[libcxx] r213615 - Fix std::make_heap's worst case time complexity
David Majnemer
david.majnemer at gmail.com
Tue Jul 29 19:53:22 PDT 2014
Does anything else have to happen before this gets merged for 3.5? I don't
see this change in the 3.5 branch.
On Thu, Jul 24, 2014 at 12:12 PM, Marshall Clow <mclow.lists at gmail.com>
wrote:
>
> On Jul 22, 2014, at 8:48 PM, David Majnemer <david.majnemer at gmail.com>
> wrote:
>
> Should this be merged for 3.5?
>
>
> Yes.
>
> — Marshall
>
>
>
> On Mon, Jul 21, 2014 at 11:07 PM, David Majnemer <david.majnemer at gmail.com
> > wrote:
>
>> Author: majnemer
>> Date: Tue Jul 22 01:07:09 2014
>> New Revision: 213615
>>
>> URL: http://llvm.org/viewvc/llvm-project?rev=213615&view=rev
>> Log:
>> 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.
>>
>> Modified:
>> libcxx/trunk/include/algorithm
>>
>> libcxx/trunk/test/algorithms/alg.sorting/alg.heap.operations/make.heap/make_heap_comp.pass.cpp
>>
>> Modified: libcxx/trunk/include/algorithm
>> URL:
>> http://llvm.org/viewvc/llvm-project/libcxx/trunk/include/algorithm?rev=213615&r1=213614&r2=213615&view=diff
>>
>> ==============================================================================
>> --- libcxx/trunk/include/algorithm (original)
>> +++ libcxx/trunk/include/algorithm Tue Jul 22 01:07:09 2014
>> @@ -4794,49 +4794,8 @@ is_heap(_RandomAccessIterator __first, _
>>
>> 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,
>> - typename
>> iterator_traits<_RandomAccessIterator>::difference_type __len)
>> +__sift_up(_RandomAccessIterator __first, _RandomAccessIterator __last,
>> _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;
>> @@ -4869,10 +4828,10 @@ push_heap(_RandomAccessIterator __first,
>> #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
>> }
>>
>> @@ -4887,6 +4846,60 @@ push_heap(_RandomAccessIterator __first,
>> // 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
>> __pop_heap(_RandomAccessIterator __first, _RandomAccessIterator __last,
>> _Compare __comp,
>> @@ -4895,7 +4908,7 @@ __pop_heap(_RandomAccessIterator __first
>> 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 __firs
>> 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 __f
>> 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 __fir
>> _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);
>> }
>>
>> Modified:
>> libcxx/trunk/test/algorithms/alg.sorting/alg.heap.operations/make.heap/make_heap_comp.pass.cpp
>> URL:
>> http://llvm.org/viewvc/llvm-project/libcxx/trunk/test/algorithms/alg.sorting/alg.heap.operations/make.heap/make_heap_comp.pass.cpp?rev=213615&r1=213614&r2=213615&view=diff
>>
>> ==============================================================================
>> ---
>> libcxx/trunk/test/algorithms/alg.sorting/alg.heap.operations/make.heap/make_heap_comp.pass.cpp
>> (original)
>> +++
>> libcxx/trunk/test/algorithms/alg.sorting/alg.heap.operations/make.heap/make_heap_comp.pass.cpp
>> Tue Jul 22 01:07:09 2014
>> @@ -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);
>>
>>
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