, MaxArity>::doubleK()
{
 STXXL_VERBOSE3("loser_tree::doubleK (before) k=" << k << " logK=" << logK << " MaxArity=" << MaxArity << " #free=" << free_slots.size());
 assert(k > 0);
 assert(k < MaxArity);
 assert(free_slots.empty()); // stack was free (probably not needed)

 // make all new entries free
 // and push them on the free stack
 for (unsigned_type i = 2 * k - 1; i >= k; i--) // backwards
 {
 current[i] = &sentinel;
 current_end[i] = &sentinel;
 segment[i] = NULL;
 free_slots.push(i);
 }

 // double the size
 k *= 2;
 logK++;

 STXXL_VERBOSE3("loser_tree::doubleK (after) k=" << k << " logK=" << logK << " MaxArity=" << MaxArity << " #free=" << free_slots.size());
 assert(!free_slots.empty());

 // recompute loser tree information
 rebuildLoserTree();
}

// compact nonempty segments in the left half of the tree
template <class ValueType, class CompareType, unsigned MaxArity>
void loser_tree<ValueType, CompareType, MaxArity>::compactTree()
{
 STXXL_VERBOSE3("loser_tree::compactTree (before) k=" << k << " logK=" << logK << " #free=" << free_slots.size());
 assert(logK > 0);

 // compact all nonempty segments to the left
 unsigned_type pos = 0;
 unsigned_type last_empty = 0;
 for ( ; pos < k; pos++)
 {
 if (not_sentinel(*(current[pos])))
 {
 segment_size[last_empty] = segment_size[pos];
 current[last_empty] = current[pos];
 current_end[last_empty] = current_end[pos];
 segment[last_empty] = segment[pos];
 last_empty++;
 } /*
 else
 {
 if(segment[pos])
 {
 STXXL_VERBOSE2("loser_tree::compactTree() deleting segment "<<pos<<
 " address: "<<segment[pos]<<" size: "<<segment_size[pos]);
 delete [] segment[pos];
 segment[pos] = 0;
 mem_cons_ -= segment_size[pos];
 }
 }*/
 }

 // half degree as often as possible
 while ((k > 1) && ((k / 2) >= last_empty))
 {
 k /= 2;
 logK--;
 }

 // overwrite garbage and compact the stack of free segment indices
 free_slots.clear(); // none free
 for ( ; last_empty < k; last_empty++)
 {
 current[last_empty] = &sentinel;
 current_end[last_empty] = &sentinel;
 free_slots.push(last_empty);
 }

 STXXL_VERBOSE3("loser_tree::compactTree (after) k=" << k << " logK=" << logK << " #free=" << free_slots.size());

 // recompute loser tree information
 rebuildLoserTree();
}

// insert segment beginning at target
// require: is_space_available() == 1
template <class ValueType, class CompareType, unsigned MaxArity>
void loser_tree<ValueType, CompareType, MaxArity>::
insert_segment(Element* target, unsigned_type length)
{
 STXXL_VERBOSE2("loser_tree::insert_segment(" << target << "," << length << ")");
 //std::copy(target,target + length,std::ostream_iterator<ValueType>(std::cout, "\n"));

 if (length > 0)
 {
 assert(not_sentinel(target[0]));
 assert(not_sentinel(target[length - 1]));
 assert(is_sentinel(target[length]));

 // get a free slot
 if (free_slots.empty())
 { // tree is too small
 doubleK();
 }
 assert(!free_slots.empty());
 unsigned_type index = free_slots.top();
 free_slots.pop();

 // link new segment
 current[index] = segment[index] = target;
 current_end[index] = target + length;
 segment_size[index] = (length + 1) * sizeof(value_type);
 mem_cons_ += (length + 1) * sizeof(value_type);
 size_ += length;

#if STXXL_PQ_INTERNAL_LOSER_TREE
 // propagate new information up the tree
 Element dummyKey;
 unsigned_type dummyIndex;
 unsigned_type dummyMask;
 update_on_insert((index + k) >> 1, *target, index,
 &dummyKey, &dummyIndex, &dummyMask);
#endif //STXXL_PQ_INTERNAL_LOSER_TREE
 }
 else {
 // immediately deallocate
 // this is not only an optimization
 // but also needed to keep free segments from
 // clogging up the tree
 delete[] target;
 }
}

template <class ValueType, class CompareType, unsigned MaxArity>
loser_tree<ValueType, CompareType, MaxArity>::~loser_tree()
{
 STXXL_VERBOSE1("loser_tree::~loser_tree()");
 for (unsigned_type i = 0; i < k; ++i)
 {
 if (segment[i])
 {
 STXXL_VERBOSE2("loser_tree::~loser_tree() deleting segment " << i);
 delete[] segment[i];
 mem_cons_ -= segment_size[i];
 }
 }
 // check whether we have not lost any memory
 assert(mem_cons_ == 0);
}

// free an empty segment .
template <class ValueType, class CompareType, unsigned MaxArity>
void loser_tree<ValueType, CompareType, MaxArity>::
deallocate_segment(unsigned_type slot)
{
 // reroute current pointer to some empty sentinel segment
 // with a sentinel key
 STXXL_VERBOSE2("loser_tree::deallocate_segment() deleting segment " <<
 slot << " address: " << segment[slot] << " size: " << (segment_size[slot] / sizeof(value_type)) - 1);
 current[slot] = &sentinel;
 current_end[slot] = &sentinel;

 // free memory
 delete[] segment[slot];
 segment[slot] = NULL;
 mem_cons_ -= segment_size[slot];

 // push on the stack of free segment indices
 free_slots.push(slot);
}

// delete the length smallest elements and write them to target
// empty segments are deallocated
// require:
// - there are at least length elements
// - segments are ended by sentinels
template <class ValueType, class CompareType, unsigned MaxArity>
void loser_tree<ValueType, CompareType, MaxArity>::
multi_merge(Element* target, unsigned_type length)
{
 STXXL_VERBOSE3("loser_tree::multi_merge(target=" << target << ", len=" << length << ") k=" << k);

 if (length == 0)
 return;

 assert(k > 0);
 assert(length <= size_);

 //This is the place to make statistics about internal multi_merge calls.

#if STXXL_PARALLEL && STXXL_PARALLEL_PQ_MULTIWAY_MERGE_INTERNAL
 priority_queue_local::invert_order<CompareType, value_type, value_type> inv_cmp(cmp);
#endif
 switch (logK) {
 case 0:
 assert(k == 1);
#if STXXL_PQ_INTERNAL_LOSER_TREE
 assert(entry[0].index == 0);
#endif //STXXL_PQ_INTERNAL_LOSER_TREE
 assert(free_slots.empty());
 memcpy(target, current[0], length * sizeof(Element));
 //std::copy(current[0], current[0] + length, target);
 current[0] += length;
#if STXXL_PQ_INTERNAL_LOSER_TREE
 entry[0].key = **current;
#endif //STXXL_PQ_INTERNAL_LOSER_TREE
 if (is_segment_empty(0))
 deallocate_segment(0);

 break;
 case 1:
 assert(k == 2);
#if STXXL_PARALLEL && STXXL_PARALLEL_PQ_MULTIWAY_MERGE_INTERNAL
 {
 std::pair<Element*, Element*> seqs[2] =
 {
 std::make_pair(current[0], current_end[0]),
 std::make_pair(current[1], current_end[1])
 };
 parallel::multiway_merge_sentinels(
 seqs, seqs + 2, target, length, inv_cmp);
 current[0] = seqs[0].first;
 current[1] = seqs[1].first;
 }
#else
 merge_iterator(current[0], current[1], target, length, cmp);
 rebuildLoserTree();
#endif
 if (is_segment_empty(0))
 deallocate_segment(0);

 if (is_segment_empty(1))
 deallocate_segment(1);

 break;
 case 2:
 assert(k == 4);
#if STXXL_PARALLEL && STXXL_PARALLEL_PQ_MULTIWAY_MERGE_INTERNAL
 {
 std::pair<Element*, Element*> seqs[4] =
 {
 std::make_pair(current[0], current_end[0]),
 std::make_pair(current[1], current_end[1]),
 std::make_pair(current[2], current_end[2]),
 std::make_pair(current[3], current_end[3])
 };
 parallel::multiway_merge_sentinels(
 seqs, seqs + 4, target, length, inv_cmp);
 current[0] = seqs[0].first;
 current[1] = seqs[1].first;
 current[2] = seqs[2].first;
 current[3] = seqs[3].first;
 }
#else
 if (is_segment_empty(3))
 merge3_iterator(current[0], current[1], current[2], target, length, cmp);
 else
 merge4_iterator(current[0], current[1], current[2], current[3], target, length, cmp);

 rebuildLoserTree();
#endif
 if (is_segment_empty(0))
 deallocate_segment(0);

 if (is_segment_empty(1))
 deallocate_segment(1);

 if (is_segment_empty(2))
 deallocate_segment(2);

 if (is_segment_empty(3))
 deallocate_segment(3);

 break;
#if !(STXXL_PARALLEL && STXXL_PARALLEL_PQ_MULTIWAY_MERGE_INTERNAL)
 case 3: multi_merge_f<3>(target, length);
 break;
 case 4: multi_merge_f<4>(target, length);
 break;
 case 5: multi_merge_f<5>(target, length);
 break;
 case 6: multi_merge_f<6>(target, length);
 break;
 case 7: multi_merge_f<7>(target, length);
 break;
 case 8: multi_merge_f<8>(target, length);
 break;
 case 9: multi_merge_f<9>(target, length);
 break;
 case 10: multi_merge_f<10>(target, length);
 break;
#endif
 default:
#if STXXL_PARALLEL && STXXL_PARALLEL_PQ_MULTIWAY_MERGE_INTERNAL
 {
 std::vector<std::pair<Element*, Element*> > seqs;
 std::vector<int_type> orig_seq_index;
 for (unsigned int i = 0; i < k; ++i)
 {
 if (current[i] != current_end[i] && !is_sentinel(*current[i]))
 {
 seqs.push_back(std::make_pair(current[i], current_end[i]));
 orig_seq_index.push_back(i);
 }
 }

 parallel::multiway_merge_sentinels(
 seqs.begin(), seqs.end(), target, length, inv_cmp);

 for (unsigned int i = 0; i < seqs.size(); ++i)
 {
 int_type seg = orig_seq_index[i];
 current[seg] = seqs[i].first;
 }

 for (unsigned int i = 0; i < k; ++i)
 if (is_segment_empty(i))
 {
 STXXL_VERBOSE3("deallocated " << i);
 deallocate_segment(i);
 }
 }
#else
 multi_merge_k(target, length);
#endif
 break;
 }

 size_ -= length;

 // compact tree if it got considerably smaller
 {
 const unsigned_type num_segments_used = k - free_slots.size();
 const unsigned_type num_segments_trigger = k - (3 * k / 5);
 // using k/2 would be worst case inefficient (for large k)
 // for k \in {2, 4, 8} the trigger is k/2 which is good
 // because we have special mergers for k \in {1, 2, 4}
 // there is also a special 3-way-merger, that will be
 // triggered if k == 4 && is_segment_empty(3)
 STXXL_VERBOSE3("loser_tree compact? k=" << k << " #used=" << num_segments_used
 << " <= #trigger=" << num_segments_trigger << " ==> "
 << ((k > 1 && num_segments_used <= num_segments_trigger) ? "yes" : "no ")
 << " || "
 << ((k == 4 && !free_slots.empty() && !is_segment_empty(3)) ? "yes" : "no ")
 << " #free=" << free_slots.size());
 if (k > 1 && ((num_segments_used <= num_segments_trigger) ||
 (k == 4 && !free_slots.empty() && !is_segment_empty(3))))
 {
 compactTree();
 }
 }
 //std::copy(target,target + length,std::ostream_iterator<ValueType>(std::cout, "\n"));
}

// is this segment empty and does not point to sentinel yet?
template <class ValueType, class CompareType, unsigned MaxArity>
inline bool loser_tree<ValueType, CompareType, MaxArity>::
is_segment_empty(unsigned_type slot)
{
 return (is_sentinel(*(current[slot])) && (current[slot] != &sentinel));
}

#if STXXL_PQ_INTERNAL_LOSER_TREE
// multi-merge for arbitrary K
template <class ValueType, class CompareType, unsigned MaxArity>
void loser_tree<ValueType, CompareType, MaxArity>::
multi_merge_k(Element* target, unsigned_type length)
{
 Entry* currentPos;
 Element currentKey;
 unsigned_type currentIndex; // leaf pointed to by current entry
 unsigned_type kReg = k;
 Element* done = target + length;
 unsigned_type winnerIndex = entry[0].index;
 Element winnerKey = entry[0].key;
 Element* winnerPos;

 while (target != done)
 {
 winnerPos = current[winnerIndex];

 // write result
 *target = winnerKey;

 // advance winner segment
 ++winnerPos;
 current[winnerIndex] = winnerPos;
 winnerKey = *winnerPos;

 // remove winner segment if empty now
 if (is_sentinel(winnerKey)) //
 deallocate_segment(winnerIndex);

 // go up the entry-tree
 for (unsigned_type i = (winnerIndex + kReg) >> 1; i > 0; i >>= 1) {
 currentPos = entry + i;
 currentKey = currentPos->key;
 if (cmp(winnerKey, currentKey)) {
 currentIndex = currentPos->index;
 currentPos->key = winnerKey;
 currentPos->index = winnerIndex;
 winnerKey = currentKey;
 winnerIndex = currentIndex;
 }
 }

 ++target;
 }
 entry[0].index = winnerIndex;
 entry[0].key = winnerKey;
}
#endif // STXXL_PQ_INTERNAL_LOSER_TREE

} // namespace priority_queue_local

//! \}

STXXL_END_NAMESPACE

#endif // !STXXL_CONTAINERS_PQ_LOSERTREE_HEADER
// vim: et:ts=4:sw=4