实用类之二-----最大堆的实现

最小(大)堆是比较常用的数据结构,是实现优先队列和堆排序的基础,也可以实现例如霍夫曼编码,贪心算法等,具有很好的时间复杂性.

template<class T>
class MaxHeap{
 public:
  MaxHeap(T a[],int n);
  MaxHeap(int ms);
  ~MaxHeap();
  bool Insert(const T &x);//插入一个元素,如果空返回false，否则返回true
     bool RemoveMax(T &x);//删除最小的元素，如果空返回false，否则返回true
  void MakeEmpty();//使堆为空
  bool IsEmpty();
  bool IsFull();

protected:
  void FilterDown(const int start,const int endOfHeap);//自顶向下构造堆
  void FilterUp(const int start);//自底向上构造堆
 private:
  T *heap;
  int maxSize;
  const int defaultSize;
  int currentSize;
};
template<class T>
MaxHeap<T>::MaxHeap(int ms):defaultSize(100){
 maxSize = ms > defaultSize ? ms : defaultSize;
 heap = new T[maxSize];
 currentSize = 0;
}
template<class T>
MaxHeap<T>::MaxHeap(T a[],int n):defaultSize(100){
 maxSize = n > defaultSize ? n : defaultSize;
 heap = new T[maxSize];
 currentSize = n;
 for(int i = 0; i < n; i++)
  heap[i] = a[i];
 int curPos = (currentSize - 2) / 2;
 while(curPos >= 0){
   FilterDown(curPos,currentSize - 1);
   curPos--;
 }
}
template<class T>
MaxHeap<T>::~MaxHeap(){
 delete []heap;
}
template<class T>
void MaxHeap<T>::FilterDown(const int start,const int endOfHeap){
 int i = start,j = i * 2 + 1;
 T temp = heap[i];
 while(j <= endOfHeap){
   if(j < endOfHeap && heap[j] < heap[j+1]) j++;
   if(temp > heap[j]) break;
   else{
    heap[i] = heap[j];
    i = j;
    j = 2 * i + 1;
   }
 }
 heap[i] = temp;
}
template<class T>
void MaxHeap<T>::FilterUp(const int start){
 int i = start, j = ( i - 1 ) / 2;
 T temp = heap[i];
 while(i > 0){
   if(temp <= heap[j]) break;
   else{
    heap[i] = heap[j];
    i = j;
    j = (i - 1) / 2;
   }
 }
 heap[i] = temp;
}
template<class T>
bool MaxHeap<T>::RemoveMax(T &x){
 if(IsEmpty()){
  cerr<<"Heap empty!"<<endl;
  return false;
 }
 x = heap[0];
 heap[0] = heap[currentSize - 1];
 currentSize--;
 FilterDown(0,currentSize-1);
 return true;
}
template<class T>
bool MaxHeap<T>::Insert(const T& x){
 if(IsFull()) {
  cerr<<"Heap Full!"<<endl;
        return false;
 }
 heap[currentSize] = x;
 FilterUp(currentSize);
 currentSize++;
 return true;
}
template<class T>
bool MaxHeap<T>::IsEmpty(){
  return currentSize == 0;
}
 
template<class T>
bool MaxHeap<T>::IsFull(){
  return currentSize == maxSize;
}

template<class T>
void MaxHeap<T>::MakeEmpty(){
 currentSize = 0
}

MainApp.cpp测试文件:

#include<iostream>
#include"MaxHeap.h"
using namespace std;

void main(){
 int a[5] = {3,2,1,4,5};
    MaxHeap<int> m_heap(a,5);
 int x,i;
 for(i = 0; i < 5; i++){
   m_heap.RemoveMax(x);
   cout << x << " ";
 }
 cout << endl; 

    for(i = 0; i < 5; i++){
    m_heap.Insert(a[i]);
 }

 for(i = 0; i < 5; i++){
   m_heap.RemoveMax(x);
   cout << x << " ";
 }
 cout << endl; 
}