二叉树之数据结构

二叉搜索树的概念

二叉搜索树相关的操作

import java.util.LinkedList;
import java.util.Queue;
import java.util.Stack;

public class BST<E extends Comparable<E>> {
    private class Node{
        public E e;
        public Node left,right;

        public Node(E e){
            this.e = e;
            left = null;
            right = null;
        }
    }

    private Node root;
    private int size;

    public BST(){
        root = null;
        size = 0;
    }

    public int size(){
        return size;
    }

    public boolean isEmpty(){
        return size == 0;
    }

    //向二叉树中添加元素
    public void add(E e ){
        root = this.add(root,e);
    }
    //向以node为根的二分搜索树中插入元素e，递归算法。
    //返回插入新节点后二分搜索树的根。
    private Node add(Node node,E e){
        if(node == null){
            node = new Node(e);
        }

        if(e.compareTo(node.e) < 0){
            node.left = this.add(node.left,e);
        }else if(e.compareTo(node.e) > 0){
            node.right = this.add(node.right,e);
        }

        return node;
    }
    //看二分搜索树中是否包含元素e
    public boolean contains(E e){
        return contains(root,e);
    }
    //看以node为根的二分搜索树中是否包含元素e，递归算法
    private boolean contains(Node node, E e){
        if(node == null){
            return false;
        }

        if(e.compareTo(node.e) == 0){
            return true;
        }
        else if(e.compareTo(node.e) > 0){
            return this.contains(node.right,e);
        }
        else{
            return this.contains(node.left,e);
        }
    }

    //二分搜索树的前序遍历
    public void preOrder(){
        preOrder(root);
    }
    //前序遍历以node为根的二分搜索树，递归算法
    private void preOrder(Node node){
        if(node == null){
            return;
        }
        System.out.println(node.e);
        this.preOrder(node.left);
        this.preOrder(node.right);
    }
    //二分搜索树的非递归前序遍历
    public void preOrderNR(){
        Stack<Node> stack = new Stack<>();
        stack.push(root);
        while(!stack.isEmpty()){
            Node cur = stack.pop();
            if(cur.right != null){
                stack.push(cur.right);
            }
            if(cur.left != null){
                stack.push(cur.left);
            }
        }
    }

    //二分搜索树的中序遍历
    public void inOrder(){
        inOrder(root);
    }
    //二分搜索树的中序遍历
    private void inOrder(Node node){
        if(node == null){
            return;
        }
        inOrder(node.left);
        System.out.println(node.e);
        inOrder(node.right);
    }


    //二分搜索树的后序遍历
    public void postOrder(){
        this.postOrder(root);
    }

    private void postOrder(Node node){
        if(node == null){
            return;
        }
        this.postOrder(node.left);
        System.out.println(node.e);
        this.postOrder(node.right);
    }

    //二分搜索树的层序遍历
    public void levelOrder(){
        Queue<Node> q = new LinkedList<>();
        q.add(root);
        while(!q.isEmpty()){
            Node cur = q.remove();
            System.out.println(cur.e);

            if(cur.left != null){
                q.add(cur.left);
            }
            if(cur.right != null){
                q.add(cur.right);
            }
        }
    }

    //搜索二分搜索树的最小元素
    public E minimum(){
        if(size == 0){
            throw new IllegalArgumentException("BST is empty");
        }

        return minimum(root).e;
    }

    //返回以node为根的二分搜索树的最小值所在的节点
    private Node minimum(Node node){
        if(node.left == null){
            return node;
        }
        return minimum(node.left);
    }

    public E maximum(){
        if(size == 0){
            throw new IllegalArgumentException("BST is empty");
        }
        return maximum(root).e;
    }
    //返回以node为根的二分搜索树的最大值所在的节点
    private Node maximum(Node node){
        if(node.right == null){
            return node;
        }

        return maximum(node.right);
    }

    //从二分搜索树中删除最小值所在的节点，返回最小值
    public E removeMin(){
        E ret = minimum();
        root = removeMin(root);
        return ret;
    }

    private Node removeMin(Node node){
        if(node.left == null){
            Node rightNode = node.right;
            node.right = null;
            size --;
            return rightNode;
        }
        //删除掉以node为根的二分搜索树中的最小节点
        //返回删除节点之后新的二分搜索树的根。
        node.left = removeMin(node.left);
        return node;
    }

    public E removeMax(){
        E ret = maximum();
        root = removeMax(root);
        return ret;
    }

    private Node removeMax(Node node){
        if(node.right == null){
            Node leftNode = node.left;
            node.left = null;
            size--;
            return leftNode;
        }

        node.right = removeMax(node.right);
        return node;
    }

    //从二分搜索树中删除元素为e的节点
    public void remove(E e){
        root = remove(root,e);
    }
    //删除掉以node为根的二分搜索树中值为e的节点，递归算法
    //返回删除节点后新的二分搜索树的根。
    private Node remove(Node node, E  e){
        if(node == null){
            return null;
        }

        if(e.compareTo(node.e) < 0){
            node.left = remove(node.left,e);
            return node;
        }else if(e.compareTo(node.e) > 0){
            node.right = remove(node.right,e);
            return node;
        }else{
            if(node.left == null){
                Node rightNode = node.right;
                node.right = null;
                size--;
                return rightNode;
            }
            if(node.right == null){
                Node leftNode = node.left;
                node.left = null;
                size--;
                return leftNode;
            }

            //待删除节点左右子树都不为空

            //找到比待删除节点大的最小节点，即删除节点右子树的最小节点
            //用这个节点顶替待删除的节点
            Node successor = minimum(node.right);
            successor.right = removeMin(node.right);
            successor.left = node.left;
            node.left = node.right = null;
            return successor;

        }
    }
}