堆的删除

按定义，堆中每次都只能删除第0个数据。为了便于重建堆，实际的操作是将最后一个数据的值赋给根结点，然后再从根结点开始进行一次从上向下的调整。调整时先在左右儿子结点中找最小的，如果父结点比这个最小的子结点还小说明不需要调整了，反之将父结点和它交换后再考虑后面的结点。相当于从根结点将一个数据的“下沉”过程。

堆的插入

每次插入都是将新数据放在数组最后。可以发现从这个新数据的父结点到根结点必然为一个有序的数列，现在的任务是将这个新数据插入到这个有序数据中——这就类似于直接插入排序中将一个数据并入到有序区间中。

代码：

#include <iostream>
#include <algorithm>

   using namespace::std;

  //对排序实现类的定义
class HeapSort
{
 public:
     HeapSort(int *pArray = NULL, int nArraySize = 0);
     ~HeapSort();
 public:
    int *m_pA;
    int m_nHeapSize;
 public:
    void Sort();
    int  PopMaxHeap();
    void InsertMaxHeap(int a);
 private:
    int LeftChild(int node);
    int RightChild(int node);
    int Parent(int node);
    void MaxHeapify(int nIndex);
    void BuildMaxHeap();

 };

 //对排序类成员函数的实现
HeapSort::HeapSort( int *pArray, int nArraySize )
{
     m_pA = pArray;
     m_nHeapSize = nArraySize;
}

HeapSort::~HeapSort()
{
}
int HeapSort::Parent(int node)
{
   return (node-1)/2 ;
}
int HeapSort::LeftChild(int node)
{
   return 2*node + 1;
}

int HeapSort::RightChild(int node)
{
     return 2*node + 2;
}

void HeapSort::MaxHeapify(int nIndex)
{
     int nLeft = LeftChild(nIndex);
     int nRight = RightChild(nIndex);

     int nLargest = nIndex;

     if( (nLeft < m_nHeapSize) && (m_pA[nLeft] > m_pA[nIndex]) )
         nLargest = nLeft;

     if( (nRight < m_nHeapSize) && (m_pA[nRight] > m_pA[nLargest]) )
        nLargest = nRight;

     if ( nLargest != nIndex )
    {
         swap<int>(m_pA[nIndex], m_pA[nLargest]);
         MaxHeapify(nLargest);
     }
 }

 void HeapSort::BuildMaxHeap()
 {
     if( m_pA == NULL )
         return;

     for( int i = (m_nHeapSize - 1)/2; i >= 0; i-- )
    {
         MaxHeapify(i);
     }
}
 void HeapSort::Sort()
{
     if( m_pA == NULL )
         return;
     if( m_nHeapSize == 0 )
        return;

    BuildMaxHeap();
    for( int i = m_nHeapSize - 1; i > 0; i-- )
     {
        swap<int>(m_pA[i], m_pA[0]);
         m_nHeapSize -= 1;
         MaxHeapify(0);
    }
}

int HeapSort::PopMaxHeap()
{
   if( m_pA == NULL )
         return -1;
     if( m_nHeapSize == 0 )
        return -1;
   BuildMaxHeap();
   int a= m_pA[0];
   m_pA[0]=m_pA[m_nHeapSize-1];
   m_nHeapSize -= 1;
      MaxHeapify(0);
   return a;
}
void HeapSort::InsertMaxHeap(int a)
{
/*
   if( m_pA == NULL )
         return;
     if( m_nHeapSize == 0 )
        return;
        */
   m_nHeapSize += 1;
   m_pA[m_nHeapSize-1]=a;
   int index=m_nHeapSize-1;
   while(index>0)
   {
       if(m_pA[index]>m_pA[Parent(index)])
       swap(m_pA[index], m_pA[Parent(index)]);
       index=Parent(index);
   }
}

int main()
 {
     //int A[14] = { 27,17,3,16,13,10,1,5,7,12,4,8,9,0 };
    int A[10] = {4, 1, 3, 2, 16, 9, 10, 14, 8, 7};
cout<<"heapsort before:";
for(int i=0;i<10;++i)
   cout<<A[i]<<"  ";
cout<<endl;
    HeapSort mySort(A,10);
/*
    mySort.Sort();
cout<<"heapsort after:";
    for( int i = 0; i < 10; i++ )
         cout << A[i] << "  ";
   cout << endl;
*/
int a = mySort.PopMaxHeap();
cout<<"pop: "<<a<<endl;
for(int i=0;i<10-1;++i)
   cout<<A[i]<<"  ";
cout<<endl;
mySort.InsertMaxHeap(11);
for(int i=0;i<10;++i)
   cout<<A[i]<<"  ";
cout<<endl;
return 0;
}