Java实现 二叉搜索树算法(BST)
作者:李强强(泥瓦匠)
“岁月极美,在于它必然的流逝”
“春花 秋月 夏日 冬雪”
— 三毛
一、树 & 二叉树
树是由节点和边构成,储存元素的集合。节点分根节点、父节点和子节点的概念。
如图:树深=4; 5是根节点;同样8与3的关系是父子节点关系。
二叉树binary tree,则加了“二叉”(binary),意思是在树中作区分。每个节点至多有两个子(child),left child & right child。二叉树在很多例子中使用,比如二叉树表示算术表达式。
如图:1/8是左节点;2/3是右节点;
二、二叉搜索树 BST
顾名思义,二叉树上又加了个搜索的限制。其要求:每个节点比其左子树元素大,比其右子树元素小。
如图:每个节点比它左子树的任意节点大,而且比它右子树的任意节点小
三、BST Java实现
直接上代码,对应代码分享在 Github 主页
BinarySearchTree.java
package org.algorithm.tree; /* * Copyright [2015] [Jeff Lee] * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ /** * 二叉搜索树(BST)实现 * * Created by bysocket on 16/7/7. */ public class BinarySearchTree { /** * 根节点 */ public static TreeNode root; public BinarySearchTree() { this.root = null; } /** * 查找 * 树深(N) O(lgN) * 1. 从root节点开始 * 2. 比当前节点值小,则找其左节点 * 3. 比当前节点值大,则找其右节点 * 4. 与当前节点值相等,查找到返回TRUE * 5. 查找完毕未找到, * @param key * @return */ public TreeNode search (int key) { TreeNode current = root; while (current != null && key != current.value) { if (key < current.value ) current = current.left; else current = current.right; } return current; } /** * 插入 * 1. 从root节点开始 * 2. 如果root为空,root为插入值 * 循环: * 3. 如果当前节点值大于插入值,找左节点 * 4. 如果当前节点值小于插入值,找右节点 * @param key * @return */ public TreeNode insert (int key) { // 新增节点 TreeNode newNode = new TreeNode(key); // 当前节点 TreeNode current = root; // 上个节点 TreeNode parent = null; // 如果根节点为空 if (current == null) { root = newNode; return newNode; } while (true) { parent = current; if (key < current.value) { current = current.left; if (current == null) { parent.left = newNode; return newNode; } } else { current = current.right; if (current == null) { parent.right = newNode; return newNode; } } } } /** * 删除节点 * 1.找到删除节点 * 2.如果删除节点左节点为空 , 右节点也为空; * 3.如果删除节点只有一个子节点 右节点 或者 左节点 * 4.如果删除节点左右子节点都不为空 * @param key * @return */ public TreeNode delete (int key) { TreeNode parent = root; TreeNode current = root; boolean isLeftChild = false; // 找到删除节点 及 是否在左子树 while (current.value != key) { parent = current; if (current.value > key) { isLeftChild = true; current = current.left; } else { isLeftChild = false; current = current.right; } if (current == null) { return current; } } // 如果删除节点左节点为空 , 右节点也为空 if (current.left == null && current.right == null) { if (current == root) { root = null; } // 在左子树 if (isLeftChild == true) { parent.left = null; } else { parent.right = null; } } // 如果删除节点只有一个子节点 右节点 或者 左节点 else if (current.right == null) { if (current == root) { root = current.left; } else if (isLeftChild) { parent.left = current.left; } else { parent.right = current.left; } } else if (current.left == null) { if (current == root) { root = current.right; } else if (isLeftChild) { parent.left = current.right; } else { parent.right = current.right; } } // 如果删除节点左右子节点都不为空 else if (current.left != null && current.right != null) { // 找到删除节点的后继者 TreeNode successor = getDeleteSuccessor(current); if (current == root) { root = successor; } else if (isLeftChild) { parent.left = successor; } else { parent.right = successor; } successor.left = current.left; } return current; } /** * 获取删除节点的后继者 * 删除节点的后继者是在其右节点树种最小的节点 * @param deleteNode * @return */ public TreeNode getDeleteSuccessor(TreeNode deleteNode) { // 后继者 TreeNode successor = null; TreeNode successorParent = null; TreeNode current = deleteNode.right; while (current != null) { successorParent = successor; successor = current; current = current.left; } // 检查后继者(不可能有左节点树)是否有右节点树 // 如果它有右节点树,则替换后继者位置,加到后继者父亲节点的左节点. if (successor != deleteNode.right) { successorParent.left = successor.right; successor.right = deleteNode.right; } return successor; } public void toString(TreeNode root) { if (root != null) { toString(root.left); System.out.print("value = " + root.value + " -> "); toString(root.right); } } } /** * 节点 */ class TreeNode { /** * 节点值 */ int value; /** * 左节点 */ TreeNode left; /** * 右节点 */ TreeNode right; public TreeNode(int value) { this.value = value; left = null; right = null; } }
1. 节点数据结构
首先定义了节点的数据接口,节点分左节点和右节点及本身节点值。如图
代码如下:
/** * 节点 */ class TreeNode { /** * 节点值 */ int value; /** * 左节点 */ TreeNode left; /** * 右节点 */ TreeNode right; public TreeNode(int value) { this.value = value; left = null; right = null; } }
2. 插入
插入,和删除一样会引起二叉搜索树的动态变化。插入相对删处理逻辑相对简单些。如图插入的逻辑:
a. 从root节点开始
b.如果root为空,root为插入值
c.循环:
d.如果当前节点值大于插入值,找左节点
e.如果当前节点值小于插入值,找右节点
代码对应:
/** * 插入 * 1. 从root节点开始 * 2. 如果root为空,root为插入值 * 循环: * 3. 如果当前节点值大于插入值,找左节点 * 4. 如果当前节点值小于插入值,找右节点 * @param key * @return */ public TreeNode insert (int key) { // 新增节点 TreeNode newNode = new TreeNode(key); // 当前节点 TreeNode current = root; // 上个节点 TreeNode parent = null; // 如果根节点为空 if (current == null) { root = newNode; return newNode; } while (true) { parent = current; if (key < current.value) { current = current.left; if (current == null) { parent.left = newNode; return newNode; } } else { current = current.right; if (current == null) { parent.right = newNode; return newNode; } } } }
3.查找
其算法复杂度 : O(lgN),树深(N)。如图查找逻辑:
a.从root节点开始
b.比当前节点值小,则找其左节点
c.比当前节点值大,则找其右节点
d.与当前节点值相等,查找到返回TRUE
e.查找完毕未找到
代码对应:
/** * 查找 * 树深(N) O(lgN) * 1. 从root节点开始 * 2. 比当前节点值小,则找其左节点 * 3. 比当前节点值大,则找其右节点 * 4. 与当前节点值相等,查找到返回TRUE * 5. 查找完毕未找到, * @param key * @return */ public TreeNode search (int key) { TreeNode current = root; while (current != null && key != current.value) { if (key < current.value ) current = current.left; else current = current.right; } return current; }
4. 删除
首先找到删除节点,其寻找方法:删除节点的后继者是在其右节点树种最小的节点。如图删除对应逻辑:
结果为:
a.找到删除节点
b.如果删除节点左节点为空 , 右节点也为空;
c.如果删除节点只有一个子节点 右节点 或者 左节点
d.如果删除节点左右子节点都不为空
代码对应见上面完整代码。
案例测试代码如下,BinarySearchTreeTest.java
package org.algorithm.tree; /* * Copyright [2015] [Jeff Lee] * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ /** * 二叉搜索树(BST)测试案例 {@link BinarySearchTree} * * Created by bysocket on 16/7/10. */ public class BinarySearchTreeTest { public static void main(String[] args) { BinarySearchTree b = new BinarySearchTree(); b.insert(3);b.insert(8);b.insert(1);b.insert(4);b.insert(6); b.insert(2);b.insert(10);b.insert(9);b.insert(20);b.insert(25); // 打印二叉树 b.toString(b.root); System.out.println(); // 是否存在节点值10 TreeNode node01 = b.search(10); System.out.println("是否存在节点值为10 => " + node01.value); // 是否存在节点值11 TreeNode node02 = b.search(11); System.out.println("是否存在节点值为11 => " + node02); // 删除节点8 TreeNode node03 = b.delete(8); System.out.println("删除节点8 => " + node03.value); b.toString(b.root); } }
运行结果如下:
value = 1 -> value = 2 -> value = 3 -> value = 4 -> value = 6 -> value = 8 -> value = 9 -> value = 10 -> value = 20 -> value = 25 -> 是否存在节点值为10 => 10 是否存在节点值为11 => null 删除节点8 => 8 value = 1 -> value = 2 -> value = 3 -> value = 4 -> value = 6 -> value = 9 -> value = 10 -> value = 20 -> value = 25 ->
四、小结
与偶尔吃一碗“老坛酸菜牛肉面”一样的味道,品味一个算法,比如BST,的时候,总是那种说不出的味道。
树,二叉树的概念
BST算法
相关代码分享在 Github 主页
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