Avl树

AVL树本质上还是一棵二叉搜索树，它的特点是：

1.本身首先是一棵二叉搜索树。

2.带有平衡条件：每个非叶子结点的左右子树的高度之差的绝对值（平衡因子）最多为1。

AVL树的查找平均时间复杂度要比最坏情况下的二叉搜索树低——它是O(logn)。也就是说，在大量的随机数据中AVL树的表现要好得多。

如果在AVL树中插入或删除节点后，使得高度之差大于1，AVL树的平衡状态就被破坏，它就不再是一棵平衡二叉搜索树。为了让它重新维持在一个平衡状态，就需要对其进行旋转操作

常见的四种不平衡情况

代码：

public class AvlNode<Anytype extends Comparable> {
	
	/**
	 * Avl树，节点类
	 */
	
	Anytype element;
	AvlNode<Anytype> right;
	AvlNode<Anytype> left;
	int hight;
	
	public AvlNode(Anytype element) {
		super();
		this.element = element;
		this.right = null;
		this.left = null;
	}
	
	public AvlNode(Anytype element, AvlNode<Anytype> right, AvlNode<Anytype> left, int hight) {
		super();
		this.element = element;
		this.right = right;
		this.left = left;
		this.hight = hight;
	}
	
	private static final int ALLOW_IMBALANCE = 1;
	
	/**
	 * Avl树的高度，默认根节点高度是-1
	 * @param t
	 * @return
	 */
	private int hight(AvlNode<Anytype> t) {
		return t == null ? -1 : t.hight;
	}
	
	/**
	 * 插入节点
	 * @param x
	 * @param t
	 * @return
	 */
	private AvlNode<Anytype> insert(Anytype x,AvlNode t){
		if(t == null){
			return new AvlNode(x);
		}
		int result = x.compareTo(t);
		if(result<0) {
			t.left = insert(x, t.left);
		}else if(result>0) {
			t.right = insert(x, t.right);
		}else
			;
		return balance(t);
	}
	
	
	/**
	 * 在插入新节点后判断树结构是否平衡，不平衡则平衡树
	 * @param t
	 * @return
	 */
	private AvlNode<Anytype> balance(AvlNode<Anytype> t) {
		
		if(t==null) {
			return t;
		}
		if(hight(t.left)-hight(t.right)>ALLOW_IMBALANCE) {
			if(hight(t.left) >= hight(t.right))
				rotateWithLeftChild(t);
			else
				doubleWithLeftChild(t);
		}
		if(hight(t.right)-hight(t.left)>ALLOW_IMBALANCE) {
			if(hight(t.right) >= hight(t.left))
				rotateWithRightChild(t);
			else
				doubleWithRightChild(t);
		}
		
		t.hight = Math.max(hight(t.left), hight(t.right))+1;
		return t;
		
	}

	
	/**
	 * 左 双旋转
	 * @param t
	 */
	private AvlNode<Anytype> doubleWithLeftChild(AvlNode<Anytype> k2) {
		// TODO Auto-generated method stub
		k2.left = rotateWithLeftChild(k2.left);
		return rotateWithRightChild(k2);
	}

	
	/**
	 * 右 单旋转
	 * @param t
	 */
	private AvlNode<Anytype> rotateWithRightChild(AvlNode<Anytype> k2) {
		// TODO Auto-generated method stub
		AvlNode k1 = k2.right;
		k2.right = k1.left;
		k1.left = k2;
		
		k2.hight = Math.max(hight(k2.right), hight(k2.left))+1;
		k1.hight = Math.max(hight(k1.left), hight(k2))+1;
		
		return k1;
	}

	/**
	 * 右 双旋转
	 * @param t
	 */
	private AvlNode<Anytype> doubleWithRightChild(AvlNode<Anytype> k2) {
		// TODO Auto-generated method stub
		k2.left = rotateWithRightChild(k2.left);
		return rotateWithLeftChild(k2);
	}

	
	/**
	 * 左 单旋转
	 * @param t
	 */
	private AvlNode<Anytype> rotateWithLeftChild(AvlNode<Anytype> k2) {
		// TODO Auto-generated method stub
		AvlNode k1 = k2.left;
		k2.left = k1.right;
		k1.right = k2;
		
		k2.hight = Math.max(hight(k2.right), hight(k2.left))+1;
		k1.hight = Math.max(hight(k1.right), hight(k2))+1;
		
		return k1;
	}
	
	
}