需求

自己實現一個簡單的二叉查詢樹BinarySearchTree

二叉排序樹或者是一棵空樹，或者是具有下列性質的二叉樹：

• 若左子樹不空，則左子樹上所有結點的值均小於或等於它的根結點的值；
• 若右子樹不空，則右子樹上所有結點的值均大於或等於它的根結點的值；
• 左、右子樹也分別為二叉排序樹；

圖示

包含功能：

• insert
• remove
• contains
• findMax
• findMin
• toString

程式碼：

import java.util.NoSuchElementException;
import java.util.StringJoiner;

public
 
 class BinarySearchTree<T extends Comparable<? super T>> {
    private BinaryNode<T> root;

    public BinarySearchTree() {
        root = null;
    }

    public BinarySearchTree(T[] arr) {
        for (T t : arr) {
            insert(t);
        }
    }

    public void markEmpty
 
() {
        root = null;
    }

    public boolean isEmpty() {
        return root == null;
    }

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

    public T findMin() {
        if (isEmpty())
            throw new NoSuchElementException();
        return findMin(root).element;
    }

    public
 
 T findMax() {
        if (isEmpty())
            throw new NoSuchElementException();
        return findMax(root).element;
    }

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

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

    @Override
    public String toString() {
        StringJoiner joiner = new StringJoiner(" ", "[", "]");
        listAll(this.root, joiner);
        return joiner.toString();
    }

    private void listAll(BinaryNode<T> node, StringJoiner joiner) {
        if (node.left != null)
            listAll(node.left, joiner);
        joiner.add(node.element.toString());
        if (node.right != null)
            listAll(node.right, joiner);
    }

    private boolean contains(T t, BinaryNode<T> node) {
        if (node == null)
            return false;
        int compareResult = t.compareTo(node.element);
        if (compareResult < 0)
            return contains(t, node.left);
        else if (compareResult > 0)
            return contains(t, node.right);
        else
            return true;
    }

    private BinaryNode<T> findMin(BinaryNode<T> node) {
        if (node == null)
            return null;
        if (node.left == null)
            return node;
        return findMin(node.left);
    }

    private BinaryNode<T> findMax(BinaryNode<T> node) {
        if (node == null)
            return null;
        while (node.right != null)
            node = node.right;
        return node;
    }

    private BinaryNode<T> insert(T t, BinaryNode<T> node) {
        if (node == null)
            return new BinaryNode<T>(t);
        int compareResult = t.compareTo(node.element);
        if (compareResult < 0)
            node.left = insert(t, node.left);
        else if (compareResult > 0)
            node.right = insert(t, node.right);
        return node;
    }

    private BinaryNode<T> remove(T t, BinaryNode<T> node) {
        if (node == null)
            return null;
        int compareResult = t.compareTo(node.element);
        if (compareResult < 0) {
            node.left = remove(t, node.left);
        } else if (compareResult > 0) {
            node.right = remove(t, node.right);
        } else if (node.left != null && node.right != null) {
            // two children
            node.element = findMin(node.right).element;
            node.right = remove(node.element, node.right);
        } else {
            node = (node.left != null) ? node.left : node.right;
        }

        return node;
    }

    private static class BinaryNode<T> {
        T element;
        BinaryNode<T> left;
        BinaryNode<T> right;

        public BinaryNode(T element) {
            this(element, null, null);
        }

        public BinaryNode(T element, BinaryNode<T> left, BinaryNode<T> right) {
            this.element = element;
            this.left = left;
            this.right = right;
        }
    }
}