PAT Root of AVL Tree

Root of AVL Tree

An AVL tree is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; if at any time they differ by more than one, rebalancing is done to restore this property. Figures 1-4 illustrate the rotation rules.

 

 

这道题比较简单  只要你搞懂 avl树   就没什么问题   

看懂题目给的图很关键

关于avl树可以看我的另一篇博文  http://www.cnblogs.com/threezj/p/4509852.html

 

下面给出ac代码

  1 #include "stdio.h"
  2 #include "stdlib.h"
  3 typedef struct AVLTreeNode *AVLTree;
  4 
  5 typedef struct AVLTreeNode{
  6     int Data;
  7     AVLTree Left;
  8     AVLTree Right;
  9     int Height;
 10 };
 11 
 12 AVLTree SingleRightRotation(AVLTree A);
 13 AVLTree DoubleLeftRightRotation(AVLTree A);
 14 AVLTree SingleLeftRotation(AVLTree A);
 15 AVLTree DoubleRightLeftRotation(AVLTree A);
 16 int GetHeight(AVLTree bt);
 17 int Max(int a,int b);
 18 AVLTree AVL_Insertion(int x,AVLTree t);
 19 
 20 int main()
 21 {
 22     AVLTree t;
 23     int i,n,data;
 24     t=(AVLTree)malloc(sizeof(struct AVLTreeNode));
 25     t=NULL;
 26     scanf("%d",&n);
 27     
 28     for(i=0;i<n;i++)
 29     {
 30         scanf("%d",&data);
 31         t=AVL_Insertion(data,t);
 32     }
 33     printf("%d",t->Data);
 34 }
 35 
 36 
 37 int GetHeight(AVLTree bt)
 38 {
 39     if(bt==NULL)
 40         return 0;
 41     return (bt->Height);
 42 }
 43 int Max(int a,int b)
 44 {
 45     return a>b?a:b;
 46 }
 47 AVLTree AVL_Insertion(int x,AVLTree t)
 48 {
 49     if(!t)     
 50     {
 51         t=(AVLTree)malloc(sizeof(struct AVLTreeNode));
 52         t->Data=x;
 53         t->Height=0;
 54         t->Left=t->Right=NULL;
 55     }
 56     else if(x<t->Data)                 
 57     {
 58         t->Left=AVL_Insertion(x,t->Left);    //若x比data小，则插到左子树
 59         if(GetHeight(t->Left)-GetHeight(t->Right)==2)        //若平衡因子为2，则这个节点的平衡被破坏
 60             if(x<t->Left->Data)                                //破坏者在左子树的左子树  则右旋转
 61                 t=SingleRightRotation(t);
 62             else
 63                 t=DoubleLeftRightRotation(t);                //在左子树的右子树 则进行LR旋转 先左旋再右旋  
 64     }
 65     else if(x>t->Data)
 66     {
 67         t->Right=AVL_Insertion(x,t->Right);
 68         if(GetHeight(t->Left)-GetHeight(t->Right)==-2)            
 69             if(x>t->Right->Data)
 70                 t=SingleLeftRotation(t);                    //在右子树的右子树 进行左旋
 71             else
 72                 t=DoubleRightLeftRotation(t);                //右子树的左子树 进行RL旋转 
 73                 
 74     }
 75     t->Height=Max(GetHeight(t->Left),GetHeight(t->Right))+1;  //更新高度 
 76     
 77     return t;
 78 }
 79 
 80 AVLTree SingleRightRotation(AVLTree A)
 81 {
 82     AVLTree B=A->Left;                //a的左子树给B                            
 83     A->Left=B->Right;                //把b的右子树放到a的左边     
 84     B->Right=A;                    //a放到b的右边        
 85     A->Height=Max(GetHeight(A->Left),GetHeight(A->Right))+1;
 86     B->Height=Max(GetHeight(B->Left),A->Height)+1;
 87     return B;
 88 }
 89 
 90 AVLTree DoubleLeftRightRotation(AVLTree A)
 91 {
 92     A->Left=SingleLeftRotation(A->Left);
 93     
 94     return SingleRightRotation(A);
 95 }
 96 
 97 AVLTree SingleLeftRotation(AVLTree A)
 98 {
 99     AVLTree B=A->Right;                                        
100     A->Right=B->Left;                     
101     B->Left=A;                            
102     A->Height=Max(GetHeight(A->Left),GetHeight(A->Right))+1;
103     B->Height=Max(GetHeight(B->Right),A->Height)+1;
104     return B;
105 }
106 
107 AVLTree DoubleRightLeftRotation(AVLTree A)
108 {
109     A->Right=SingleRightRotation(A->Right);
110     
111     return SingleLeftRotation(A);
112 }