前言
堆是十分重要的数据结构，我们常用的优先队列就是基于堆实现的数据结构，堆排序也是基于堆实现的，所以，我们要理解堆的实现，之前自己根据堆的原理自己实现了堆，现在来分析一下STL中堆的实现代码，STL的堆实现相比自己实现的代码肯定要多很多，但原理是一样的，我们下面看一下。
堆的实现
STL中提供了堆的一系列代码供人使用。我们分析一下。我们知道堆的存储形式是利用数组实现的，那给定一个数组序列，怎么判断它是不是堆呢？下面给出了判断是否是堆的实现代码，其原理十分简单，就是看是否满足堆性质，父节点大于等于子节点（最大堆）。当然这里is_heap还有其他重载形式，这里不再列出。
/**
* @brief Determines whether a range is a heap using comparison functor.
* @param __first Start of range.
* @param __last End of range.
* @param __comp Comparison functor to use.
* @return True if range is a heap, false otherwise.
* @ingroup heap_algorithms
*/
template<typename _RandomAccessIterator, typename _Compare>
inline bool is_heap(_RandomAccessIterator __first, _RandomAccessIterator __last, _Compare __comp) { // 判断数组是不是满足堆性质
// concept requirements
__glibcxx_function_requires(_RandomAccessIteratorConcept<_RandomAccessIterator>)
__glibcxx_requires_valid_range(__first, __last);
__glibcxx_requires_irreflexive_pred(__first, __last, __comp);
const auto __dist = std::distance(__first, __last);
typedef __decltype(__comp) _Cmp;
__gnu_cxx::__ops::_Iter_comp_iter<_Cmp> __cmp(_GLIBCXX_MOVE(__comp));
return std::__is_heap_until(__first, __dist, __cmp) == __dist;
}
template<typename _RandomAccessIterator, typename _Distance, typename _Compare>
_Distance __is_heap_until(_RandomAccessIterator __first, _Distance __n, _Compare& __comp) {
_Distance __parent = 0;
for (_Distance __child = 1; __child < __n; ++__child) { // 实现原理比较好理解，按照堆性质，父节点要大于等于子节点（最大堆）
if (__comp(__first + __parent, __first + __child))
return __child;
if ((__child & 1) == 0)
++__parent;
}
return __n;
}
如果给定一个数组序列，不满足堆性质，怎么把他转换成具有堆性质呢？这里有make_heap实现，我们看一下其实现。其实现原理也是依据堆性质，先找到最后一个非叶子节点（有子节点的节点），检查是否满足父节点大于子节点，如果不满足，交换父子节点的值，如此，一直到根节点。
/**
* @brief Construct a heap over a range.
* @param __first Start of heap.
* @param __last End of heap.
* @ingroup heap_algorithms
*
* This operation makes the elements in [__first,__last) into a heap.
*/
template<typename _RandomAccessIterator>
inline void make_heap(_RandomAccessIterator __first, _RandomAccessIterator __last) {
// concept requirements
__glibcxx_function_requires(_Mutable_RandomAccessIteratorConcept<_RandomAccessIterator>)
__glibcxx_function_requires(_LessThanComparableConcept<typename iterator_traits<_RandomAccessIterator>::value_type>)
__glibcxx_requires_valid_range(__first, __last);
__glibcxx_requires_irreflexive(__first, __last);
__gnu_cxx::__ops::_Iter_less_iter __comp;
std::__make_heap(__first, __last, __comp);
}
template<typename _RandomAccessIterator, typename _Compare>
void __make_heap(_RandomAccessIterator __first, _RandomAccessIterator __last, _Compare& __comp) {
typedef typename iterator_traits<_RandomAccessIterator>::value_type _ValueType;
typedef typename iterator_traits<_RandomAccessIterator>::difference_type _DistanceType;
if (__last - __first < 2)
return;
const _DistanceType __len = __last - __first;
_DistanceType __parent = (__len - 2) / 2;
while (true) {
_ValueType __value = _GLIBCXX_MOVE(*(__first + __parent));
std::__adjust_heap(__first, __parent, __len, _GLIBCXX_MOVE(__value), __comp);
if (__parent == 0)
return;
__parent--;
}
}
template<typename _RandomAccessIterator, typename _Distance, typename _Tp, typename _Compare>
void __adjust_heap(_RandomAccessIterator __first, _Distance __holeIndex, _Distance __len, _Tp __value, _Compare __comp) {
const _Distance __topIndex = __holeIndex;
_Distance __secondChild = __holeIndex;
while (__secondChild < (__len - 1) / 2) {
__secondChild = 2 * (__secondChild + 1);
if (__comp(__first + __secondChild, __first + (__secondChild - 1)))
__secondChild--;
*(__first + __holeIndex) = _GLIBCXX_MOVE(*(__first + __secondChild));
__holeIndex = __secondChild;
}
if ((__len & 1) == 0 && __secondChild == (__len - 2) / 2) {
__secondChild = 2 * (__secondChild + 1);
*(__first + __holeIndex) = _GLIBCXX_MOVE(*(__first + (__secondChild - 1)));
__holeIndex = __secondChild - 1;
}
__decltype(__gnu_cxx::__ops::__iter_comp_val(_GLIBCXX_MOVE(__comp)))
__cmp(_GLIBCXX_MOVE(__comp));
std::__push_heap(__first, __holeIndex, __topIndex, _GLIBCXX_MOVE(__value), __cmp);
}
template<typename _RandomAccessIterator, typename _Distance, typename _Tp, typename _Compare>
void __push_heap(_RandomAccessIterator __first, _Distance __holeIndex, _Distance __topIndex, _Tp __value, _Compare& __comp) {
_Distance __parent = (__holeIndex - 1) / 2;
while (__holeIndex > __topIndex && __comp(__first + __parent, __value)) {
*(__first + __holeIndex) = _GLIBCXX_MOVE(*(__first + __parent));
__holeIndex = __parent;
__parent = (__holeIndex - 1) / 2;
}
*(__first + __holeIndex) = _GLIBCXX_MOVE(__value);
}
向堆中添加元素后，调用push_heap使之满足堆性质。在堆尾添加了一个元素后，可能破坏堆性质，进行“上移”，直到满足堆性质。
/**
* @brief Push an element onto a heap.
* @param __first Start of heap.
* @param __last End of heap + element.
* @ingroup heap_algorithms
*
* This operation pushes the element at last-1 onto the valid heap
* over the range [__first,__last-1). After completion,
* [__first,__last) is a valid heap.
*/
template<typename _RandomAccessIterator>
inline void push_heap(_RandomAccessIterator __first, _RandomAccessIterator __last) {
typedef typename iterator_traits<_RandomAccessIterator>::value_type _ValueType;
typedef typename iterator_traits<_RandomAccessIterator>::difference_type _DistanceType;
// concept requirements
__glibcxx_function_requires(_Mutable_RandomAccessIteratorConcept<_RandomAccessIterator>)
__glibcxx_function_requires(_LessThanComparableConcept<_ValueType>)
__glibcxx_requires_valid_range(__first, __last);
__glibcxx_requires_irreflexive(__first, __last);
__glibcxx_requires_heap(__first, __last - 1);
__gnu_cxx::__ops::_Iter_less_val __comp;
_ValueType __value = _GLIBCXX_MOVE(*(__last - 1));
std::__push_heap(__first, _DistanceType((__last - __first) - 1), _DistanceType(0), _GLIBCXX_MOVE(__value), __comp);
}
弹出一个元素到内部容器的尾端，破坏了堆性质后，执行“下移”保证堆性质。
/**
* @brief Pop an element off a heap using comparison functor.
* @param __first Start of heap.
* @param __last End of heap.
* @param __comp Comparison functor to use.
* @ingroup heap_algorithms
*
* This operation pops the top of the heap. The elements __first
* and __last-1 are swapped and [__first,__last-1) is made into a
* heap. Comparisons are made using comp.
*/
template<typename _RandomAccessIterator, typename _Compare>
inline void pop_heap(_RandomAccessIterator __first, _RandomAccessIterator __last, _Compare __comp) {
// concept requirements
__glibcxx_function_requires(_Mutable_RandomAccessIteratorConcept<_RandomAccessIterator>)
__glibcxx_requires_valid_range(__first, __last);
__glibcxx_requires_irreflexive_pred(__first, __last, __comp);
__glibcxx_requires_non_empty_range(__first, __last);
__glibcxx_requires_heap_pred(__first, __last, __comp);
if (__last - __first > 1) {
typedef __decltype(__comp) _Cmp;
__gnu_cxx::__ops::_Iter_comp_iter<_Cmp> __cmp(_GLIBCXX_MOVE(__comp));
--__last;
std::__pop_heap(__first, __last, __last, __cmp);
}
}
template<typename _RandomAccessIterator, typename _Compare>
inline void __pop_heap(_RandomAccessIterator __first, _RandomAccessIterator __last, _RandomAccessIterator __result, _Compare& __comp) {
typedef typename iterator_traits<_RandomAccessIterator>::value_type _ValueType;
typedef typename iterator_traits<_RandomAccessIterator>::difference_type _DistanceType;
_ValueType __value = _GLIBCXX_MOVE(*__result);
*__result = _GLIBCXX_MOVE(*__first);
std::__adjust_heap(__first, _DistanceType(0), _DistanceType(__last - __first), _GLIBCXX_MOVE(__value), __comp);
}
STL中也给出了堆排序的实现，代码如下：
/**
* @brief Sort a heap using comparison functor.
* @param __first Start of heap.
* @param __last End of heap.
* @param __comp Comparison functor to use.
* @ingroup heap_algorithms
*
* This operation sorts the valid heap in the range [__first,__last).
* Comparisons are made using __comp.
*/
template<typename _RandomAccessIterator, typename _Compare>
inline void sort_heap(_RandomAccessIterator __first, _RandomAccessIterator __last, _Compare __comp) {
// concept requirements
__glibcxx_function_requires(_Mutable_RandomAccessIteratorConcept<_RandomAccessIterator>)
__glibcxx_requires_valid_range(__first, __last);
__glibcxx_requires_irreflexive_pred(__first, __last, __comp);
__glibcxx_requires_heap_pred(__first, __last, __comp);
typedef __decltype(__comp) _Cmp;
__gnu_cxx::__ops::_Iter_comp_iter<_Cmp> __cmp(_GLIBCXX_MOVE(__comp));
std::__sort_heap(__first, __last, __cmp);
}
template<typename _RandomAccessIterator, typename _Compare>
void __sort_heap(_RandomAccessIterator __first, _RandomAccessIterator __last, _Compare& __comp) {
while (__last - __first > 1) {
--__last;
std::__pop_heap(__first, __last, __last, __comp);
}
}
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