浙大数据结构：04-树5 Root of AVL Tree

这道题核心平衡树的代码在MOOC上有，需要完善修改即可。

机翻

1、条件准备

定义结构体，高度，值，左结点，右结点

cpp 复制代码

#include <iostream>
#include <stdlib.h>
using namespace std;
typedef struct AVLNode *position;
typedef position AVLTree;
typedef int ElementType;
struct AVLNode
{
  ElementType data;
  AVLTree Left;
  AVLTree Right;
  int height;
};

主函数读入结点，调用insert函数插入，最后输出根节点值

cpp 复制代码

int main()
{
  int n;
  cin >> n;
  AVLTree T = NULL;
  for (int i = 0; i < n; i++)
  {
    int a;
    cin >> a;
    T = insert(T, a);
  }
  cout << T->data;

  return 0;
}

2、平衡树四种旋转

具体逻辑在MOOC的ppt上有讲述，如果对代码不太理解我建议举例子推一遍比较好

cpp 复制代码

AVLTree singleleftrotation(AVLTree A)
{
 //左左
  AVLTree B = A->Left;
  A->Left = B->Right;
  B->Right = A;
  A->height = max(getheight(A->Left), getheight(A->Right)) + 1;
  B->height = max(getheight(B->Left), A->height) + 1;
  return B;
}

AVLTree singlerightrotation(AVLTree A)
{
//右右
  AVLTree B = A->Right;
  A->Right = B->Left;
  B->Left = A;
  A->height = max(getheight(A->Left), getheight(A->Right)) + 1;
  B->height = max(getheight(B->Right), A->height) + 1;

  return B;
}

AVLTree doubleleftrotation(AVLTree A)
{
//左右
  A->Left = singlerightrotation(A->Left);
  return singleleftrotation(A);
}

AVLTree doublerightrotation(AVLTree A)
{
//右左
  A->Right = singleleftrotation(A->Right);
  return singlerightrotation(A);
}

3、getheight函数

获取树高度，递归实现

cpp 复制代码

int getheight(AVLTree A)
{
  if (!A)
    return 0;
  return max(getheight(A->Left), getheight(A->Right)) + 1;
}

4、insert函数

跟MOOC上代码逻辑基本一样。

cpp 复制代码

AVLTree insert(AVLTree T, ElementType x)
{

  if (!T)
  {
    AVLTree T = (AVLTree)malloc(sizeof(struct AVLNode));
    T->data = x;
    T->Right = T->Left = NULL;
    return T;
  }
  else if (x < T->data)
  {
    T->Left = insert(T->Left, x);
    if (getheight(T->Left) - getheight(T->Right) == 2)
    {
      if (x < T->Left->data)
        T = singleleftrotation(T);
      else
        T = doubleleftrotation(T);
    }
  }
  else if (x > T->data)
  {
    T->Right = insert(T->Right, x);
    if (getheight(T->Right) - getheight(T->Left) == 2)
    {
      if (x > T->Right->data)
        T = singlerightrotation(T);
      else
        T = doublerightrotation(T);
    }
  }
  T->height = max(getheight(T->Left), getheight(T->Right)) + 1;

  return T;
}

5、总结

这个题最难的在于平衡树代码和插入代码的实现，不过MOOC上也写出了不少，所以难度不算大。

完整代码如下：

cpp 复制代码

#include <iostream>
#include <stdlib.h>
using namespace std;
typedef struct AVLNode *position;
typedef position AVLTree;
typedef int ElementType;
struct AVLNode
{
  ElementType data;
  AVLTree Left;
  AVLTree Right;
  int height;
};

int getheight(AVLTree A)
{
  if (!A)
    return 0;
  return max(getheight(A->Left), getheight(A->Right)) + 1;
}

AVLTree singleleftrotation(AVLTree A)
{
  AVLTree B = A->Left;
  A->Left = B->Right;
  B->Right = A;
  A->height = max(getheight(A->Left), getheight(A->Right)) + 1;
  B->height = max(getheight(B->Left), A->height) + 1;
  return B;
}

AVLTree singlerightrotation(AVLTree A)
{
  AVLTree B = A->Right;
  A->Right = B->Left;
  B->Left = A;
  A->height = max(getheight(A->Left), getheight(A->Right)) + 1;
  B->height = max(getheight(B->Right), A->height) + 1;

  return B;
}

AVLTree doubleleftrotation(AVLTree A)
{
  A->Left = singlerightrotation(A->Left);
  return singleleftrotation(A);
}

AVLTree doublerightrotation(AVLTree A)
{
  A->Right = singleleftrotation(A->Right);
  return singlerightrotation(A);
}

AVLTree insert(AVLTree T, ElementType x)
{

  if (!T)
  {
    AVLTree T = (AVLTree)malloc(sizeof(struct AVLNode));
    T->data = x;
    T->Right = T->Left = NULL;
    return T;
  }
  else if (x < T->data)
  {
    T->Left = insert(T->Left, x);
    if (getheight(T->Left) - getheight(T->Right) == 2)
    {
      if (x < T->Left->data)
        T = singleleftrotation(T);
      else
        T = doubleleftrotation(T);
    }
  }
  else if (x > T->data)
  {
    T->Right = insert(T->Right, x);
    if (getheight(T->Right) - getheight(T->Left) == 2)
    {
      if (x > T->Right->data)
        T = singlerightrotation(T);
      else
        T = doublerightrotation(T);
    }
  }
  T->height = max(getheight(T->Left), getheight(T->Right)) + 1;

  return T;
}

int main()
{
  int n;
  cin >> n;
  AVLTree T = NULL;
  for (int i = 0; i < n; i++)
  {
    int a;
    cin >> a;
    T = insert(T, a);
  }
  cout << T->data;

  return 0;
}