最大堆

//最大堆
//用完全二叉树来存储堆，因为是完全二叉树，所以用顺序表比较方便
#include<stdio.h>
#include<stdlib.h>
#define Maxdata 10000
typedef int Elemtype;
//用顺序表来存储
typedef struct HeadStuct{
Elemtype *data;
int Size;
int Capacity;
}*MaxHeap;
//创建堆
MaxHeap Creat(int MaxSize)
{
MaxHeap H=(struct HeadStuct *)malloc(sizeof(struct HeadStuct));
H->data=(Elemtype *)malloc((MaxSize+1)*sizeof(Elemtype));
H->Size=0;
H->Capacity=MaxSize;
H->data[0]=Maxdata;//定义哨兵，大于堆中所有元素，那么插入时少一个判断条件，加快效率
return H;
}
//判断数组是否满了
int isFull(MaxHeap H)
{
return H->Size==H->Capacity;
}
//插入
void Insert(Elemtype x,MaxHeap H)
{
int i;
if(isFull(H))
{
printf("This heap is ful\n");
return ;
}
i=++H->Size;
while(x>H->data[i/2])//因为有一个哨兵，输入的值都小于哨兵，所以不用判断i>1
{
H->data[i]=H->data[i/2];
i/=2;
}
H->data[i]=x;
}
//判断是否为空
int isEmpty(MaxHeap H)
{
return H->Size==0;
}
//删除最大元素
Elemtype DeleteMax(MaxHeap H)
{
Elemtype temp,Maxitem;
int parent,child;
if(isFull(H))
{
printf("This heap is empty\n");
return 0;
}
Maxitem=H->data[1];
temp=H->data[H->Size--];
for(parent=1;parent*2<=H->Size;parent=child)
{
child=parent*2;
if(parent!=H->Size&&(H->data[child]<H->data[child+1]))//parent!=H->Size的原因是：这样做H结点才有右子树，才有后面的条件比较的必要
child++;
if(temp>=H->data[child])
break;
else
H->data[parent]=H->data[child];
parent=child;
}
H->data[parent]=temp;
return Maxitem;
}
//调整交换
void swap(int i,int max,MaxHeap H)
{
Elemtype t=H->data[i];
H->data[i]=H->data[max];
H->data[max]=t;
}
//调整
void HeapAdjust(MaxHeap H,int i)
{
int lchild=i*2;
int rchild=i*2+1;
int max=i;
if(i<=H->Size/2)
{
if(lchild<=H->Size&&H->data[lchild]>H->data[max])
max=lchild;
if(rchild<=H->Size&&H->data[rchild]>H->data[max])
max=rchild;
if(max!=i){
swap(i,max,H);
HeapAdjust(H,max);
}
}
}
int main()
{
MaxHeap H;
int MaxSize;
scanf("%d",&MaxSize);
//    int item;
int cnt=1;
H=Creat(MaxSize);
//    while(scanf("%d",&item)&&item)
//        Insert(item,H);
while(scanf("%d",&H->data[cnt])&&H->data[cnt]){cnt++;H->Size++;}
for(int i=H->Size/2;i>=1;i--)
HeapAdjust(H,i);
for(int i=1;i<=H->Size;i++)
printf("%3d",H->data[i]);
printf("\n");
DeleteMax(H);
for(int i=1;i<=H->Size;i++)
printf("%3d",H->data[i]);
printf("\n");
return 0;
}