AVL樹的代碼實現

二叉平衡查找樹又稱AVL樹，以及紅黑樹，其實就是在普通的二叉樹結構裏面不斷加入規則。用程序來知足這些規則。

/**
 * Created by Administrator on 2018-02-23.
 */
public class AVLTree<AnyType extends Comparable> {
    private static final int ALLOWED_IMBALANCE = 1;
    private static class AvlNode<AnyType> {
        AvlNode(AnyType theElement) {
            this(theElement,null,null);
        }
        AvlNode(AnyType theElement,AvlNode<AnyType> lt,AvlNode<AnyType> rt) {
            element = theElement;
            left = lt;
            right = rt;
            height = 0;
        }
        AnyType element;
        AvlNode<AnyType> left;
        AvlNode<AnyType> right;
        int height;
    }
    private int height(AvlNode<AnyType> t) {
        return t == null ? -1:t.height;
    }
    private AvlNode<AnyType> insert(AnyType x,AvlNode<AnyType> t) {
        if (t == null)
            return new AvlNode<>(x,null,null);
        int compareResult = x.compareTo(t.element);
        if (compareResult < 0) {
            t.left = insert(x,t.left);
        }else if (compareResult > 0) {
            t.right = insert(x,t.right);
        }else {

        }
        return balance(t);
    }
    private AvlNode<AnyType> balance(AvlNode<AnyType> t) {
        if (t == null) {
            return t;
        }
        if (height(t.left) - height(t.right) > ALLOWED_IMBALANCE) {
            if (height(t.left.left) >= height(t.left.right))
                t = rotateWithLeftChild(t);
            else
                t = doubleWithLeftChild(t);
        }else {
            if (height(t.right) - height(t.left) > ALLOWED_IMBALANCE) {
                if (height(t.right.right) >= height(t.right.left))
                    t = rotateWhitRightChild(t);
                else
                    t = doubleWithLeftChild(t);
            }
        }
        t.height = Math.max(height(t.left),height(t.right)) + 1;
        return t;
    }
    private AvlNode<AnyType> rotateWithLeftChild(AvlNode<AnyType> k2) {
        AvlNode<AnyType> k1 = k2.left;
        k2.left = k1.right;
        k1.right = k2;
        k2.height = Math.max(height(k2.left),height(k2.right)) + 1;
        k1.height = Math.max(height(k1.left),k2.height) + 1;
        return k1;
    }
    private AvlNode<AnyType> doubleWithLeftChild(AvlNode<AnyType> k3) {
        k3.left = rotateWhitRightChild(k3.left);
        return rotateWithLeftChild(k3);
    }
    private AvlNode<AnyType> rotateWhitRightChild(AvlNode<AnyType> k1) {
        AvlNode<AnyType> k2 = k1.right;
        k1.right = k2.left;
        k2.left = k1;
        k1.height = Math.max(height(k1.left), height(k1.right)) + 1;
        k2.height = Math.max(height(k2.left), height(k2.right)) + 1;
        return k2;
    }
    private AvlNode<AnyType> remove(AnyType x,AvlNode<AnyType> t) {
        if (t == null)
            return t;
        int compareResult = x.compareTo(t.element);
        if (compareResult < 0) {
            t.left = remove(x,t.left);
        }else if (compareResult > 0) {
            t.right = remove(x,t.right);
        }else if (t.left != null && t.right != null) {
            t.element = findMin(t.right).element;
            t.right = remove(t.element,t.right);
        }else
            t = (t.left != null) ? t.left : t.right;
        return balance(t);
    }
    private AvlNode<AnyType> findMin(AvlNode<AnyType> t){
        if(t == null){
            return t;
        }
        while(t.left != null){
            t = t.left;
        }
        return t;
}
}