AVL树实现

最新推荐文章于 2025-05-11 15:55:14 发布

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本文详细介绍了AVL树的Java实现，包括插入、删除、查找等核心操作，并提供了完整的代码示例。AVL树是一种自平衡的二叉搜索树，能够保持树的高度平衡，从而确保树的操作效率。

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public class Avl<T extends Comparable<? super T>> {
    private AvlNode root;
    private static final int ALLOWED_IMBALANCE = 1;



    public  Avl(){
        this.root=null;
    }

    private static class AvlNode<T>{
        T element;
        AvlNode<T> left;
        AvlNode<T> right;
        int height;

        AvlNode(T theElement){
            this(theElement,null,null);

        }

        AvlNode(T theElement,AvlNode<T> lt,AvlNode<T> rt){
            left=lt;
            right=rt;
            element=theElement;
            height=0;
        }
    }

    public void insert(T x){
        root=insert(x,root);
    }

    private AvlNode<T> insert(T x,AvlNode<T> 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<T> balance(AvlNode<T> 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=rotateWithRightChild(t);
            }else{
                t=doubleWithRightChild(t);
            }
        }

        t.height = Math.max( height( t.left ), height( t.right ) ) + 1;
        return t;



    }

    private AvlNode<T> rotateWithLeftChild(AvlNode<T> k2){
        AvlNode<T> 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<T> rotateWithRightChild(AvlNode<T> k1){
        AvlNode<T> 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.right),k1.height)+1;

        return k2;
    }

    private AvlNode<T> doubleWithLeftChild(AvlNode<T> k3){
        k3.left=rotateWithRightChild(k3.left);
        return rotateWithLeftChild(k3);
    }

    private AvlNode<T> doubleWithRightChild(AvlNode<T> k1){
        k1.right=rotateWithLeftChild(k1.right);
        return rotateWithRightChild(k1);
    }

    private int height(AvlNode<T> t){
        return t==null?-1:t.height;
    }

    public void remove( T x ) {
        root = remove( x, root );
    }

    private AvlNode<T> remove(T x,AvlNode<T> t){
        if(t==null){
            return null;
        }

        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<T> findMin(AvlNode<T> t){
        if(t==null){
            return null;
        }

        while (t.left!=null){
            t=t.left;
        }

        return t;
    }

    private AvlNode<T> findMax(AvlNode<T> t){
        if(t==null){
            return null;
        }

        while (t.right!=null){
            t=t.right;
        }

        return t;
    }

    public boolean contains(T x){
        return contains(x,root);
    }

    private boolean contains(T x,AvlNode<T> t){
        while (t!=null){
            int compareResult=x.compareTo(t.element);
            if(compareResult<0){
                t=t.left;
            }else if(compareResult>0){
                t=t.right;
            }else{
                return true;
            }
        }

        return false;
    }

    private void printTree(AvlNode<T> t){
        if(t!=null){
            printTree(t.left);
            System.out.println(t.element);
            printTree(t.right);
        }
    }


}