【数据结构】实现大小堆也叫二叉堆（类似c++中的优先队列）

二叉堆：

是一种特殊的堆，依赖于完成完全二叉树和向量实现的。分为最大堆和最小堆。

最大堆：父节点的键值总是大于或等于任何一个子节点的键值。

最小堆：父节点的键值总是小于或等于任何一个子节点的键值。

存储：二叉树一般用数组来存储表示，在下面的实现中使用了STL中的vector。根节点在数组中的位置是0，第n个位置的左孩子下标为n*2+1，右孩子为2*n+2 ，当前孩子存在的前提是计算后下标要小于数组总个数。而用孩子结点的下标c,可以计算出双亲的下标(c-1)/2。

基本操作：可以进行插入结点，移除最小的结点，和返回最小的结点，返回当前堆中元素个数。

代码：这个是用模板参数实现，传入函数对象生成大小堆，默认小堆：

#ifndef _HEAP_H_#define  _HEAP_H_#include <cassert>#include <vector>#include <iostream>using namespace std;// 仿函数小堆调用 template <class T>class Less{public:bool operator()(const T& left, const T& right){return left <= right;}};// 仿函数大堆调用template <class T>class Greater{public:bool operator()(const T& left, const T& right){return left > right;}}; // 模板参数的大小堆template <class T, class Compare = Less<T>>class Heap{public:Heap(){}Heap(const T arr[] , int size){for (int i=0; i<size; ++i){_heap.push_back(arr[i]);}int last = (size - 2)/2; for (int i=last; last>=0; --last){_AdjustDown(last, size);}}void Insert(const T data){_heap.push_back(data);_AdjustUp(_heap.size());}T& Top(){assert(!_heap.empty());return _heap[0]; }const T& Top()const{assert(!_heap.empty());return _heap[0]; }void Remove(){int size = _heap.size();if (size > 1){std::swap(_heap[0], _heap[size-1]);_heap.pop_back();_AdjustDown(0, _heap.size());}else{_heap.pop_back();}}private:void _AdjustUp(int size){int child = size - 1;int parent = (child-1)/2;while (child != 0){// 孩子小于父亲if (Compare()(_heap[child], _heap[parent])){std::swap(_heap[child], _heap[parent]);child = parent;parent = (child - 1 )/2;}else{break;}}}void _AdjustDown(int root, int size){int child = root*2 + 1;int parent = root;while (child < size){if (child+1 < size && Compare()(_heap[child+1], _heap[child]) ){child += 1;}// 小 less if (Compare()(_heap[child], _heap[parent])){std::swap(_heap[child], _heap[parent]);parent = child;child = child *2 + 1;}else{break;}}}private:vector<T> _heap;};#endif _HEAP_H_

这个是用模板的模板参数实现：

#ifndef _HEAP_H_#define  _HEAP_H_#include <cassert>#include <vector>#include <iostream>using namespace std;// 仿函数小堆调用 template <class T>class Less{public:bool operator()(const T& left, const T& right){return left <= right;}};// 仿函数大堆调用template <class T>class Greater{public:bool operator()(const T& left, const T& right){return left > right;}};// 模板的模板参数 大小堆template<class T, template<class> class Compare = Less>class Heap{public:Heap(){}Heap(const T arr[], int size){for (int i=0; i<size; ++i){_heap.push_back(arr[i]);}int root = (size - 2)/2;for (int i=root; i>=0; --i){_AdjustDown(i, size);}}void Insert(const T& data){_heap.push_back(data);_AdjustUp(_heap.size());}void Remove(){if (!_heap.empty()){if (_heap.size()>1){std::swap(_heap[0], _heap[_heap.size()-1]);_heap.pop_back();_AdjustDown(0, _heap.size());}else{_heap.pop_back();}}}T& Top(){assert(!_heap.empty());return _heap[0]; }const T& Top()const{assert(!_heap.empty());return _heap[0]; }private:void _AdjustUp(int size){int child = size-1;int  parent= (child-1)/2;while (child != 0){if (Compare<T>()(_heap[child], _heap[parent])){std::swap(_heap[child], _heap[parent]);child = parent;parent = (child-1)/2;}else{break;}}}    void _AdjustDown(int root, int size){int parent = root;int child = root*2 + 1;while (child < size){if (child+1 < size && Compare<T>()(_heap[child+1],_heap[child]) ){child  = child+1;}if (Compare<T>()(_heap[child], _heap[parent])){std::swap(_heap[child], _heap[parent]);parent = child;child = child*2 + 1;}else{break;}}}private:vector<T> _heap;};#endif _HEAP_H_