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--;

 }

}