Heap堆是常用的数据结构，Heap中也可以存放元素。但是STL中并没有提供Heap容器，只是提供了关于Heap操作的算法。只要支持RandomAccessIterator的容器都可以作为Heap容器。
Heap分为max heap和min heap，max heap中每次取出的结点时heap结构中值最大的结点，min heap中每次取出的结点时heap结构中值最小的结点。
在实际应用中，经常用vector作为heap容器，heap经常作为priority queue。对于二叉堆，这里有描述http://blog.csdn.net/kangroger/article/details/8718732
当向heap中插入元素时，插入到末尾，“向上维护”即可：指的是把插入结点与其父结点比较，如果不符合堆得要求则交换，再向上维护其父结点……
当在heap取出元素时，把末尾元素放到Heap头，"向下维护“即可：指的是父结点与孩子结点比较，如果不满足要求，与较大（较小）一个交换，再维护交换的孩子结点……
Heap不允许遍历其结点，所以Heap没有迭代器。
G++ 2.91.57，cygnus\cygwin-b20\include\g++\stl_heap.h 完整列表
/*
*
* Copyright (c) 1994
* Hewlett-Packard Company
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* Permission to use, copy, modify, distribute and sell this software
* and its documentation for any purpose is hereby granted without fee,
* provided that the above copyright notice appear in all copies and
* that both that copyright notice and this permission notice appear
* in supporting documentation. Hewlett-Packard Company makes no
* representations about the suitability of this software for any
* purpose. It is provided "as is" without express or implied warranty.
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* Copyright (c) 1997
* Silicon Graphics Computer Systems, Inc.
*
* Permission to use, copy, modify, distribute and sell this software
* and its documentation for any purpose is hereby granted without fee,
* provided that the above copyright notice appear in all copies and
* that both that copyright notice and this permission notice appear
* in supporting documentation. Silicon Graphics makes no
* representations about the suitability of this software for any
* purpose. It is provided "as is" without express or implied warranty.
*/
/* NOTE: This is an internal header file, included by other STL headers.
* You should not attempt to use it directly.
*/
#ifndef __SGI_STL_INTERNAL_HEAP_H
#define __SGI_STL_INTERNAL_HEAP_H
__STL_BEGIN_NAMESPACE
#if defined(__sgi) && !defined(__GNUC__) && (_MIPS_SIM != _MIPS_SIM_ABI32)
#pragma set woff 1209
#endif
//向上维护
template <class RandomAccessIterator, class Distance, class T>
void __push_heap(RandomAccessIterator first, Distance holeIndex,
Distance topIndex, T value) {
Distance parent = (holeIndex - 1) / 2; // 找出父结点
//父结点不是heap顶 且 父节点的值小于孩子结点（小于号<可以看出STL维护的是max heap）
while (holeIndex > topIndex && *(first + parent) < value) {
*(first + holeIndex) = *(first + parent); // 父结点下调
holeIndex = parent; // 维护父结点
parent = (holeIndex - 1) / 2;
}
//已达到heap顶或者满足heap性质后，给新插入元素找到合适位置
*(first + holeIndex) = value;
}
template <class RandomAccessIterator, class Distance, class T>
inline void __push_heap_aux(RandomAccessIterator first,
RandomAccessIterator last, Distance*, T*) {
__push_heap(first, Distance((last - first) - 1), Distance(0),
T(*(last - 1)));
}
//往heap添加元素。注意：此函数调用时，元素已经添加到末尾了，且迭代器已经加1了
template <class RandomAccessIterator>
inline void push_heap(RandomAccessIterator first, RandomAccessIterator last) {
// 注意，此函式被呼叫時，新元素應已置於底層容器的最尾端。
__push_heap_aux(first, last, distance_type(first), value_type(first));
}
//向上维护，允许用自己定义的comp函数，这是未必是max heap了
template <class RandomAccessIterator, class Distance, class T, class Compare>
void __push_heap(RandomAccessIterator first, Distance holeIndex,
Distance topIndex, T value, Compare comp) {
Distance parent = (holeIndex - 1) / 2;//找到父结点的位置
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 T>
inline void __push_heap_aux(RandomAccessIterator first,
RandomAccessIterator last, Compare comp,
Distance*, T*) {
__push_heap(first, Distance((last - first) - 1), Distance(0),
T(*(last - 1)), comp);
}
template <class RandomAccessIterator, class Compare>
inline void push_heap(RandomAccessIterator first, RandomAccessIterator last,
Compare comp) {
__push_heap_aux(first, last, comp, distance_type(first), value_type(first));
}
// 以下這個 __adjust_heap() 不允許指定「大小比較標準」
//向下维护heap
template <class RandomAccessIterator, class Distance, class T>
void __adjust_heap(RandomAccessIterator first, Distance holeIndex,
Distance len, T value) {
Distance topIndex = holeIndex;
Distance secondChild = 2 * holeIndex + 2; // 找到右孩子的位置
while (secondChild < len) {//还没到达末尾
// 比较左右孩子大小， secondChild 代表其中较大者
if (*(first + secondChild) < *(first + (secondChild - 1)))
secondChild--;
// 较大的孩子放到父结点位置
*(first + holeIndex) = *(first + secondChild);
holeIndex = secondChild;
// 维护较大的孩子
secondChild = 2 * (secondChild + 1);
}
// 没有右孩子，只有左孩子，只需维护一次，因为左孩子是heap的最后一个元素
if (secondChild == len) {
*(first + holeIndex) = *(first + (secondChild - 1));
holeIndex = secondChild - 1;
}
//把调整值放到合适位置，等价于*(first + holeIndex) = value;
__push_heap(first, holeIndex, topIndex, value);
}
//向下维护heap
template <class RandomAccessIterator, class T, class Distance>
inline void __pop_heap(RandomAccessIterator first, RandomAccessIterator last,
RandomAccessIterator result, T value, Distance*) {
*result = *first; // 把堆顶的值放到堆尾，堆尾的值保存在参数value中
__adjust_heap(first, Distance(0), Distance(last - first), value);
}
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));
/*
根据implicit representation heap的次序性，pop后的结果是容器的第一个元素。
把最后一个元素放到到容器头，因此维护时维护区间是[first last-1)。
*/
}
//取出heap顶元素，按照max heap属性来维护heap
template <class RandomAccessIterator>
inline void pop_heap(RandomAccessIterator first, RandomAccessIterator last) {
__pop_heap_aux(first, last, value_type(first));
}
//向下维护heap，允许执行比较函数comp
template <class RandomAccessIterator, class Distance, class T, class Compare>
void __adjust_heap(RandomAccessIterator first, Distance holeIndex,
Distance len, T 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);
}
// 取出堆顶元素，允许定义比较函数comp
template <class RandomAccessIterator, class T, class Compare, class Distance>
inline void __pop_heap(RandomAccessIterator first, RandomAccessIterator last,
RandomAccessIterator result, T value, Compare comp,
Distance*) {
*result = *first;
__adjust_heap(first, Distance(0), Distance(last - first), value, comp);
}
template <class RandomAccessIterator, class T, class Compare>
inline void __pop_heap_aux(RandomAccessIterator first,
RandomAccessIterator last, T*, Compare comp) {
__pop_heap(first, last - 1, last - 1, T(*(last - 1)), comp,
distance_type(first));
}
//取出heap顶元素，根据comp调整heap
template <class RandomAccessIterator, class Compare>
inline void pop_heap(RandomAccessIterator first, RandomAccessIterator last,
Compare comp) {
__pop_heap_aux(first, last, value_type(first), comp);
}
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 - 2)/2;
//从heap的中间开始向下维护。一次维护[parent, parent-1,……,0]
while (true) {
__adjust_heap(first, parent, len, T(*(first + parent)));
if (parent == 0) return;
parent--;
}
}
// 将 [first,last) 排列成一个 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 Compare, class T, class Distance>
void __make_heap(RandomAccessIterator first, RandomAccessIterator last,
Compare comp, T*, Distance*) {
if (last - first < 2) return;
Distance len = last - first;
//从heap的中间开始向下维护。一次维护[parent, parent-1,……,0]
Distance parent = (len - 2)/2;
while (true) {
__adjust_heap(first, parent, len, T(*(first + parent)), comp);
if (parent == 0) return;
parent--;
}
}
// 将 [first,last) 排列成一个 heap。允许执行大小比较函数
template <class RandomAccessIterator, class Compare>
inline void make_heap(RandomAccessIterator first, RandomAccessIterator last,
Compare comp) {
__make_heap(first, last, comp, value_type(first), distance_type(first));
}
// 排序（升序）两个迭代器之间的元素，这两个迭代器之间的元素已经满足heap性质了
template <class RandomAccessIterator>
void sort_heap(RandomAccessIterator first, RandomAccessIterator last) {
/*
pop_heap()功能是删除heap顶元素，把heap大小减小1，heap顶元素放到末尾。
由此可以看出，sort的结果是升序。
*/
while (last - first > 1)
pop_heap(first, last--); // 每執行 pop_heap() 一次，操作範圍即退縮一格。
}
// 排序（升序）两个迭代器之间的元素，这两个迭代器之间的元素已经满足heap性质了。
//允许指定比较函数comp
template <class RandomAccessIterator, class Compare>
void sort_heap(RandomAccessIterator first, RandomAccessIterator last,
Compare comp) {
while (last - first > 1)
pop_heap(first, last--, comp);
}
#if defined(__sgi) && !defined(__GNUC__) && (_MIPS_SIM != _MIPS_SIM_ABI32)
#pragma reset woff 1209
#endif
__STL_END_NAMESPACE
#endif /* __SGI_STL_INTERNAL_HEAP_H */
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// mode:C++
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