Java实现 二叉搜索树算法（BST）

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/*
* 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：

<span style="font-family:Microsoft YaHei, 宋体, Myriad Pro, Lato, Helvetica Neue, Helvetica, Arial, sans-serif;"><span style="font-size: 14px; line-height: 21px;"></span></span><pre name="code" class="java">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

树，二叉树的概念

BST算法

相关代码分享在 Github 主页