堆的操作实现—大根堆

// 堆的操作实现.cpp : 定义控制台应用程序的入口点。
//
#include "stdafx.h"
#include<iostream>
#include<stdio.h>
#include<malloc.h>
#define MAXDATA 1000
#define Error -1
using namespace std;
typedef int ElementType;
typedef struct HNode *Heap;
struct HNode
{
ElementType *Data;
int Size;
int Capactity;
};
typedef Heap MaxHeap;
typedef Heap MinHeap;

MaxHeap CreateHeap(int MaxSize)
{//创建容量为MaxSize的空的最大堆
MaxHeap H = (MaxHeap)malloc(sizeof(struct HNode));
H->Data = (ElementType *)malloc((MaxSize + 1)*sizeof(ElementType));
H->Size = 0;
H->Capactity = MaxSize;
H->Data[0] = MAXDATA;
return H;
}
bool IsFull(MaxHeap H)
{
return (H->Size == H ->Capactity);
}
bool IsEmpty(MaxHeap H)
{
return (H->Size == 0);
}
void Insert(MaxHeap H, ElementType X)
{// 将元素X插入最大堆H，其中H->Data[0]已经定义为哨兵
int i;
if (IsFull(H))
{
cout << "最大堆已满！" << endl;
exit(1);
}
i = ++H->Size;
H->Data[i] = X;
for (; H->Data[i / 2] < H->Data[i]; i / 2)
{
int Temp = H->Data[i];
H->Data[i] = H->Data[i / 2];
H->Data[i / 2] =Temp;
}

}
//堆实际上是完全二叉树
ElementType DeleteMax(MaxHeap H)
{// 从最大堆H中取出键值为最大的元素，并删除一个结点
int Parent, Child;
ElementType MaxItem, X;
if (IsEmpty(H))
{
cout << "最大堆已空！" << endl;
return Error;
}
MaxItem = H->Data[1];
X = H->Data[H->Size--];
// 用最大堆中最后一个元素从根结点开始向上过滤下层结点
for (Parent = 1; Parent * 2<H->Size; Parent = Child)
{//判断是否有左孩子
Child = Parent * 2;
if ((Child != H->Size) && (H->Data[Child]<H->Data[Child + 1]))//判断是否有右孩子
Child++;//Child始终指向左右孩子中的最大值
if (X >= H->Data[Child])  break;
else
H->Data[Parent] = H->Data[Child];
}
H->Data[Parent] = X;
return MaxItem;
}

//建造一个最大堆
void PercDown(MaxHeap H, int p)
{// 下滤：将H中以H->Data[p]为根的子堆调整为最大堆
int Parent, Child;
ElementType X;
X = H->Data[p];
// 用最大堆中最后一个元素从根结点开始向上过滤下层结点
for (Parent = p; Parent * 2<H->Size; Parent = Child)
{//判断是否有左孩子
Child = Parent * 2;
if ((Child != H->Size) && (H->Data[Child]<H->Data[Child + 1]))//判断是否有右孩子
Child++;//Child始终指向左右孩子中的最大值
if (X >= H->Data[Child])  break;
else
H->Data[Parent] = H->Data[Child];
}
H->Data[Parent] = X;
}
void BuildHeap(MaxHeap H)
{
int i;
//从最后一个结点的父节点开始，到根结点1
for (i = H->Size / 2; i>0; i--)
PercDown(H, i);
}
void PrintHeap(MaxHeap H)
{
for (int i = 1; i < H->Size+1; i++)
cout << H->Data[i] << " ";
cout << endl;
}

int _tmain(int argc, _TCHAR* argv[])
{
MaxHeap  MHeap;
int MaxSize;
int Size;
cout << "请输入堆中允许存放最多元素个数：";
cin >> MaxSize;
MHeap = CreateHeap(MaxSize);
cout << "请输入堆中元素个数：";
cin >> Size;
for (int i =1; i < Size+1; i++)
{
cin >> MHeap->Data[i];
MHeap->Size++;
}
BuildHeap(MHeap);
cout << "调整好的大根堆：" << endl;
PrintHeap(MHeap);
int Data;
cout << "请输入要插入的元素：";
cin >> Data;
Insert(MHeap, Data);
cout << "插入后调整好的大根堆：" << endl;
PrintHeap(MHeap);
int Max = DeleteMax(MHeap);
cout << "该大根堆的最大值是：" <<Max<< endl;
cout << "删除最大值后调整好的大根堆：" << endl;
PrintHeap(MHeap);
return 0;
}