（日志，《算法导论》.6.4）优先队列，堆，代码

堆形式：MAX-HEADIFY

/*********************************************************************************** 程序名称  :priorityqueue_test 功能描述  : MAXpq,堆 , 优先队列，修改历史      :  1.日    期   : 2015/10/6 作    者   : gqkly 内容       :   ************************************************************************************/  #include <iostream>  #include <string>  #include <time.h>  #include <stdio.h>  using namespace std;  typedef int ElemType;  #define InitHeap(heap,len)  { memset(&heap,0,sizeof(heap));heap.length=len;}  #define InitHeapA(heap) {heap.A=(ElemType*)malloc(heap.length*sizeof(ElemType));for(int i=0;i<heap.length;i++)heap.A[i]=rand()%50;}  #define Right_Of_I(i) (2*i+1)  #define Left_Of_I(i) (2*i)  #define Right_Parent(i) ((i-1)>>2)#define Left_Parent(i) (i>>2)#define swap1(a,b) {a=a+b;b=a-b;a=a-b;}  #define swap2(a,b) {a=a+b-(b=a);}  #define swap3(a,b) {b=a+(a=b)*0;}  #define swap4(a,b) {a=a^b;b=a^b;a=a^b;}  #define N 10  typedef struct HEAP_TYPE  {  ElemType *A;  int length;  }HEAP,*HEAP_PTR;//最大优先队列相关函数ElemType Heap_Get_Maxnum(HEAP heap);//返回最大元素，即数学位置1的元素ElemType Heap_Extract_Max(HEAP *heap);//返回最大元素，即数学位置1的元素，并删除它，之后仍然要维持性质void Heap_Increase_Key(HEAP *heap,int i,ElemType key);//增大数学位置i的元素的keyvoid Max_Heap_Insert(HEAP *heap,ElemType key);//插入一个新的元素//之下是维护堆性质的函数void Max_Heapify(HEAP* heap,int i);//中间层和第三层  void Build_Max_Heap(HEAP* heap);//中间层  void Heap_Sort(HEAP* heap);//第一层函数  void Print_Heap(HEAP heap,char *string);  int main(){HEAP heap;InitHeap(heap,N);InitHeapA(heap);//随机初始化堆内容Print_Heap(heap,"Init heap:");Build_Max_Heap(&heap);Print_Heap(heap,"Builded heap:");int max_num=Heap_Get_Maxnum(heap);cout<<"\nGet_Maxnum:"<<max_num<<endl;Print_Heap(heap,"Heap_Get_Maxnum:");max_num=Heap_Extract_Max(&heap);cout<<"\nGet_Maxnum:"<<max_num<<endl;Print_Heap(heap,"Heap_Extract_Max:");Heap_Increase_Key(&heap,heap.length-3,34);Print_Heap(heap,"Heap_Increase_Key:(length-3),34");Max_Heap_Insert(&heap,35);Print_Heap(heap,"Max_Heap_Insert:(35)");getchar();return 0;}ElemType Heap_Get_Maxnum(HEAP heap){if (heap.length<0){cout<<"\nerror: heap underflow"<<endl;return -65532;}return heap.A[0];//数学位置1}ElemType Heap_Extract_Max(HEAP *heap){if ((*heap).length<0){cout<<"\nerror: heap underflow"<<endl;return -65532;}int max_num=(*heap).A[0];(*heap).A[0]=(*heap).A[(*heap).length-1];//把最后一个元素移到首位以维护堆性质(*heap).length--;Max_Heapify(heap,1);//传入的是数学位置，内部会修正为数组下标return max_num;}void Heap_Increase_Key(HEAP *heap,int i,ElemType key){int parent;int pos=i-1;if (key<=(*heap).A[pos]){cout<<"\nerror:new key is smaller";return ;}(*heap).A[pos]=key;if (i/2==0){parent=Left_Parent(i)-1;}elseparent=Right_Parent(i)-1;if (parent<0){cout<<"\nerror: it has been the max num "<<endl;return ;}while(pos>0&& ( ((*heap).A[parent]) < ( (*heap).A[pos]) ) ){swap1( (*heap).A[pos],(*heap).A[parent]);pos=parent;}}void Max_Heap_Insert(HEAP *heap,ElemType key){(*heap).length++;ElemType* tmp =(*heap).A+(*heap).length;if ((*heap).length>N){tmp=(ElemType*)malloc(sizeof(ElemType));}(*heap).A[(*heap).length-1]=-65532;Heap_Increase_Key(heap,(*heap).length,key);}//一下是维护堆性质的函数void Max_Heapify(HEAP* heap,int i)//这个参数i为数学位置，函数内部转化为数组坐标  {  int largest;  int l=Left_Of_I(i);  int r=Right_Of_I(i);  if ( (l<=(*heap).length) && ((*heap).A[l-1])>((*heap).A[i-1]) )  {  largest=l;  }  else   largest=i;  if ( (r<=(*heap).length) && ((*heap).A[r-1])>((*heap).A[largest-1]) )  {  largest=r;  }  if (largest!=i)  {  swap1( (*heap).A[i-1],(*heap).A[largest-1] );  Max_Heapify(heap,largest);  }  }  void Build_Max_Heap(HEAP* heap)  {  int len=(*heap).length;  for (int i=(len/2);i>0;i--)  {  Max_Heapify(heap,i);  }  }  void Heap_Sort(HEAP* heap)  {  int tmp_size=(*heap).length;  Build_Max_Heap(heap);  for (int i=(*heap).length-1;i>0;i--)//长度的大小和坐标不一样  {  swap1((*heap).A[0],(*heap).A[i]);  (*heap).length--;//此处通过减小堆大小来为排序服务，所以需要在之后还原  Max_Heapify(heap,1);//1是数学位置--第一个元素  }  (*heap).length=tmp_size;//还原堆大小  }  void Print_Heap(HEAP heap,char *string)  {  int tmp=0;  int t=2;  cout<<"***********************************************"<<endl;  cout<<string<<endl;  for (int i=0;i<heap.length;i++)  {  tmp=i+1;  if ((i+1)==t)  {  t*=2;  tmp=i+1;  cout<<endl;  }  cout<<heap.A[i]<<' ';  }  cout<<endl;  }  

运行结果：