STL中heap算法（堆算法）



①push_heap算法
以下是push_heap算法的实现细节。该函数接收两个迭代器，用来表现一个heap底部容器（vector）的头尾，而且新元素已经插入究竟部的最尾端。
template <class RandomAccessIterator>
inline void push_heap(RandomAccessIterator first,RandomAccessIterator last)
{
 //注意，此函数被调用时，新元素应已置于底部容器的最尾端
 _push_heap_aux(first,last,distance_type(first),value_type(first)); 
}

template <class RandomAccessIterator,class Distance,class T>
inline void _push_heap_aux(RandomAccessIterator first,RandomAccessIterator last,
Distance*,T*)
{
 //以上系依据heap的结构特性：新值必置于底部容器的最尾端，此即第一个洞号：（last-first）-1
 _push_heap(first,Distance((last-first)-1),Distance(0),T(*(last-1)));
}

template <class RandomAccessIterator,class Distance,class T>
void _push_heap(RandomAccessIterator first,Distance holeIndex,Distance topIndex,T value)
{
 Distance parent = (holeIndex-1)/2;
 while (parent > topIndex && *(first+parent)<value)
 {
  *(first + holeIndex) = *(first + parent);
  holeIndex = parent;
  parent = (holeIndex-1)/2;
 }
 *(first + holeIndex) = value;
}
②pop_heap算法
pop操作取走根节点（事实上是设至底部容器vector的尾端节点）后，为了满足complete binary tree的条件，必须割舍最下层最右边的叶节点，并将其值又一次安插至最大堆。
template <class RandomAccessIterator>
inline void pop_heap(RandomAccessIterator first,RandomAccessIterator last)
{
 _pop_heap_aux(first,last,value_type(first));
}

template <class RandomAccessIterator,class T>
inline void _pop_heap_aux(RandomAccessIterator first,RandomAccessIterator last,T*)
{
 _pop_heap(first,last-1,last-1,T(*(last-1)),distance_type(first));
}

template <class RandomAccessIterator,class T,class Distance>
inline void _pop_heap(RandomAccessIterator first,RandomAccessIterator last,RandomAccessIterator result,
T value,Distance*)
{
 *result = *first;
 _adjust_heap(first,Distance(0),Distance(last-first),value);
 //以上欲又一次调整heap，洞号为0（亦即树根处），欲调整值为value（原尾值）
}

template <class RandomAccessIterator,class Distance,class T>
void _adjust_heap(RandomAccessIterator first,Distance holeIndex,Distance len,T value)
{
 Distance topIndex = holeIndex;
 Distance secondChild = holeIndex*2+2;
 while (secondChild < len)
 {
  if(*(first+secondChild) < *(first+secondChild-1))
   secondChild--;
  *(first+holeIndex) = *(first+secondChild);
  holeIndex = secondChild;
  secondChild = holeIndex*2+2;
 }
 if (secondChild == len)
 {
  *(first+holeIndex) = *(first+secondChild-1);
  holeIndex = secondChild-1;
 }
 _push_heap(first,holeIndex,topIndex,value);
}
注意:pop_heap之后，最大元素仅仅是被置于底部容器的最尾端，尚未被取走。假设要取其值，可使用底部容器（vector）所提供的back()操作函数。假设要移除它，可使用底部容器（vector）所提供的pop_back()操作函数。
③sort_heap算法
既然每次pop_heap可获得heap中键值最大的元素，假设持续对整个heap做pop_heap操作，每次将操作范围从后向前缩减一个元素（由于pop_heap会把键值最大的元素放在底部容器的最尾端），当整个程序运行完成时，我们便有了一个递增序列。
template<class RandomAccessIterator>
void sort_heap(RandomAccessIterator first,RandomAccessIterator last)
{
 while(last - first > 1)
  pop_heap(first,last--);
}
④make_heap算法
这个算法用来将一段现有的数据转化为一个heap。
template <class RandomAccessIterator>
inline void make_heap(RandomAccessIterator first,RandomAccessIterator last)
{
 _make_heap(first,last,value_type(first),distance_type(first));
}

template <class RandomAccessIterator,class T,class Distance>
void _make_heap(RandomAccessIterator first,RandomAccessIterator last,T*,Distance*)
{
 if (last - first < 2) return;
 Distance len  = last-first;
 Distance parent = (len-1)/2;

 while (true)
 {
  _adjust_heap(first,parent,len,T(*(first+parent)));
  if (parent == 0)
   return;
  parent--;
 }
}