C++实现堆、最大堆、最小堆 -- 堆排序插入删除操作

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堆是一种经过排序的完全二叉树，其中任一非终端节点的数据值均不大于（或不小于）其左孩子和右孩子节点的值。

最大堆和最小堆是二叉堆的两种形式。

最大堆：根结点的键值是所有堆结点键值中最大者。

最小堆：根结点的键值是所有堆结点键值中最小者。

而最大-最小堆集结了最大堆和最小堆的优点，这也是其名字的由来。

最大-最小堆是最大层和最小层交替出现的二叉树，即最大层结点的儿子属于最小层，最小层结点的儿子属于最大层。

以最大（小）层结点为根结点的子树保有最大（小）堆性质：根结点的键值为该子树结点键值中最大（小）项。

一：堆

我们构建一个堆类，用最大堆和最小堆来继承他。

#ifndef _HEAP_H#define _HEAP_H#include <iostream>using namespace std;enum{DEFAULT_SIZE = 10};template <typename T>class Heap{public:Heap() = default;virtual ~Heap() = default;public: virtual void show_heap()const = 0;virtual bool insert_heap(const T&) = 0;virtual bool remove_heap(T &) = 0;};//public interface#endif   /*Heap.h*/

二：最大堆

下面是最大堆的实现：

#ifndef _MAXHEAP_H#define _MAXHEAP_H#include <iostream>#include "Heap.h"template <typename T>class MaxHeap : public Heap<T>{public:MaxHeap(int);MaxHeap(const T [], const int);~MaxHeap();public:bool insert_heap(const T&);bool remove_heap(T &);void show_heap()const;protected:void sift_down(int, int);void sift_up(int);private:T *heap;int size;int capacity;};//public interfacetemplate <typename T>MaxHeap<T>::MaxHeap(int sz = DEFAULT_SIZE){capacity = sz > DEFAULT_SIZE ? sz : DEFAULT_SIZE;heap = new T[capacity];assert(heap != NULL);size = 0;}template <typename T>MaxHeap<T>::MaxHeap(const T arr[], const int arrSize){capacity = arrSize > DEFAULT_SIZE ? arrSize : DEFAULT_SIZE;heap = new T[capacity];assert(heap != NULL);size = arrSize;for(int i=0; i<size; ++i)heap[i] = arr[i];int curPos = size/2 - 1;while(curPos >= 0){sift_down(curPos, size-1);--curPos;}}template <typename T>MaxHeap<T>::~MaxHeap(){delete []heap;heap = NULL;capacity = size = 0;}template <typename T>bool MaxHeap<T>::insert_heap(const T& val){if(size >= capacity)return false;heap[size] = val;sift_up(size);++size;return true;}template <typename T>bool MaxHeap<T>::remove_heap(T &val){if(size <= 0)return false;val = heap[0];heap[0] = heap[size-1];--size;sift_down(0, size-1);return true;}template <typename T>void MaxHeap<T>::show_heap()const{for(int i=0; i<size; ++i)std::cout << heap[i] << " ";std::cout << std::endl;}//protected interfacetemplate <typename T>void MaxHeap<T>::sift_down(int start, int end){int i = start;int j = i*2 + 1;T tmp = heap[i];while(j <= end){if(j+1 <= end && heap[j] < heap[j+1])++j;if(tmp < heap[j])heap[i] = heap[j];elsebreak;i = j;j = j*2 + 1;}heap[i] = tmp;}template <typename T>void MaxHeap<T>::sift_up(int start){int j = start;int i = (start-1) / 2;T tmp = heap[j];while(j > 0){if(tmp < heap[i])break;elseheap[j] = heap[i];j = i;i = (i-1) / 2;}heap[j] = tmp;}#endif   /*MaxHeap.h*/

三：最小堆

下面是最小堆的实现：

#ifndef _MINHEAP_H#define _MINHEAP_H#include <assert.h>#include "Heap.h"template <typename T>class MinHeap : public Heap<T>{public:MinHeap(int);MinHeap(const T [], const int );~MinHeap();public:bool insert_heap(const T&);bool remove_heap(T &);void show_heap()const;protected:void sift_down(int, int);void sift_up(int);private:T* heap;int size;int capacity;};//interfacetemplate <typename T>MinHeap<T>::MinHeap(int sz = DEFAULT_SIZE){capacity = sz > DEFAULT_SIZE ? sz : DEFAULT_SIZE;heap = new T[capacity];assert(heap != NULL);size = 0;}template <typename T>MinHeap<T>::MinHeap(const T arr[], const int arrSize){capacity = arrSize > DEFAULT_SIZE ? arrSize : DEFAULT_SIZE;heap = new T[capacity];assert(heap != NULL);size = arrSize;for(int i=0; i<arrSize; ++i)heap[i] = arr[i];int curPos = arrSize/2 - 1;while(curPos >= 0){sift_down(curPos, arrSize-1);--curPos;}}template <typename T>MinHeap<T>::~MinHeap(){delete []heap;heap = NULL;capacity = size = 0;}template <typename T>bool MinHeap<T>::insert_heap(const T& val){if(size >= capacity)return false;heap[size] = val;sift_up(size);++size;return true;}template <typename T>bool MinHeap<T>::remove_heap(T& val){if(size <= 0)return false;val = heap[0];heap[0] = heap[size-1];--size;sift_down(0, size-1);return true;}template <typename T>void MinHeap<T>::show_heap()const{for(int i=0; i<size; ++i)std::cout << heap[i] << " ";std::cout << std::endl;}//protected interfacetemplate <typename T>void MinHeap<T>::sift_down(int start, int end){int i = start;int j = start*2 + 1;T tmp = heap[i];while(j <= end){if(j+1 < end && heap[j] > heap[j+1])++j;if(tmp < heap[j])break;elseheap[i] = heap[j];i = j;j = j*2 + 1;}heap[i] = tmp;}template <typename T>void MinHeap<T>::sift_up(int start){int j = start;int i = (start-1) / 2;T tmp = heap[j];while(j > 0){if(tmp > heap[i])break;elseheap[j] = heap[i];j = i;i = (i-1) / 2;}heap[j] = tmp;}#endif

四：测试如下：

#include "MinHeap.h"#include "MaxHeap.h"#include <iostream>using namespace std;int main(){int array[] = {23, 9, 34, 2, 56, 89, 35, 54};cout << "***************************MinHeap***************************" << endl;MinHeap<int> min_heap(array, sizeof(array)/sizeof(int));min_heap.show_heap();min_heap.insert_heap(1);min_heap.show_heap();for(int i=0; i<9; ++i){int val;min_heap.remove_heap(val);cout << val << " ";}cout << endl;MaxHeap<int> max_heap(array, sizeof(array)/sizeof(int));cout << "***************************MaxHeap**************************" << endl; max_heap.show_heap();max_heap.insert_heap(99);max_heap.show_heap();for(int i=0; i<9; ++i){int val;max_heap.remove_heap(val);cout << val << " ";}cout << endl;return 0;}

结果如下：

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