STL之堆和优先队列
Posted randyniu
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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。
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