深入理解数据结构第二弹——二叉树（2）——堆排序及其时间复杂度

typedef int HPDataType;
typedef struct Heap
{
  HPDataType* a;
  int sz;
  int capacity;
}HP;
 
//初始化
void HeapInit(HP* php);
//销毁
void HeapDestory(HP* php);
//插入
void HeapPush(HP* php, HPDataType x);
//删除
void HeapPop(HP* php);
//找堆顶元素
HPDataType HeapTop(HP* php);
//判断是否为空
bool HeapEmpty(HP* php);
//算个数
int HeapSize(HP* php);

//堆排序
void HeapSort(int* a, int n)
{
  //建堆——向下调整建堆O(N-log(n))
  for (int i = (n - 1 - 1) / 2; i >= 0; i--)
  {
    AdjustDown(a, n, i);
  }
  int end = n - 1;
  while (end > 0)
  {
    Swap(&a[0], &a[end]);
 
    //再调整，选出次小数
    AdjustDown(a, end, 0);
    end--;
  }
}
int main()
{
  int a[] = { 7,8,3,5,1,9,5,4 };
  HeapSort(a, sizeof(a) / sizeof(int));
  return 0;
}

//堆
//初始化
void HeapInit(HP* php)
{
  assert(php);
  php->a = NULL;
  php->capacity = 0;
  php->sz = 0;
}
//销毁
void HeapDestory(HP* php)
{
  free(php->a);
  free(php);
}
//交换
void Swap(HPDataType* p1, HPDataType* p2)
{
  HPDataType tmp = *p1;
  *p1 = *p2;
  *p2 = tmp;
}
//删除
 
//向上调整(小堆)
void AdjustUp(HPDataType* a, int child)
{
  int parent = (child - 1) / 2;
  while (child > 0)
  {
    if (a[child] < a[parent])
    {
      Swap(&a[child], &a[parent]);
 
      child = parent;
      parent = (child - 1) / 2;
    }
    else
    {
      break;
    }
  }
}
//向下调整
void AdjustDown(int* a, int n, int parent)
{
  int child = parent * 2 + 1;
  while (child<n)
  {
    if (child+1<n&&a[child + 1] < a[child])
    {
      ++child;
    }
    if (a[child] < a[parent])
    {
      Swap(&a[child], &a[parent]);
      parent = child;
      child = parent * 2 + 1;
    }
    else
    {
      break;
    }
  }
}
 
//插入
void HeapPush(HP* php, HPDataType x)
{
  assert(php);
  if (php->sz == php->capacity)
  {
    int newcapacity = php->capacity == 0 ? 4 : php->capacity * 2;
    HPDataType* tmp = (HPDataType*)realloc(php->a, sizeof(HPDataType) * newcapacity);
    php->a = tmp;
    php->capacity = newcapacity;
  }
  php->a[php->sz] = x;
  php->sz++;
 
  //向上调整
  AdjustUp(php->a, php->sz - 1);
}
//删除
void HeapPop(HP* php)
{
  assert(php);
  assert(!HeapEmpty(php));
  Swap(&php->a[0], &php->a[php->sz - 1]);
  php->sz--;
  //向下调整
  AdjustDown(php->a, php->sz,0);
}
//判断是否为空
bool HeapEmpty(HP* php)
{
  assert(php);
  return php->sz == 0;
}
//找堆顶元素
HPDataType HeapTop(HP* php)
{
  assert(php);
  assert(!HeapEmpty(php));
  return php->a[0];
}
//算个数
int HeapSize(HP* php)
{
  assert(php);
  return php->sz;
}