优先队列

堆的一个常见的应用：作为高效的优先队列。

优先队列是用来维护有一组元素构成的集合S的数据结构，其中的每一个元素都有一个相关的值，称为关键字。一个最大优先队列支持一下操作：

INSERT（S,x）: 将元素x插入集合中。

MAXIMUM（S）:返回S中具有最大键字的元素。

EXTRACT-MAX(S):去掉并返回S中的具有最大键字的元素。

INCREASE-KEY(S,x,k):将元素x的关键字值增加到k，这里假设k的值不小于x原关键字值。

#include<iostream>using namespace std;void maxHeap(int *a,int i,int heapSize)     //建立最大树堆{int l = 2*i;int r = 2*i+1;int largest=0;if(l<=heapSize&&a[l-1]>a[i-1])          //左孩子大于父节点largest = l;elselargest = i;if(r<=heapSize&&a[r-1]>a[largest-1])    //若右孩子比左孩子、父节点都大largest = r;if(largest!=i){swap(a[i-1],a[largest-1]);maxHeap(a,largest,heapSize);      //检测孩子树}}void buildMaxHeap(int *a,int heapSize)   //建立堆{for(int i=heapSize/2;i>=1;--i)       //从heapSize/2开始建堆maxHeap(a,i,heapSize);}void heapSort(int *a,int heapSize)     //堆排序{buildMaxHeap(a,heapSize);          //建堆for(int i=heapSize;i>=2;--i){swap(a[0],a[i-1]);--heapSize;maxHeap(a,1,heapSize);        //调整}}void print(int *a,int num)  {      for(int i=0;i<num;++i)          cout<<a[i]<<ends;  } void reallocate(int *a,int num,int key)       //重新分配数组空间{a = (int *)realloc(a,num*sizeof(int));a[num-1] = key;}//优先序列priority queueint heapMaximum(int *a,int heapSize)           //返回a中具有最大键字的元素{buildMaxHeap(a,heapSize);          //建堆return a[0];}int heapExtractMax(int *a,int heapSize)      //去掉并返回a中的具有最大键字的元素{if(heapSize<1)cerr<<"heap nuderflow";buildMaxHeap(a,heapSize);int max = a[0];a[0] = a[heapSize-1];--heapSize;maxHeap(a,1,heapSize);return max;}void heapIncreaseKey(int *a,int incNum,int key)   //将元素incNum的关键字值增加到key，这里假设key的值不小于incNum原关键字值{if(a[incNum-1]>key)cerr<<"new key is smaller than current key"<<endl;a[incNum-1] = key;while(incNum>1 && a[incNum/2-1]<a[incNum-1]){swap(a[incNum-1],a[incNum/2-1]);incNum = incNum/2;}}void maxHeapInsert(int *a,int heapSize,int key)  //将元素key插入集合a中。{buildMaxHeap(a,heapSize);++heapSize;int minest = -65535;reallocate(a,heapSize,minest);heapIncreaseKey(a,heapSize,key);         }int main(){int b[]={16,4,10,14,7,9,3,2,8,1};int num = sizeof(b)/sizeof(b[0]);int *a = (int*)malloc(num*sizeof(int));for(int i=0;i<num;++i)a[i] = b[i];int inc;cin>>inc;maxHeapInsert(a,num,inc);//print(a,num);cout<<endl;free(a);return 0;}

由于函数过多，调用起来很不方便，所以可以将堆排序和优先队列封装成类，且优先队列公有继承堆排序

#include<iostream>using namespace std;class Heap{public:void maxHeap(int *a,int i,int heapSize)     //建立最大树堆{int l = 2*i;int r = 2*i+1;int largest=0;if(l<=heapSize&&a[l-1]>a[i-1])          //左孩子大于父节点largest = l;elselargest = i;if(r<=heapSize&&a[r-1]>a[largest-1])    //若右孩子比左孩子、父节点都大largest = r;if(largest!=i){swap(a[i-1],a[largest-1]);maxHeap(a,largest,heapSize);      //检测孩子树}}void buildMaxHeap(int *a,int heapSize)   //建立堆{for(int i=heapSize/2;i>=1;--i)       //从heapSize/2开始建堆maxHeap(a,i,heapSize);}void heapSort(int *a,int heapSize)     //堆排序{buildMaxHeap(a,heapSize);          //建堆for(int i=heapSize;i>=2;--i){swap(a[0],a[i-1]);--heapSize;maxHeap(a,1,heapSize);        //调整}}};void print(int *a,int num)  {      for(int i=0;i<num;++i)          cout<<a[i]<<ends;  } void reallocate(int *a,int num,int key)       //重新分配数组空间{a = (int *)realloc(a,num*sizeof(int));a[num-1] = key;}//优先序列priority queueclass PriorityQueue:public Heap{  //继承堆类public:int heapMaximum(int *a,int heapSize)           //返回a中具有最大键字的元素{buildMaxHeap(a,heapSize);          //建堆return a[0];}int heapExtractMax(int *a,int heapSize)      //去掉并返回a中的具有最大键字的元素{if(heapSize<1)cerr<<"heap nuderflow";buildMaxHeap(a,heapSize);int max = a[0];a[0] = a[heapSize-1];--heapSize;maxHeap(a,1,heapSize);return max;}void heapIncreaseKey(int *a,int incNum,int key)   //将元素incNum的关键字值增加到key，这里假设key的值不小于incNum原关键字值{if(a[incNum-1]>key)cerr<<"new key is smaller than current key"<<endl;a[incNum-1] = key;while(incNum>1 && a[incNum/2-1]<a[incNum-1]){swap(a[incNum-1],a[incNum/2-1]);incNum = incNum/2;}}void maxHeapInsert(int *a,int heapSize,int key)  //将元素key插入集合a中。{buildMaxHeap(a,heapSize);++heapSize;int minest = -65535;reallocate(a,heapSize,minest);heapIncreaseKey(a,heapSize,key);         }};int main(){Heap heap;PriorityQueue priQueue;int b[]={16,4,10,14,7,9,3,2,8,1};int num = sizeof(b)/sizeof(b[0]);int *a = (int*)malloc(num*sizeof(int));for(int i=0;i<num;++i)a[i] = b[i];//heap.heapSort(a,num);//print(a,num);int inc;cin>>inc;priQueue.maxHeapInsert(a,num,inc);          //可以将heapSize调整为全局静态变量，print(a,++num);cout<<endl;free(a);return 0;}

由于每个函数几乎都要调用heapSize，所以可以将heapSize调整为全局静态变量会更方便。