STL源码：heap

        heap不归属STL容器组件，它是priority queue的幕后英雄。而heap的底层可以用array或vector来实现。STL实现了大根堆，使用的是vector作为底部容器。

二叉堆其实是一个以vector表现的完全二叉树。

为什么用二叉大根堆作为优先队列的底层机制？

        答：优先队列允许用户以任何次序将任何元素插入容器，但取出时要从优先权最大的元素开始取。二叉大根堆具有这样的特性，因此作为优先队列的底层机制。

        关于二叉堆实现优先队列的可行性见《二叉堆的插入删除等操作C++实现》

能不能用list作为优先队列底层机制？

        答：list作为优先队列底层机制可以实现元素插入的常数时间，但是要找到list的最值，却要对list做线性扫描。我们可以先对元素排序，这样，找到最值以及元素删除为常数时间，但是元素的插入又是线性时间。

能不能用二叉搜索树作为优先队列底层机制？

          答：用二叉搜索树元素插入和最值取得都可以在O(logn)内完成，但是这样小题大做：第一，二叉搜索树的输入需要足够的随机性；第二，二叉搜索树的实现不容易。

heap源码

STL实现的是大根堆，底层容器为vector，使用迭代器。

之前使用vector作为底层容器，使用下标，自己实现过小根堆的操作堆的插入删除操作，以及堆排序

//stl_heap.h#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////////////////////////////////////////////////////////push_heap()操作前要保证新添加的元素已经加入到容器末尾!!!///////////////////////////////////////////////////////template <class RandomAccessIterator, class Distance, class T>void __push_heap(RandomAccessIterator first, Distance holeIndex,                 Distance topIndex, T value){  // 首先找出待处理元素的父结点  Distance parent = (holeIndex - 1) / 2;  // 判断当前待处理结点是否优先级高于其父结点, 如果是则将其父结点向下移动  // 设置当前结点为父结点位置, 继续, 直到优先级小于父结点或者已经到达heap顶端  while (holeIndex > topIndex && *(first + parent) < value) {  //当尚未到达顶端且父节点小于新值    *(first + holeIndex) = *(first + parent); //令洞值为父值    holeIndex = parent;  //调整洞号，向上提升至父节点    parent = (holeIndex - 1) / 2;  //新洞的父节点  }  // 将找到的合适的位置设置成正确值  *(first + holeIndex) = value;}template <class RandomAccessIterator, class Distance, class T>inline void __push_heap_aux(RandomAccessIterator first,                            RandomAccessIterator last, Distance*, T*){  // 因为first所指的那个元素不是heap的组成元素, 所以计算距离要减去1  __push_heap(first, Distance((last - first) - 1), Distance(0),              T(*(last - 1)));}// 调用此函数前要先把待处理元素追加到容器末尾template <class RandomAccessIterator>inline void push_heap(RandomAccessIterator first, RandomAccessIterator last){  __push_heap_aux(first, last, distance_type(first), value_type(first));}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;  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);}// 这个除了用户自己指定优先级决策判别式外和默认的无区别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));}/////////////////////////////////////////////////////////// 注意: pop_heap()操作, 执行完操作后要自己将容器尾元素弹出//////////////////////////////////////////////////////////// 这里以默认的heap优先级决策来说// STL采用的是先将待pop的元素复制到heap尾部, 然后将整个heap向上调整// 这样就会将最后空出一个hole, 将原来最后的元素在这里进行push()操作// 这就是两个shift_up的过程// 个人感觉使用使用shift_down的算法更高效, 虽然时间复杂度一样, 但是shift_down// 进行操作的元素会更少,// 之所以用shift_up这可能也是STL设计理念的问题吧, 能复用就不写新的^_^////////////////////////////////////////////////////////////////////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;     // 弹出元素的有子孩  // 调整heap元素位置  while (secondChild < len) {    // 选择两个子孩中较大的进行操作, 使用secondChild表示其偏移    if (*(first + secondChild) < *(first + (secondChild - 1)))      secondChild--;    // 将较大元素向上填充, 并将整体偏移向下调整, 继续调整    *(first + holeIndex) = *(first + secondChild);    holeIndex = secondChild;    secondChild = 2 * (secondChild + 1);  }  if (secondChild == len) {    *(first + holeIndex) = *(first + (secondChild - 1));    holeIndex = secondChild - 1;  }  // 这里就是shift_up过程了, 将最初的heap末尾元素向上调整  // 侯捷老师对这里的理解有误, :-), 人非圣贤, 孰能无过, ^_^  __push_heap(first, holeIndex, topIndex, value);}template <class RandomAccessIterator, class T, class Distance>inline void __pop_heap(RandomAccessIterator first, RandomAccessIterator last,                       RandomAccessIterator result, T value, Distance*){  // 将弹出的元素调整到heap末尾, 这个元素需要用户手动弹出  *result = *first;  // 去掉末尾哪个弹出的元素, 调整heap  __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));}template <class RandomAccessIterator>inline void pop_heap(RandomAccessIterator first, RandomAccessIterator last){  __pop_heap_aux(first, last, value_type(first));}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; //洞节点的右孩子节点  while (secondChild < len) {  //比较洞节点左右两孩子，然后以secondChild代表大的子节点    if (comp(*(first + secondChild), *(first + (secondChild - 1))))      secondChild--;//下滤：令较大的孩子值为洞值，令洞号下移到较大的孩子节点    *(first + holeIndex) = *(first + secondChild);     holeIndex = secondChild;     secondChild = 2 * (secondChild + 1); //找到新洞节点的右孩子节点  }  if (secondChild == len) { //没有右孩子，只有左孩子  //下滤：令左孩子为洞值，再令洞下移到左孩子节点    *(first + holeIndex) = *(first + (secondChild - 1));    holeIndex = secondChild - 1;  }   //将欲调整值插入目前的洞内  __push_heap(first, holeIndex, topIndex, value, 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));}template <class RandomAccessIterator, class Compare>inline void pop_heap(RandomAccessIterator first, RandomAccessIterator last,                     Compare comp){    __pop_heap_aux(first, last, value_type(first), comp);}// 建立堆的过程就是一系列插入，即下滤过程template <class RandomAccessIterator, class T, class Distance>void __make_heap(RandomAccessIterator first, RandomAccessIterator last, T*,                 Distance*){  if (last - first < 2) return;  //堆仅含0或1个元素，不必重新排序  Distance len = last - first;  Distance parent = (len - 2)/2;  while (true) {    __adjust_heap(first, parent, len, T(*(first + parent)));    if (parent == 0) return; //走完了根节点，结束    parent--;   }}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;  Distance parent = (len - 2)/2;  while (true) {    __adjust_heap(first, parent, len, T(*(first + parent)), comp);    if (parent == 0) return;    parent--;  }}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));}// 堆排序，保证heap有序，每次将堆的最值放在vector的末尾template <class RandomAccessIterator>void sort_heap(RandomAccessIterator first, RandomAccessIterator last){  while (last - first > 1) pop_heap(first, last--);}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 */