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Fix std::make_heap's worst case time complexity 

std::make_heap is currently implemented by iteratively applying a
siftup-type algorithm.  Since sift-up is O(ln n), this gives
std::make_heap a worst case time complexity of O(n ln n).

The C++ standard mandates that std::make_heap make no more than O(3n)
comparisons, this makes our std::make_heap out of spec.

Fix this by introducing an implementation of __sift_down and switch
std::make_heap to create the heap using it.
This gives std::make_heap linear time complexity in the worst case.

This fixes PR20161.

llvm-svn: 213615
This commit is contained in:
David Majnemer 2014-07-22 06:07:09 +00:00
parent fc3d8f0a78
commit 8b51260274
2 changed files with 90 additions and 55 deletions
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120
libcxx/include/algorithm
View File

@ -4794,48 +4794,7 @@ is_heap(_RandomAccessIterator __first, _RandomAccessIterator __last)
template <class _Compare, class _RandomAccessIterator>
void
__push_heap_front(_RandomAccessIterator __first, _RandomAccessIterator, _Compare __comp,
typename iterator_traits<_RandomAccessIterator>::difference_type __len)
{
typedef typename iterator_traits<_RandomAccessIterator>::difference_type difference_type;
typedef typename iterator_traits<_RandomAccessIterator>::value_type value_type;
if (__len > 1)
{
difference_type __p = 0;
_RandomAccessIterator __pp = __first;
difference_type __c = 2;
_RandomAccessIterator __cp = __first + __c;
if (__c == __len || __comp(*__cp, *(__cp - 1)))
{
--__c;
--__cp;
}
if (__comp(*__pp, *__cp))
{
value_type __t(_VSTD::move(*__pp));
do
{
*__pp = _VSTD::move(*__cp);
__pp = __cp;
__p = __c;
__c = (__p + 1) * 2;
if (__c > __len)
break;
__cp = __first + __c;
if (__c == __len || __comp(*__cp, *(__cp - 1)))
{
--__c;
--__cp;
}
} while (__comp(__t, *__cp));
*__pp = _VSTD::move(__t);
}
}
}
template <class _Compare, class _RandomAccessIterator>
void
__push_heap_back(_RandomAccessIterator __first, _RandomAccessIterator __last, _Compare __comp,
__sift_up(_RandomAccessIterator __first, _RandomAccessIterator __last, _Compare __comp,
typename iterator_traits<_RandomAccessIterator>::difference_type __len)
{
typedef typename iterator_traits<_RandomAccessIterator>::difference_type difference_type;
@ -4869,10 +4828,10 @@ push_heap(_RandomAccessIterator __first, _RandomAccessIterator __last, _Compare
#ifdef _LIBCPP_DEBUG
typedef typename add_lvalue_reference<__debug_less<_Compare> >::type _Comp_ref;
__debug_less<_Compare> __c(__comp);
__push_heap_back<_Comp_ref>(__first, __last, __c, __last - __first);
__sift_up<_Comp_ref>(__first, __last, __c, __last - __first);
#else // _LIBCPP_DEBUG
typedef typename add_lvalue_reference<_Compare>::type _Comp_ref;
__push_heap_back<_Comp_ref>(__first, __last, __comp, __last - __first);
__sift_up<_Comp_ref>(__first, __last, __comp, __last - __first);
#endif // _LIBCPP_DEBUG
}
@ -4886,6 +4845,60 @@ push_heap(_RandomAccessIterator __first, _RandomAccessIterator __last)
// pop_heap
template <class _Compare, class _RandomAccessIterator>
void
__sift_down(_RandomAccessIterator __first, _RandomAccessIterator __last, _Compare __comp,
typename iterator_traits<_RandomAccessIterator>::difference_type __len,
_RandomAccessIterator __start)
{
typedef typename iterator_traits<_RandomAccessIterator>::difference_type difference_type;
typedef typename iterator_traits<_RandomAccessIterator>::value_type value_type;
// left-child of __start is at 2 * __start + 1
// right-child of __start is at 2 * __start + 2
difference_type __child = __start - __first;
if (__len < 2 || (__len - 2) / 2 < __child)
return;
__child = 2 * __child + 1;
_RandomAccessIterator __child_i = __first + __child;
if ((__child + 1) < __len && __comp(*__child_i, *(__child_i + 1))) {
// right-child exists and is greater than left-child
++__child_i;
++__child;
}
// check if we are in heap-order
if (__comp(*__child_i, *__start))
// we are, __start is larger than it's largest child
return;
value_type __top(_VSTD::move(*__start));
do
{
// we are not in heap-order, swap the parent with it's largest child
*__start = _VSTD::move(*__child_i);
__start = __child_i;
if ((__len - 2) / 2 < __child)
break;
// recompute the child based off of the updated parent
__child = 2 * __child + 1;
__child_i = __first + __child;
if ((__child + 1) < __len && __comp(*__child_i, *(__child_i + 1))) {
// right-child exists and is greater than left-child
++__child_i;
++__child;
}
// check if we are in heap-order
} while (!__comp(*__child_i, __top));
*__start = _VSTD::move(__top);
}
template <class _Compare, class _RandomAccessIterator>
inline _LIBCPP_INLINE_VISIBILITY
void
@ -4895,7 +4908,7 @@ __pop_heap(_RandomAccessIterator __first, _RandomAccessIterator __last, _Compare
if (__len > 1)
{
swap(*__first, *--__last);
__push_heap_front<_Compare>(__first, __last, __comp, __len-1);
__sift_down<_Compare>(__first, __last, __comp, __len - 1, __first);
}
}
@ -4932,10 +4945,11 @@ __make_heap(_RandomAccessIterator __first, _RandomAccessIterator __last, _Compar
difference_type __n = __last - __first;
if (__n > 1)
{
__last = __first;
++__last;
for (difference_type __i = 1; __i < __n;)
__push_heap_back<_Compare>(__first, ++__last, __comp, ++__i);
// start from the first parent, there is no need to consider children
for (difference_type __start = (__n - 2) / 2; __start >= 0; --__start)
{
__sift_down<_Compare>(__first, __last, __comp, __n, __first + __start);
}
}
}
@ -5010,7 +5024,7 @@ __partial_sort(_RandomAccessIterator __first, _RandomAccessIterator __middle, _R
if (__comp(*__i, *__first))
{
swap(*__i, *__first);
__push_heap_front<_Compare>(__first, __middle, __comp, __len);
__sift_down<_Compare>(__first, __middle, __comp, __len, __first);
}
}
__sort_heap<_Compare>(__first, __middle, __comp);
@ -5051,15 +5065,15 @@ __partial_sort_copy(_InputIterator __first, _InputIterator __last,
_RandomAccessIterator __r = __result_first;
if (__r != __result_last)
{
typename iterator_traits<_RandomAccessIterator>::difference_type __len = 0;
for (; __first != __last && __r != __result_last; ++__first, ++__r, ++__len)
for (; __first != __last && __r != __result_last; ++__first, ++__r)
*__r = *__first;
__make_heap<_Compare>(__result_first, __r, __comp);
typename iterator_traits<_RandomAccessIterator>::difference_type __len = __r - __result_first;
for (; __first != __last; ++__first)
if (__comp(*__first, *__result_first))
{
*__result_first = *__first;
__push_heap_front<_Compare>(__result_first, __r, __comp, __len);
__sift_down<_Compare>(__result_first, __r, __comp, __len, __result_first);
}
__sort_heap<_Compare>(__result_first, __r, __comp);
}

23
libcxx/test/algorithms/alg.sorting/alg.heap.operations/make.heap/make_heap_comp.pass.cpp
View File

@ -35,14 +35,35 @@ struct indirect_less
void test(unsigned N)
{
int* ia = new int [N];
{
for (int i = 0; i < N; ++i)
ia[i] = i;
{
std::random_shuffle(ia, ia+N);
std::make_heap(ia, ia+N, std::greater<int>());
assert(std::is_heap(ia, ia+N, std::greater<int>()));
}
// Ascending
{
binary_counting_predicate<std::greater<int>, int, int> pred ((std::greater<int>()));
for (int i = 0; i < N; ++i)
ia[i] = i;
std::make_heap(ia, ia+N, std::ref(pred));
assert(pred.count() <= 3*N);
assert(std::is_heap(ia, ia+N, pred));
}
// Descending
{
binary_counting_predicate<std::greater<int>, int, int> pred ((std::greater<int>()));
for (int i = 0; i < N; ++i)
ia[N-1-i] = i;
std::make_heap(ia, ia+N, std::ref(pred));
assert(pred.count() <= 3*N);
assert(std::is_heap(ia, ia+N, pred));
}
// Random
{
binary_counting_predicate<std::greater<int>, int, int> pred ((std::greater<int>()));
std::random_shuffle(ia, ia+N);