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。
打开ＩＤＥ
我们来创建一个工程
类声明如下
#if !defined(AFX_MINHEAP_H__5F262696_5BC2_4DC3_BD5A_54F6DEAD15DA__INCLUDED_)
#define AFX_MINHEAP_H__5F262696_5BC2_4DC3_BD5A_54F6DEAD15DA__INCLUDED_
#if _MSC_VER > 1000
#pragma once
#endif // _MSC_VER > 1000
#include "stdafx.h"
//最小堆的类定义minheap.h
#define HeapSIZE 10
#define MaxHeapSize 100
class minheap
{private:
ElemType *heapArray;
int maxheapSize;
int heapsize;
public:
//构造一个空堆S
minheap(int);
//堆存在则堆被销毁
void Destroyheap();
//堆存在则清为空堆
void Clearheap();
//堆空则返回true,否则false
bool heapEmpty();
//堆满则返回true,否则false
bool heapFull();
// 堆存在则返回堆的元素个数,即堆的长度
int heapLength();
//堆存在且非空则返回堆的堆顶元素
ElemType GetTop();
// 插入后的堆调整,使之符合最小堆的定义
void FilterUp();
//删除后的堆调整,使之符合最小堆的定义
void FilterDown();
//堆插入
void heapInsert(ElemType item);
//堆删除
ElemType heapDelete();
};
#endif // !defined(AFX_MINHEAP_H__5F262696_5BC2_4DC3_BD5A_54F6DEAD15DA__INCLUDED_)
类实现如下
#include "stdafx.h"
#include "minheap.h"
//最小堆的实现minheap.cpp
#include "minheap.h"
minheap::minheap(int MaxSize)
{if(MaxSize<=0) {
cerr<<"参数MaxSize非法!\n";exit(1);}
heapArray=(ElemType *) new ElemType[MaxSize];
if(!heapArray) exit(-1);
maxheapSize=HeapSIZE;
heapsize=0;
}
void minheap::Destroyheap()
{free(heapArray);}
void minheap::Clearheap()
{heapsize=0;}
bool minheap::heapEmpty()
{ if(heapsize==0) return true;
else return false;
}
bool minheap::heapFull()
{return heapsize==maxheapSize;}
int minheap::heapLength()
{ return heapsize;}
ElemType minheap::GetTop()
{ if(heapsize==0)
{cerr<<"堆已空!\n";exit(1);}
return heapArray[0];
}
void minheap::FilterUp()
{int c,p;
ElemType temp;
c=heapsize-1;
p=(c-1)/2;
temp=heapArray[c];
while(c!=0)
{if(heapArray[p]<=temp) break;
heapArray[c]=heapArray[p];
c=p;
p=(c-1)/2;}
heapArray[c]=temp;
}
void minheap::FilterDown()
{int c,p;
ElemType temp;
p=0;
c=2*p+1;
temp=heapArray[p];
while(c<heapsize)
{if(c+1<heapsize&&heapArray[c+1]<heapArray[c])
c=c+1;
if(temp<=heapArray[c]) break;
heapArray[p]=heapArray[c];
p=c;
c=2*p+1;}
heapArray[p]=temp;
}
void minheap::heapInsert(ElemType item)
{if(heapsize==HeapSIZE)
{cerr<<"堆已满!\n";exit(1);}
heapArray[heapsize]=item;
heapsize++;
FilterUp();
}
ElemType minheap::heapDelete()
{ElemType temp;
if(heapsize==0)
{cerr<<"堆已空!\n";exit(1);}
temp=heapArray[0];
heapArray[0]=heapArray[heapsize-1];
heapsize--;
FilterDown();
return(temp);}
类调用如下
#include "stdafx.h"
#include "minheap.h"
void PrintArray(int a[],int n)
{for(int i=0;i<n;i++)
cout<<setw(3)<<a[i];
cout<<endl;
}
void main()
{cout<<"运行结果:\n";
ElemType b[10];
srand(350);
for(int i=0;i<10;i++)
b[i]=rand()%100;
cout<<"输出数组b:\n";
PrintArray(b,10);
minheap H(10),H1(10);
for(int i=0;i<10;i++)
H.heapInsert(b[i]);
cout<<"输出当前堆H的堆顶元素:\n";
cout<<setw(3)<<H.GetTop()<<endl;
cout<<"输出插入后数组b:\n";
PrintArray(b,10);
cout<<"输出逐个删除的H堆中元素:\n";
while(!H.heapEmpty())
cout<<setw(3)<<H.heapDelete();
cout<<endl;
for(int i=0;i<10;i++)
H1.heapInsert(rand()%100);
cout<<"输出当前堆H1的堆顶元素:\n";
cout<<setw(3)<<H1.GetTop()<<endl;
cout<<"输出逐个删除的H1堆中元素:\n";
while(!H1.heapEmpty())
cout<<setw(3)<<H1.heapDelete();
cout<<endl;
H.Destroyheap();H1.Destroyheap();
getch();}效果如下
代码下载