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:

5
88 70 61 96 120

Sample Output 1:

70

Sample Input 2:

7
88 70 61 96 120 90 65

Sample Output 2:

88

 AVL平衡搜索树二叉树.
import java.util.Scanner;

class Node{
	Node left,right;
	int data;
	int height;
	public Node(int data){
		this.data = data;
		this.left = null;
		this.right = null;
		this.height = 0;
	}
}

class AVLTree{

	//RR旋转
	private Node RR(Node root){
		Node newroot = root.right;
		root.right = newroot.left;
		newroot.left = root;
		root.height = setHeight(root);
		newroot.height = setHeight(newroot);
		return newroot;
	}

	//LL旋转
	private Node LL(Node root){
		Node newroot = root.left;
		root.left = newroot.right;
		newroot.right = root;
		root.height = setHeight(root);
		newroot.height = setHeight(newroot);
		return newroot;
	}

	//RL旋转
	private Node RL(Node root){
		root.right = LL(root.right);
		return RR(root);
	}

	//LR旋转
	private Node LR(Node root){
		root.left = RR(root.left);
		return LL(root);
	}

	//设置height
	private int setHeight(Node root){
		if(root==null){
			return 0;
		}
		return 1+Math.max((root.left!=null?root.left.height:0),(root.right!=null?root.right.height:0));
	}

	//获取height
	private int getHeight(Node root){
		if(root==null){
			return 0;
		}
		return root.height;
	}

	//获得平衡因子
	private int balance(Node root){
		return getHeight(root.left)-getHeight(root.right);
	}

	//插入节点
	public Node insert(Node root,int data){
		if(root==null){
			root = new Node(data);
		}else if(data>=root.data){
			root.right = insert(root.right,data);
			//需要进行R旋转
			if(balance(root)<-1){
				if(getHeight(root.right.right)>getHeight(root.right.left)){//需要进行RR旋转
					root = RR(root);
				}else if(getHeight(root.right.right)<getHeight(root.right.left)){//需要进行RL旋转
					root = RL(root);
				}
			}
		}else if(data<root.data){
			root.left = insert(root.left,data);
			//需要进行L旋转
			if(balance(root)>1){
				if(getHeight(root.left.left)>getHeight(root.left.right)){//需要进行LL旋转
					root = LL(root);
				}else if(getHeight(root.left.left)<getHeight(root.left.right)){//需要进行LR旋转
					root = LR(root);
				}
			}
		}
		root.height = setHeight(root);
		return root;
	}
}

public class Main{
	public static void main(String[] args) {
			Scanner scan = new Scanner(System.in);
			int T = scan.nextInt();
			AVLTree avl = new AVLTree();
			Node root = null;
			while(T--!=0){
				int num = scan.nextInt();
				root = avl.insert(root,num);
			}
			System.out.println(root.data);
	}
}