C++ STL源码学习（priority_queue内部heap篇）

stl_heap.h

///STL中使用的是大顶堆
/// Heap-manipulation functions: push_heap, pop_heap, make_heap, sort_heap.
template <class _RandomAccessIterator, class _Distance, class _Tp>
void
__push_heap(_RandomAccessIterator __first,
            _Distance __holeIndex, _Distance __topIndex, _Tp __value)
{
  _Distance __parent = (__holeIndex - 1) / 2;

  ///逐层上溯,查找要插入的位置
  while (__holeIndex > __topIndex && *(__first + __parent) < __value) {
    *(__first + __holeIndex) = *(__first + __parent);
    __holeIndex = __parent;
    __parent = (__holeIndex - 1) / 2;
  }

  ///找到位置,插入
  *(__first + __holeIndex) = __value;
}

template <class _RandomAccessIterator, class _Distance, class _Tp>
inline void
__push_heap_aux(_RandomAccessIterator __first,
                _RandomAccessIterator __last, _Distance*, _Tp*)
{
  __push_heap(__first, _Distance((__last - __first) - 1), _Distance(0),
              _Tp(*(__last - 1)));
}

template <class _RandomAccessIterator>
inline void
push_heap(_RandomAccessIterator __first, _RandomAccessIterator __last)
{
  __STL_REQUIRES(_RandomAccessIterator, _Mutable_RandomAccessIterator);
  __STL_REQUIRES(typename iterator_traits<_RandomAccessIterator>::value_type,
                 _LessThanComparable);

  __push_heap_aux(__first, __last,
                  __DISTANCE_TYPE(__first), __VALUE_TYPE(__first));
}

template <class _RandomAccessIterator, class _Distance, class _Tp,
          class _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) = *(__first + __parent);
    __holeIndex = __parent;
    __parent = (__holeIndex - 1) / 2;
  }
  *(__first + __holeIndex) = __value;
}

template <class _RandomAccessIterator, class _Compare,
          class _Distance, class _Tp>
inline void
__push_heap_aux(_RandomAccessIterator __first,
                _RandomAccessIterator __last, _Compare __comp,
                _Distance*, _Tp*)
{
  __push_heap(__first, _Distance((__last - __first) - 1), _Distance(0),
              _Tp(*(__last - 1)), __comp);
}

template <class _RandomAccessIterator, class _Compare>
inline void
push_heap(_RandomAccessIterator __first, _RandomAccessIterator __last,
          _Compare __comp)
{
  __STL_REQUIRES(_RandomAccessIterator, _Mutable_RandomAccessIterator);
  __push_heap_aux(__first, __last, __comp,
                  __DISTANCE_TYPE(__first), __VALUE_TYPE(__first));
}

///将__holeIndex处的结点摘掉,并保持合法的大顶堆状态,然后插入__value
///执行此函数前,必须保证以__holeIndex为根节点构成的完全二叉树符合大顶堆的定义
template <class _RandomAccessIterator, class _Distance, class _Tp>
void
__adjust_heap(_RandomAccessIterator __first, _Distance __holeIndex,
              _Distance __len, _Tp __value)
{
  _Distance __topIndex = __holeIndex;
  _Distance __secondChild = 2 * __holeIndex + 2;
  ///向下遍历,从__holeIndex中找出两个孩子中较大的一个填入__holeIndex,并令__holeIndex
  ///等于该孩子,继续执行,直至__holeIndex无孩子或者只有一个孩子(为了占被摘取的那个节点的位置)
  while (__secondChild < __len) {
    if (*(__first + __secondChild) < *(__first + (__secondChild - 1)))
      __secondChild--;
    *(__first + __holeIndex) = *(__first + __secondChild);
    __holeIndex = __secondChild;
    __secondChild = 2 * (__secondChild + 1);
  }

  if (__secondChild == __len) {          ///__holeIndex只有一个孩子,补充上去
    *(__first + __holeIndex) = *(__first + (__secondChild - 1));
    __holeIndex = __secondChild - 1;
  }

  ///至此,大顶堆合法,插入__value
  __push_heap(__first, __holeIndex, __topIndex, __value);
}

template <class _RandomAccessIterator, class _Tp, class _Distance>
inline void
__pop_heap(_RandomAccessIterator __first, _RandomAccessIterator __last,
           _RandomAccessIterator __result, _Tp __value, _Distance*)
{
    ///该函数并未删除弹出的那个元素,而只是将它移动到最后面
  *__result = *__first;
  __adjust_heap(__first, _Distance(0), _Distance(__last - __first), __value);
}

template <class _RandomAccessIterator, class _Tp>
inline void
__pop_heap_aux(_RandomAccessIterator __first, _RandomAccessIterator __last,
               _Tp*)
{
  __pop_heap(__first, __last - 1, __last - 1,
             _Tp(*(__last - 1)), __DISTANCE_TYPE(__first));
}

template <class _RandomAccessIterator>
inline void pop_heap(_RandomAccessIterator __first,
                     _RandomAccessIterator __last)
{
  __STL_REQUIRES(_RandomAccessIterator, _Mutable_RandomAccessIterator);
  __STL_REQUIRES(typename iterator_traits<_RandomAccessIterator>::value_type,
                 _LessThanComparable);

  __pop_heap_aux(__first, __last, __VALUE_TYPE(__first));
}

template <class _RandomAccessIterator, class _Distance,
          class _Tp, class _Compare>
void
__adjust_heap(_RandomAccessIterator __first, _Distance __holeIndex,
              _Distance __len, _Tp __value, _Compare __comp)
{
  _Distance __topIndex = __holeIndex;
  _Distance __secondChild = 2 * __holeIndex + 2;
  while (__secondChild < __len) {
    if (__comp(*(__first + __secondChild), *(__first + (__secondChild - 1))))
      __secondChild--;
    *(__first + __holeIndex) = *(__first + __secondChild);
    __holeIndex = __secondChild;
    __secondChild = 2 * (__secondChild + 1);
  }
  if (__secondChild == __len) {
    *(__first + __holeIndex) = *(__first + (__secondChild - 1));
    __holeIndex = __secondChild - 1;
  }
  __push_heap(__first, __holeIndex, __topIndex, __value, __comp);
}

template <class _RandomAccessIterator, class _Tp, class _Compare,
          class _Distance>
inline void
__pop_heap(_RandomAccessIterator __first, _RandomAccessIterator __last,
           _RandomAccessIterator __result, _Tp __value, _Compare __comp,
           _Distance*)
{
  *__result = *__first;
  __adjust_heap(__first, _Distance(0), _Distance(__last - __first),
                __value, __comp);
}

template <class _RandomAccessIterator, class _Tp, class _Compare>
inline void
__pop_heap_aux(_RandomAccessIterator __first,
               _RandomAccessIterator __last, _Tp*, _Compare __comp)
{
  __pop_heap(__first, __last - 1, __last - 1, _Tp(*(__last - 1)), __comp,
             __DISTANCE_TYPE(__first));
}

template <class _RandomAccessIterator, class _Compare>
inline void
pop_heap(_RandomAccessIterator __first,
         _RandomAccessIterator __last, _Compare __comp)
{
  __STL_REQUIRES(_RandomAccessIterator, _Mutable_RandomAccessIterator);
  __pop_heap_aux(__first, __last, __VALUE_TYPE(__first), __comp);
}

template <class _RandomAccessIterator, class _Tp, class _Distance>
void
__make_heap(_RandomAccessIterator __first,
            _RandomAccessIterator __last, _Tp*, _Distance*)
{
  if (__last - __first < 2) return;
  _Distance __len = __last - __first;

  ///由于__adjust_heap的要求,必须从最底层开始逐层向上调整.
  _Distance __parent = (__len - 2)/2;   ///此时它的两个孩子分别为__len-1,len

  while (true) {
    __adjust_heap(__first, __parent, __len, _Tp(*(__first + __parent)));
    if (__parent == 0) return;
    __parent--;
  }
}

template <class _RandomAccessIterator>
inline void
make_heap(_RandomAccessIterator __first, _RandomAccessIterator __last)
{
  __STL_REQUIRES(_RandomAccessIterator, _Mutable_RandomAccessIterator);
  __STL_REQUIRES(typename iterator_traits<_RandomAccessIterator>::value_type,
                 _LessThanComparable);

  __make_heap(__first, __last,
              __VALUE_TYPE(__first), __DISTANCE_TYPE(__first));
}

template <class _RandomAccessIterator, class _Compare,
          class _Tp, class _Distance>
void
__make_heap(_RandomAccessIterator __first, _RandomAccessIterator __last,
            _Compare __comp, _Tp*, _Distance*)
{
  if (__last - __first < 2) return;
  _Distance __len = __last - __first;
  _Distance __parent = (__len - 2)/2;

  while (true) {
    __adjust_heap(__first, __parent, __len, _Tp(*(__first + __parent)),
                  __comp);
    if (__parent == 0) return;
    __parent--;
  }
}

template <class _RandomAccessIterator, class _Compare>
inline void
make_heap(_RandomAccessIterator __first,
          _RandomAccessIterator __last, _Compare __comp)
{
  __STL_REQUIRES(_RandomAccessIterator, _Mutable_RandomAccessIterator);

  __make_heap(__first, __last, __comp,
              __VALUE_TYPE(__first), __DISTANCE_TYPE(__first));
}

template <class _RandomAccessIterator>
void sort_heap(_RandomAccessIterator __first, _RandomAccessIterator __last)
{
  __STL_REQUIRES(_RandomAccessIterator, _Mutable_RandomAccessIterator);
  __STL_REQUIRES(typename iterator_traits<_RandomAccessIterator>::value_type,
                 _LessThanComparable);

    ///由于pop_heap函数并未正真将结点删除,此函数得以实现
  while (__last - __first > 1)
    pop_heap(__first, __last--);
}

template <class _RandomAccessIterator, class _Compare>
void
sort_heap(_RandomAccessIterator __first,
          _RandomAccessIterator __last, _Compare __comp)
{
  __STL_REQUIRES(_RandomAccessIterator, _Mutable_RandomAccessIterator);
  while (__last - __first > 1)
    pop_heap(__first, __last--, __comp);
}

由此可见，向heap中插入一个元素、删除heap的一个元素（只能是堆顶元素）的时间复杂度都为lg(N) , (这两种操作都调用了adjust_heap操作，而adjust_heap的时间复杂度为lg(N).有一个无序的数组建立一个堆的时间复杂度为N。根据已建立的堆得到排序数组的时间复杂度为Nlg(N) , 因为调用了N次adjust_heap操作。同时，heap_sort也没有辅助空间的要求，所以heap_sort的空间复杂度为O(1)。heap_sort的原理实际上就是每次把堆顶的元素（第一个元素，也是最大/小的元素）挪到数组末尾处，将第二大/小的元素挪到堆顶，即成为数组第一个元素。如此操作n次，便可得到一个有序数组。