算法导论 第六章：优先级队列

        虽然堆排序的时间复杂度为O(nlgn),但在实际中，快速排序(下一章将介绍)往往要优于堆排序。尽管如此，堆数据结构在其他方面有着很大的用处，如用于优先级队列的实现。因为堆可让优先级队列的所有操作的时间复杂度为O(lgn)。最大优先级队列常用于共享主机上的作业调度，最小优先级队列常用于事件驱动的模拟中。

以最大优先级队列为例，其支持的操作如下:

1)INSERT(S,x): 向集合中插入元素x

2)MAXIMUM(S): 返回集合S的最大值

3)EXTRACT-MAX(S):删除集合S的最大值

4)INCREASE-KEY(S,x,k):将集合S中的元素x的值增加为k

最大优先级队列实现的完整代码如下：

#include<iostream>#include<cstdlib>#include<climits>#define PARENT(i) (i/2)#define LEFT(i)   (2*i)#define RIGHT(i)  (2*i+1)using namespace std;void Print(int *a){int n=a[0];for(int i=1;i<=n;i++)cout<<a[i]<<"   ";cout<<endl;}int *Transform(int *a,int n){  int * A=new int[n+1];   A[0]=n;   for(int i=0;i<n;i++)   A[i+1]=a[i];   return A;}void swap(int &a,int &b){int temp;temp=a;a=b;b=temp;}void Max_Heapify(int *A,int i){//adjust the heap to maintain the heap propertyint heap_size=A[0];int l=LEFT(i) ;   //index of i's left childint r=RIGHT(i);int largest;     //At each step,the largest of the element A[i],A[LEFT(i)] //A[RIGHT(i)] is determined,and its index is stored in largest. if(l<=heap_size && A[l]>A[i])largest= l;elselargest = i;if(r<=heap_size && A[r]>A[largest])largest = r;if(largest!=i)     //the subtree rooted at i violate the max-heap property{ swap(A[i],A[largest]);Max_Heapify(A,largest);  //after exchanging ,the subtree rooted at largest might violate the max-heap property }}void Build_MaxHeap(int *A){//Transform array A into max-heap A,where A[0]=heap-sizeint A_length=A[0];for(int i=A_length/2;i>=1;i--)Max_Heapify(A,i);}int GetHeapMaximum(int *A){//return the elements of S with the largest keyBuild_MaxHeap(A);return A[1];}int Heap_ExtractMax(int *A){int max;int heap_size;heap_size=A[0];if(heap_size<1){ cout<<"heap underflow"<<endl;return -1;}Build_MaxHeap(A);max=A[1];A[1]=A[heap_size];heap_size--;A[0]=heap_size;Max_Heapify(A,1);return max;}void Heap_IncreaseKey(int *A,int i,int key){Build_MaxHeap(A);   if(key<A[i]){cout<<"new key is smaller than the current key."<<endl;return;}A[i]=key;while(i>1 && A[PARENT(i)]<A[i]) {swap(A[PARENT(i)],A[i]);i=PARENT(i); }}void Heap_InsertKey(int *A,int key){int heap_size=A[0];heap_size=heap_size+1;A[0]=heap_size;A[heap_size]=INT_MIN;Heap_IncreaseKey(A,heap_size,key);}int main(){int a[]={4,1,3,2,16,9,10,14,8,7};int n=sizeof(a)/sizeof(int);int *A=new int[n+1];cout<<"---------------Init the set--------------------"<<endl;cout<<"After initing,S[1..n] is:"<<endl;A=Transform(a,n);   //Transform a[0...n-1] into a[1...n];a[0]=a.lengthPrint(A);cout<<"---------------Excute MAXIMUM------------------"<<endl;int hMaxN;hMaxN=GetHeapMaximum(A);cout<<"The largest key is:"<<hMaxN<<endl;cout<<"------------Excute EXTRACT-MAX-----------------"<<endl;hMaxN=Heap_ExtractMax(A);cout<<"The largest key is:"<<hMaxN<<endl;cout<<"After removing the largest,the heap is:"<<endl;Print(A);cout<<"------------Excute INCREASE-KEY----------------"<<endl;int key=11;int index=6;Heap_IncreaseKey(A,index,key);cout<<"After increasing ,the heap is:"<<endl;Print(A);cout<<"--------------Excute HEAP-INSERT---------------"<<endl;int ikey=13;Heap_InsertKey(A,ikey);Print(A);cout<<"-----------------------------------------------"<<endl;return 0;}

运行结果如下：

若有错误，请指正~~~