Root of AVL Tree - Java實作

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 (≤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

思路：

根據給出的序列逐一插入樹中，在插入過程中判斷一旦出現需要調整的情況，立即對AVL樹進行調整；

代碼如下：

import java.io.BufferedReader;
import java.io.FileDescriptor;
import java.io.FileReader;

public class Main {

    AVLNode tree = null;

    public static void main(String[] args){
        Main self = new Main();
        BufferedReader br = new BufferedReader(new FileReader(FileDescriptor.in));
        try {
            int[] nodes = self.readInput(br);
            AVLNode head = self.buildAVLTree(nodes, self.tree);
            System.out.print(head.getData());
        } catch (Exception e) {
            e.printStackTrace();
        }

    }

    //讀取輸入資訊
    public int[] readInput(BufferedReader br) throws Exception{
        int num = Integer.parseInt(br.readLine().trim());
        String[] s = br.readLine().trim().split(" ");
        int[] nodes = new int[num];
        for (int i = 0; i < num; i++) {
            nodes[i] = Integer.parseInt(s[i]);
        }
        return nodes;
    }

    //插入節點，形成一顆AVL樹
    public AVLNode buildAVLTree(int[] nodes,AVLNode tree){
        for (int i = 0; i < nodes.length; i++) {
            tree = insertNode(tree,nodes[i]);
        }
        return tree;

    }

    //插入一個節點
    private AVLNode insertNode(AVLNode head, int data){
        if (head == null){
            return new AVLNode(data);
        }
        //插入右子樹
        if (data > head.getData()){
            head.right = insertNode(head.right,data);
            head.setHeight(max(getTreeHeight(head.left),getTreeHeight(head.right)) + 1);
            int temp = head.getData();
            if (getTreeHeight(head.left) - getTreeHeight(head.right)== -2){
                if (head.right.getData() > data){
                    head = rightLeftRotation(head);
                }else {
                    head =  singleRightRotation(head);
                }
            }
        }
        //插入左子樹
        if (data < head.getData()){
            int headData = head.getData();
            head.left = insertNode(head.left,data);
            head.setHeight(max(getTreeHeight(head.left),getTreeHeight(head.right)) + 1);
            if (getTreeHeight(head.left) - getTreeHeight(head.right)== 2){
                if (head.left.getData() < data){
                    head = leftRightRotation(head);
                }else {
                    head = singleLeftRotation(head);
                }
            }
        }

        return head;
    }

    private int max(int a, int b){
        return a>b?a:b;
    }
    //右單旋
    private AVLNode singleRightRotation(AVLNode head){
        AVLNode right = head.right;
        AVLNode temp = right.left;
        right.left = head;
        head.right = temp;
        head.setHeight(max(getTreeHeight(head.left),getTreeHeight(head.right)) + 1);
        right.setHeight(max(getTreeHeight(right.left),getTreeHeight(right.right)) + 1);
        return right;
    }
    //左單旋
    private AVLNode singleLeftRotation(AVLNode head){
        AVLNode left = head.left;
        AVLNode temp = left.right;
        left.right = head;
        head.left = temp;
        head.setHeight(max(getTreeHeight(head.left),getTreeHeight(head.right)) + 1);
        left.setHeight(max(getTreeHeight(left.left),getTreeHeight(left.right)) + 1);
        return left;
    }
    //左右旋轉
    private AVLNode leftRightRotation(AVLNode head){
        head.left = singleRightRotation(head.left);
        return singleLeftRotation(head);
    }
    //右左旋轉
    private AVLNode rightLeftRotation(AVLNode head){
        head.right = singleLeftRotation(head.right);
         return singleRightRotation(head);

    }

    //獲得一個節點的高度
    private int getTreeHeight(AVLNode head){
        if (head == null){
            return 0;
        }
        return head.getHeight();
    }


}

class AVLNode{
    private int data;
    AVLNode left;
    AVLNode right;
    private int height;

    public AVLNode(int data) {
        this.data = data;
        this.left = null;
        this.right = null;
        this.height = 1;
    }

    public AVLNode() { }

    public int getData() {
        return data;
    }

    public void setData(int data) {
        this.data = data;
    }

    public int getHeight() {
       return this.height;
    }

    public void setHeight(int height) {
        this.height = height;
    }
}