[libcxx] r213615 - Fix std::make_heap's worst case time complexity
Marshall Clow
mclow.lists at gmail.com
Thu Jul 24 12:12:04 PDT 2014
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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