STL之堆和优先队列

STL中的heap是用数组来进行模拟的，heap 本身的定义就是一颗完全的二叉树（注意和满二叉树的区别）。

heap分为大根堆和小根堆。

堆的主要操作由构建堆，调整堆，这两个。

其中有一个heap算法就是在此基础之上的。

构建好一颗大根堆，然后 将根顶元素和最后一个元素呼唤，将堆的大小减1，同时再次调整堆为大根堆，重复直至堆的大小为0。

由于堆结构本上是类似分组划分的，其中修改也就是修改这条路径上的，和其他元素没有关系，因此，每次修改的时候也就是路径长度，也就是二叉树的高度。

template <class _RandomAccessIterator, class _Distance, class _Tp>
void 
__push_heap(_RandomAccessIterator __first,
            _Distance __holeIndex, _Distance __topIndex, _Tp __value)
{//当前节点标号为__holeIndex- 1即为新插入元素标号，因为根节点标号是从0开始，所以这里要-1
  _Distance __parent = (__holeIndex - 1) / 2;//找出当前节点的父节点
  //尚未达到根节点,且所插入数据value大于父节点的关键字值  
  while (__holeIndex > __topIndex && *(__first + __parent) < __value) {
    *(__first + __holeIndex) = *(__first + __parent);//交换当前节点元素与其父节点元素的值
    __holeIndex = __parent;//更新当前节点标号，上溯
    __parent = (__holeIndex - 1) / 2;//更新父节点
  }   //持续达到根节点，或满足heap的性质
  *(__first + __holeIndex) = __value;//插入正确的位置
}

template <class _RandomAccessIterator, class _Distance, class _Tp>
inline void 
__push_heap_aux(_RandomAccessIterator __first,
                _RandomAccessIterator __last, _Distance*, _Tp*)
{
    //__last - __first) - 1表示插入后元素的个数，也是容器的最后一个下标数字
    //新插入的元素必须位于容器的末尾
    __push_heap(__first, _Distance((__last - __first) - 1), _Distance(0), 
              _Tp(*(__last - 1)));
}

//第一个版本push_heap默认是operator<操作
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);
}
//第二个版本push_heap自定义比较操作函数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));
}

//注意: pop_heap()操作, 执行完操作后要自己将容器尾元素弹出
//default (1):    
//            template <class RandomAccessIterator>
//            void pop_heap (RandomAccessIterator first, RandomAccessIterator last);
//custom (2):    
//            template <class RandomAccessIterator, class Compare>
//            void pop_heap (RandomAccessIterator first, RandomAccessIterator last,
//                 Compare comp);
//***********************************************************************
template <class _RandomAccessIterator, class _Distance, class _Tp>
void 
__adjust_heap(_RandomAccessIterator __first, _Distance __holeIndex,
              _Distance __len, _Tp __value)
{
  _Distance __topIndex = __holeIndex;//根节点标号
  _Distance __secondChild = 2 * __holeIndex + 2;//获取子节点
  while (__secondChild < __len) {//若子节点标号比总的标号数小
    if (*(__first + __secondChild) < *(__first + (__secondChild - 1)))
      __secondChild--;//找出堆中最大关键字值的节点
    //若堆中存在比新根节点元素（即原始堆最后节点关键字值）大的节点,则交换位置 
    *(__first + __holeIndex) = *(__first + __secondChild);
    __holeIndex = __secondChild;//更新父节点
    __secondChild = 2 * (__secondChild + 1);//更新子节点
  }
  if (__secondChild == __len) {
    *(__first + __holeIndex) = *(__first + (__secondChild - 1));
    __holeIndex = __secondChild - 1;
  }
  __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*)
{
  *__result = *__first;//把原始堆的根节点元素放在容器的末尾
  //调整剩下的节点元素，使其成为新的heap
  __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);
}


//创建堆
//default(1):    
//            template <class RandomAccessIterator>
//            void make_heap (RandomAccessIterator first, RandomAccessIterator last);
//custom (2):    
//            template <class RandomAccessIterator, class Compare>
//            void make_heap (RandomAccessIterator first, RandomAccessIterator last,Compare 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;
  _Distance __parent = (__len - 2)/2;
    
  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));
}

//排序堆里面的内容
//default(1):    
//            template <class RandomAccessIterator>
//            void sort_heap (RandomAccessIterator first, RandomAccessIterator last);
//custom (2):    
//            template <class RandomAccessIterator, class Compare>
//            void sort_heap (RandomAccessIterator first, RandomAccessIterator last,
//                          Compare comp);
//**************************************************************************
template <class _RandomAccessIterator>
void sort_heap(_RandomAccessIterator __first, _RandomAccessIterator __last)
{
  __STL_REQUIRES(_RandomAccessIterator, _Mutable_RandomAccessIterator);
  __STL_REQUIRES(typename iterator_traits<_RandomAccessIterator>::value_type,
                 _LessThanComparable);
  while (__last - __first > 1)
    pop_heap(__first, __last--);//每次取出根节点元素，直到heap为空
}

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);
}

不过 STL提供了完整的封装操作，可以直接用make_heap来构建堆。 sort_heap来对堆进行排序。 很是方便的。

STL中的优先队列是利用一个大根堆，用vector来模拟完全二叉树的结构。 优先队列包含在queue这个头文件下面。