04-树5 Root of AVL Tree (25分)

04-树5 Root of AVL Tree   (25分)

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.

Now given a sequence of insertions, you are supposed to tell the root of the resulting AVL tree.

Input Specification:

Each input file contains one test case. For each case, the first line contains a positive integer $N$ ($\le 20$) which is the total number of keys to be inserted. Then $N$ distinct integer keys are given in the next line. All the numbers in a line are separated by a space.

Output Specification:

For each test case, print the root of the resulting AVL tree in one line.

Sample Input 1:

588 70 61 96 120

Sample Output 1:

70

Sample Input 2:

788 70 61 96 120 90 65

Sample Output 2:

88

主要思路：

1、二叉平衡树的插入新结点的四种情况判断（此处递归插入）

2、LL，RR，LR，RL旋转的实现

#include <iostream>#include <vector>using namespace std;#define Max_Node 1000000typedef struct node//树的结点{    int left;    int right;    int height;}Node;int Get_Height(vector<Node>& Tree,int root)//递归求该结点在二叉树中的高度{    int HL,HR,MaxH;    if (root)    {        HL=Get_Height(Tree, Tree[root].left);        HR=Get_Height(Tree, Tree[root].right);        if (HL>HR)        {            MaxH=HL;        }else        {            MaxH=HR;        }        return (MaxH+1);    }else    {        return 0;    }}int SingleLeftRotation(int A,vector<Node>& Tree)//LL旋转{    int B=Tree[A].left;    Tree[A].left=Tree[B].right;    Tree[B].right=A;    Tree[A].height=Get_Height(Tree, A);    Tree[B].height=Get_Height(Tree, B);    return B;}int SingleRightRotation(int A,vector<Node>& Tree)//RR旋转{    int B=Tree[A].right;    Tree[A].right=Tree[B].left;    Tree[B].left=A;    Tree[A].height=Get_Height(Tree, A);    Tree[B].height=Get_Height(Tree, B);    return B;}int DoubleLeftRightRotation(int A,vector<Node>& Tree)//LR旋转{    Tree[A].left=SingleRightRotation(Tree[A].left, Tree);    return SingleLeftRotation(A, Tree);}int DoubleRightLeftRotation(int A,vector<Node>& Tree)//RL旋转{    Tree[A].right=SingleLeftRotation(Tree[A].right, Tree);    return SingleRightRotation(A, Tree);}int AVL_Insertion(int X,vector<Node>& Tree,int T)//二叉平衡树插入一个新结点{    if(!T)    {        Tree[X].left=0;        Tree[X].right=0;        Tree[X].height=0;        T=X;    }else    {        if (X<T)//小于当前结点，插入到当前结点的左子树        {            Tree[T].left=AVL_Insertion(X, Tree, Tree[T].left);            if (Get_Height(Tree, Tree[T].left)-Get_Height(Tree, Tree[T].right)==2)//插入后出现不平衡的情形（只可能为LL或LR的情形）            {                if (X<Tree[T].left)                {                    T=SingleLeftRotation(T, Tree);                }else                {                    T=DoubleLeftRightRotation(T, Tree);                }            }        }else if(X>T)//大于当前结点，插入到当前结点的右子树        {            Tree[T].right=AVL_Insertion(X, Tree, Tree[T].right);            if (Get_Height(Tree, Tree[T].left)-Get_Height(Tree, Tree[T].right)==-2)            {                if (X>Tree[T].right)                {                    T=SingleRightRotation(T, Tree);                }else                {                    T=DoubleRightLeftRotation(T, Tree);                }            }        }    }    Tree[T].height=Get_Height(Tree, T);    return T;}int main(){    vector<Node> Tree(Max_Node);    int Root=0;    int N=0;    cin>>N;    int X=0;    while (N--)    {        cin>>X;        Root=AVL_Insertion(X, Tree, Root);    }    cout<<Root;    return 0;}