C++ STL源碼學習（priority_queue內部heap篇）

stl_heap.h

///STL中使用的是大頂堆
/// 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;

  ///逐層上溯,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));
}

///將__holeIndex處的結點摘掉,並保持合法的大頂堆狀態,然後插入__value
///執行此函數前,必須保證以__holeIndex爲根節點構成的完全二叉樹符合大頂堆的定義
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;
  ///向下遍歷,從__holeIndex中找出兩個孩子中較大的一個填入__holeIndex,並令__holeIndex
  ///等於該孩子,繼續執行,直至__holeIndex無孩子或者只有一個孩子(爲了佔被摘取的那個節點的位置)
  while (__secondChild < __len) {
    if (*(__first + __secondChild) < *(__first + (__secondChild - 1)))
      __secondChild--;
    *(__first + __holeIndex) = *(__first + __secondChild);
    __holeIndex = __secondChild;
    __secondChild = 2 * (__secondChild + 1);
  }

  if (__secondChild == __len) {          ///__holeIndex只有一個孩子,補充上去
    *(__first + __holeIndex) = *(__first + (__secondChild - 1));
    __holeIndex = __secondChild - 1;
  }

  ///至此,大頂堆合法,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*)
{
    ///該函數並未刪除彈出的那個元素,而只是將它移動到最後面
  *__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;

  ///由於__adjust_heap的要求,必須從最底層開始逐層向上調整.
  _Distance __parent = (__len - 2)/2;   ///此時它的兩個孩子分別爲__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);

    ///由於pop_heap函數並未正真將結點刪除,此函數得以實現
  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);
}

由此可見，向heap中插入一個元素、刪除heap的一個元素（只能是堆頂元素）的時間複雜度都爲lg(N) , (這兩種操作都調用了adjust_heap操作，而adjust_heap的時間複雜度爲lg(N).有一個無序的數組建立一個堆的時間複雜度爲N。根據已建立的堆得到排序數組的時間複雜度爲Nlg(N) , 因爲調用了N次adjust_heap操作。同時，heap_sort也沒有輔助空間的要求，所以heap_sort的空間複雜度爲O(1)。heap_sort的原理實際上就是每次把堆頂的元素（第一個元素，也是最大/小的元素）挪到數組末尾處，將第二大/小的元素挪到堆頂，即成爲數組第一個元素。如此操作n次，便可得到一個有序數組。