面试基础知识整理 —— 二叉搜索树

来源：互联网发布：2013excel不能粘贴数据编辑：程序博客网时间：2024/05/17 09:14

1. 定义

二叉查找树（英语：Binary Search Tree），也称二叉搜索树、有序二叉树（英语：ordered binary tree），排序二叉树（英语：sorted binary tree），是指一棵空树或者具有下列性质的二叉树：

若任意节点的左子树不空，则左子树上所有结点的值均小于它的根结点的值；

若任意节点的右子树不空，则右子树上所有结点的值均大于它的根结点的值；

任意节点的左、右子树也分别为二叉查找树；

没有键值相等的节点。

摘自维基百科二叉搜索树

2. 实现

二叉搜索树节点

package tree;/** * Created by song on 4/8/17. * * 二叉搜索树节点 */public class BinaryNode<T extends Comparable> {    private T value;    private BinaryNode<T> left;    private BinaryNode<T> right;    public BinaryNode() {        /*do nothing*/    }    public BinaryNode(T value) {        this(value, null, null);    }    public BinaryNode(T value, BinaryNode<T> left, BinaryNode<T> right) {        this.value = value;        this.left = left;        this.right = right;    }    public T getValue() {        return value;    }    public void setValue(T value) {        this.value = value;    }    public BinaryNode<T> getLeft() {        return left;    }    public void setLeft(BinaryNode<T> left) {        this.left = left;    }    public BinaryNode<T> getRight() {        return right;    }    public void setRight(BinaryNode<T> right) {        this.right = right;    }}

二叉搜索树

package tree;/** * Created by song on 4/8/17. * <p> * 二叉搜索树 */public class BinarySearchTree<T extends Comparable> {    private BinaryNode<T> root;    public BinarySearchTree() {        this(null);    }    public BinarySearchTree(BinaryNode<T> root) {        this.root = root;    }    public boolean isEmpty() {        return this.root == null;    }    public void clean() {        this.root = null;    }    public T find(T t) {        return valueAt(find(t, root));    }    public T findMin() {        return valueAt(findMin(root));    }    public T findMax() {        return valueAt(findMax(root));    }    public void insert(T t) {        root = insert(t, root);    }    public void remove(T t) {        root = remove(t, root);    }    public void printTree() {    }    private T valueAt(BinaryNode<T> node) {        return node == null ? null : node.getValue();    }    @SuppressWarnings("unchecked")    private BinaryNode<T> find(T x, BinaryNode<T> node) {        if (node == null) {            return null;        }        if (x.compareTo(node.getValue()) < 0) {            return find(x, node.getLeft());        } else if (x.compareTo(node.getValue()) > 0) {            return find(x, node.getRight());        } else {            return node;        }    }    private BinaryNode<T> findMin(BinaryNode<T> node) {        if (node == null) {            return null;        }        if (node.getLeft() == null) {            return node;        }        return findMin(node.getLeft());    }    private BinaryNode<T> findMax(BinaryNode<T> node) {        if (node == null) {            return null;        }        if (node.getRight() == null) {            return node;        }        return findMax(node.getRight());    }    @SuppressWarnings("unchecked")    private BinaryNode<T> insert(T t, BinaryNode<T> node) {        if (node == null) {            node = new BinaryNode<>(t, null, null);        }        if (t.compareTo(node.getValue()) < 0) {            node = insert(t, node.getLeft());        } else if (t.compareTo(node.getValue()) > 0) {            node = insert(t, node.getRight());        } else {            throw new RuntimeException("duplicate node");        }        return node;    }    @SuppressWarnings("unchecked")    private BinaryNode<T> remove(T t, BinaryNode<T> node) {        if (node == null) {            return null;        }        if (t.compareTo(node.getValue()) < 0) {            node.setLeft(remove(t, node.getLeft()));        } else if (t.compareTo(node.getValue()) > 0) {            node.setRight(remove(t, node.getRight()));        } else if (node.getLeft() != null && node.getRight() != null) {            node.setValue(findMin(node.getRight()).getValue());            node.setRight(remove(node.getValue(), node.getRight()));        } else {            node = (node.getLeft() != null) ? node.getLeft() : node.getRight();        }        return node;    }}

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