首先给出最小优先级队列和最大优先级队列完整代码，稍后分析博文奉上

//最大堆实现的最大优先级队列

#include <iostream>
#include <cstdlib>

using namespace std;

int array_size;
int heap_size;

//几个内联函数
inline int left(int i)
{
 return i<<1;
}

inline int right(int i)
{
 return i<<1|1;
}

inline int parent(int i)
{
 return i>>1;
}

//最大化堆
void max_heapify(int *heap,int pos)
{
 int l = left(pos);
 int r = right(pos);
 int largest;
 if(l <= heap_size && heap[l] > heap[pos])
  largest = l;
 else largest = pos;
 if(r <= heap_size && heap[r] > heap[largest])
  largest = r;
 if(largest != pos)
 {
  int t = heap[largest];
  heap[largest] = heap[pos];
  heap[pos] = t;
  max_heapify(heap, largest);
 }
}

//建堆
void build_max_heap(int *heap)
{
 heap_size = array_size;
 for(int i = array_size/2; i >= 1; i--)
  max_heapify(heap, i);
}

//堆排序
void heap_sort(int *heap)
{
 build_max_heap(heap);
 for(int i = array_size; i >= 2; i--)
 {
  int t = heap[1];
  heap[1] = heap[heap_size];
  heap[heap_size] = t;
  heap_size--;
  max_heapify(heap, 1);
 }
}

//取出最大元素
int heap_extract_max(int *heap)
{
 if(heap_size < 1)
 {
  cout<<"heap is empty!"<<endl;
  exit(1);//异常退出
 }
 int max = heap[1];
 heap[1] = heap[heap_size];
 heap_size--;
 max_heapify(heap,1);
 return max;
}

//增大指定元素的大小
void heap_increase_key(int *heap, int pos, int key)
{
 if(key < heap[pos])
 {
  cout<<"new key is smaller than current key!"<<endl;
  exit(1);
 }
 heap[pos] = key;
 while(pos > 1 && heap[parent(pos)] < heap[pos])//当双亲大于孩子时结束
 {
  int t = heap[parent(pos)];
  heap[parent(pos)] = heap[pos];
  heap[pos] = t;
  pos = parent(pos);//一直往上寻找
 }
}

//插入操作
//这里涉及到一种思想，可以使插入操作变得很方便
//思想是这样的：首先插入在堆的末尾插入一个最小值，然后再利用上面的增加元素的值得形式将节点上流
//这样大大节省了时间
void max_heap_insert(int *heap, int key)
{
 heap[++heap_size] = -INT_MAX;
 heap_increase_key(heap, heap_size, key);
}

int main()
{
 int n;//堆元素个数
 cout<<"please enter:"<<endl;
 while(cin >> n)
 {
  array_size = n;
  int i,j;
  int heap[20] = { 0 };
        cout<<"please enter heap's element:"<<endl;
  for(i = 1; i <= n; i++)
   cin>>heap[i];

  //heap_sort(heap);
       
  //建堆
        build_max_heap(heap);
       
  //取出最大元素
  cout<<"max element:"<<heap_extract_max(heap)<<endl;
       
  //插入一个元素
  int insert_element;
  cout<<"please enter the element to insert:"<<endl;
  cin>>insert_element;
  max_heap_insert(heap, insert_element);

  //增大指定元素的大小
  int increase_element;
  cout<<"please enter the element to increase:"<<endl;
  cin>>increase_element;
  heap_increase_key(heap, 2, increase_element);
   
  for(i = 1; i <= heap_size; i++)
   cout<<heap[i]<<" ";
  cout<<endl;
  cout<<endl<<"please enter:"<<endl;
 }
 return 0;
}

 

//利用最小堆实现最小优先级队列

#include <iostream>
#include <cstdlib>

using namespace std;

int heap_size;
int array_size;

//几个内联函数
inline int left(int i)
{
 return i<<1;
}

inline int right(int i)
{
 return i<<1|1;
}

inline int parent(int i)
{
 return i>>1;
}

//最小化堆
void min_heapify(int *heap, int pos)
{
 int l = left(pos);
 int r = right(pos);
 int smallest;
  
 if(l <= heap_size && heap[l] < heap[pos])
  smallest = l;
 else smallest = pos;
 if(r <= heap_size && heap[r] < heap[smallest])
  smallest = r;
 if(smallest != pos)
 {
  int t = heap[pos];
  heap[pos] = heap[smallest];
  heap[smallest] = t;
  min_heapify(heap, smallest);
 }
}

//建堆
void build_min_heap(int *heap)
{
 heap_size = array_size;
 for(int i = array_size/2; i >= 1; i--)
  min_heapify(heap, i);
}

//取出最小元素
int heap_extract_min(int *heap)
{
 int min = heap[1];
 int t = heap[1];
 heap[1] = heap[heap_size];
 heap[heap_size] = t;

 heap_size--;
 min_heapify(heap, 1);
 return min;
}

//减小某元素的值
void heap_decrease_key(int *heap, int pos, int key)
{
 if(key > heap[pos])
 {
  cout<<"the element is bigger than current key!"<<endl;
  exit(1);
 }
 heap[pos] = key;
 while(pos >= 1 && heap[pos] < heap[parent(pos)])
 {
  int t = heap[pos];
  heap[pos] = heap[parent(pos)];
  heap[parent(pos)] = t;
  pos = parent(pos);
 }
}

//插入元素
//插入的思想与最大优先级队列相似，首先在堆尾插入一个最大的元素
void min_heap_insert(int *heap, int key)
{
 heap_size++;
 heap[heap_size] = INT_MAX;
    heap_decrease_key(heap, heap_size, key);
}

int main()
{
 int n;
 cout<<"please enter:"<<endl;
 while(cin >> n)
 {
        array_size = n;
  int heap[30];
        int i, j;
  cout<<"please heap's elements:"<<endl;
  for(i = 1; i <= n; i++)
   cin>>heap[i];
       
  //建堆
  build_min_heap(heap);
  
  //取出最小元素
  cout<<"minimum: "<<heap_extract_min(heap)<<endl;
       
  //插入一个元素
  int insert_element;
  cout<<"please enter the element to insert:"<<endl;
  cin>>insert_element;
  min_heap_insert(heap, insert_element);

        for(i = 1; i <= heap_size; i++)
   cout<<heap[i]<<" ";
  cout<<endl;

  cout<<"please enter:"<<endl;
 }
 return 0;
}