Java实现二叉搜索树

一、二叉搜索树概念

​ 二叉搜索树（Binary Search Tree,BST），相比与普通树，有以下四点性质

• 非空左子树的所有键值小于其根结点的键值；
• 非空右子树的所有键值大于其根结点的键值；
• 左右子树均为二叉搜索树；
• 树中没有键值相等的结点。

​ 因为性质特殊，所以在查询的时候十分便捷。

二、二叉搜索树常规操作

• Position Find(TreeNode X,BinarySearchTree BST) 从二叉搜索树中找到节点 X并返回其地址。
• Position FindMin(BinarySearchTree BST) 从二叉搜索树中找到最小节点 X并返回其地址。
• Position FindMan(BinarySearchTree BST) 从二叉搜索树中找到最大节点 X并返回其地址。
• BinarySearchTree Insert(TreeNode X,BinarySearchTree BST) 在二叉搜索树中插入节点 X并返回二叉搜索树。
• BinarySearchTree Delete(TreeNode X,BinarySearchTree BST) 在二叉搜索树中删除节点 X并返回二叉搜索树。

三、TreeNode 存储结构实现

package org.example.bcbd;/*** @ClassName TreeNode* @Description TODO* @Author 枫飘长安* @Date 2024/4/16 20:49* @Version 1.0**/public class TreeNode<T extends Comparable<T>> {// 数据域private T data;// 左子树public TreeNode leftChild;// 右子树public TreeNode rightChild;public TreeNode(T data) {this(null, data, null);}public TreeNode(TreeNode leftChild, T data, TreeNode rightChild) {this.leftChild = leftChild;this.data = data;this.rightChild = rightChild;}public T getData() {return data;}public TreeNode<T> getLeftChild() {return leftChild;}public TreeNode<T> getRightChild() {return rightChild;}public void setData(T data) {this.data = data;}private TreeNode<T> insert(TreeNode<T> node,T value) {if (node == null) {return  new TreeNode<>(value);} else {if (compare(node,value) < 0) {node.leftChild = insert(node.getLeftChild(),value);}else if (compare(node,value) > 0) {node.rightChild = insert(node.getRightChild(),value);}return node;}}private int compare(TreeNode<T> node,T value) {return value.compareTo(node.getData());}}

四、二叉搜索树及其常规操作实现

1. 二叉搜索树插入

Tips: 因为其特殊性质，我们很容易用递归实现插入操作

每次插入一个结点，从根节点出发作比较，小的往左子树插，大的往右子树插。

    public void insert(T value) {if (value == null) {return;}this.root = insert(this.root, value);}private TreeNode<T> insert(TreeNode<T> node, T value) {if (node == null) {return new TreeNode<>(value);}else {if (compare(node, value) < 0) {node.leftChild = insert(node.getLeftChild(), value);}else if (compare(node,value) > 0) {node.rightChild = insert(node.getRightChild(), value);}}return node;}

2.二叉搜索树查找

Tips:在一颗二叉搜索树上，最小的值一定在最左边的结点上，最大值一定在最右边的结点上。查找二叉树最值递归实现即可。在查找特定值时注意如果查找的元素不在树中，我们得对其做出异常处理

    public TreeNode<T> find(T value) {if (this.root == null) return null;return find(this.root, value);}private TreeNode<T> find(TreeNode<T> node, T value) {if (node == null) throw new RuntimeException("the value must not in the tree");if (compare(node, value) < 0) {return find(node.getLeftChild(), value);}else if (compare(node,value) > 0) {return find(node.getRightChild(), value);}else {return node;}}public T findMax() {if (this.root == null) return null;return findMax(this.root);}private T findMax(TreeNode<T> node) {TreeNode<T> temp = node;while (temp.getRightChild() != null) {temp = temp.getRightChild();}return temp.getData();}public T findMin() {if (this.root == null) return null;return findMin(this.root);}private T findMin(TreeNode<T> node) {TreeNode<T> temp = node;while (temp.getLeftChild() != null) {temp = temp.getLeftChild();}return temp.getData();}

3.二叉搜索树删除

Tips: 删除是最难的操作了，因为删掉节点后，整棵树仍然需要为二叉搜索树

• 叶子结点：直接删除，其父结点指向null
• 包含一个孩子的结点 ：父结点指向要删除结点的自结点（相当于链表中间删除一个元素）；
• 包含左右子树的结点：右子树最小值或左子树最大值替换此结点

    public void delete(T value) {if (this.root == null || value == null) return;this.root = delete(this.root, value);}public TreeNode<T> delete(TreeNode<T> node, T value) {if (node == null) return null;if (compare(node, value) < 0) { // 去删左子树node.leftChild = delete(node.getLeftChild(), value);}else if (compare(node, value) > 0) { // 去删右子树node.rightChild = delete(node.getRightChild(), value);}else { // 找到要删除的节点if (node.getLeftChild() != null && node.getRightChild() != null) {// 被删除的结点，包含左右子树T temp = findMin(node.getRightChild()); // 得到右子树的最小值node.setData(temp); //右子树最小值替换当前结点node.rightChild = delete(node.getRightChild(), temp); // 从右子树删除这个最小值的结点} else {// 被删除的结点，包含一个子树或没有子树if (node.getLeftChild() != null) {node = node.getLeftChild();} else {node = node.getRightChild();}}}return node;}

4.二叉搜索树高度

Tips: 就是求树的高度，没什么好讲的。

    public int getTreeHeight() {if (this.root == null) return 0;return getTreeHeight(this.root);}private int getTreeHeight(TreeNode<T> node) {if (node == null) return 0;int leftHeight = getTreeHeight(node.getLeftChild());int rightHeight = getTreeHeight(node.getRightChild());return Math.max(leftHeight, rightHeight) + 1;}

5. 中序遍历打印二叉搜索树

    public void printTree() {printTree(this.root);}private void printTree(TreeNode<T> node) {if (node == null) {return;}printTree(node.getLeftChild());System.out.print(node.getData() + " ");printTree(node.getRightChild());}

五、BinarySearchTree完整代码

package org.example.bcbd; // 包名请按照自己的程序设置/*** @ClassName BinarySearchTree* @Description TODO* @Author 枫飘长安* @Date 2024/4/16 20:59* @Version 1.0**/
public class BinarySearchTree<T extends Comparable<T>> {private TreeNode<T> root;public BinarySearchTree() {this.root = null;}public BinarySearchTree(TreeNode<T> root) {this.root = root;}public void insert(T value) {if (value == null) {return;}this.root = insert(this.root, value);}private TreeNode<T> insert(TreeNode<T> node, T value) {if (node == null) {return new TreeNode<>(value);}else {if (compare(node, value) < 0) {node.leftChild = insert(node.getLeftChild(), value);}else if (compare(node,value) > 0) {node.rightChild = insert(node.getRightChild(), value);}}return node;}private int compare(TreeNode<T> node, T value) {return value.compareTo(node.getData());}public void printTree() {printTree(this.root);}private void printTree(TreeNode<T> node) {if (node == null) {return;}printTree(node.getLeftChild());System.out.print(node.getData() + " ");printTree(node.getRightChild());}public T findMax() {if (this.root == null) return null;return findMax(this.root);}private T findMax(TreeNode<T> node) {TreeNode<T> temp = node;while (temp.getRightChild() != null) {temp = temp.getRightChild();}return temp.getData();}public T findMin() {if (this.root == null) return null;return findMin(this.root);}private T findMin(TreeNode<T> node) {TreeNode<T> temp = node;while (temp.getLeftChild() != null) {temp = temp.getLeftChild();}return temp.getData();}public TreeNode<T> find(T value) {if (this.root == null) return null;return find(this.root, value);}private TreeNode<T> find(TreeNode<T> node, T value) {if (node == null) throw new RuntimeException("the value must not in the tree");if (compare(node, value) < 0) {return find(node.getLeftChild(), value);}else if (compare(node,value) > 0) {return find(node.getRightChild(), value);}else {return node;}}public int getTreeHeight() {if (this.root == null) return 0;return getTreeHeight(this.root);}private int getTreeHeight(TreeNode<T> node) {if (node == null) return 0;int leftHeight = getTreeHeight(node.getLeftChild());int rightHeight = getTreeHeight(node.getRightChild());return Math.max(leftHeight, rightHeight) + 1;}public void delete(T value) {if (this.root == null || value == null) return;this.root = delete(this.root, value);}public TreeNode<T> delete(TreeNode<T> node, T value) {if (node == null) return null;if (compare(node, value) < 0) { // 去删左子树node.leftChild = delete(node.getLeftChild(), value);}else if (compare(node, value) > 0) { // 去删右子树node.rightChild = delete(node.getRightChild(), value);}else { // 找到要删除的节点if (node.getLeftChild() != null && node.getRightChild() != null) {// 被删除的结点，包含左右子树T temp = findMin(node.getRightChild()); // 得到右子树的最小值node.setData(temp); //右子树最小值替换当前结点node.rightChild = delete(node.getRightChild(), temp); // 从右子树删除这个最小值的结点} else {// 被删除的结点，包含一个子树或没有子树if (node.getLeftChild() != null) {node = node.getLeftChild();} else {node = node.getRightChild();}}}return node;}
}