From f7ae9c8a024c604d32f65501ee44315f234d52ca Mon Sep 17 00:00:00 2001
From: krahets <krahets@163.com>
Date: Fri, 14 Apr 2023 05:47:20 +0800
Subject: [PATCH] Fix the return type of binary search tree and avl tree

---
 codes/c/chapter_tree/avl_tree.c               | 21 ++++-----
 codes/c/chapter_tree/binary_search_tree.c     | 44 ++++++++-----------
 codes/cpp/chapter_tree/avl_tree.cpp           | 24 ++++------
 codes/cpp/chapter_tree/binary_search_tree.cpp | 42 +++++++-----------
 codes/csharp/chapter_tree/avl_tree.cs         | 24 +++-------
 .../csharp/chapter_tree/binary_search_tree.cs | 42 ++++++------------
 codes/dart/chapter_tree/avl_tree.dart         | 21 +++------
 .../dart/chapter_tree/binary_search_tree.dart | 38 ++++++----------
 codes/go/chapter_tree/avl_tree.go             | 27 ++++--------
 codes/go/chapter_tree/binary_search_tree.go   | 40 ++++++-----------
 .../chapter_tree/binary_search_tree_test.go   |  2 +-
 codes/java/chapter_tree/avl_tree.java         | 22 +++-------
 .../java/chapter_tree/binary_search_tree.java | 30 ++++++-------
 codes/javascript/chapter_tree/avl_tree.js     | 17 ++-----
 .../chapter_tree/binary_search_tree.js        | 36 ++++++---------
 codes/python/chapter_tree/avl_tree.py         | 22 +++-------
 .../python/chapter_tree/binary_search_tree.py | 44 ++++++++-----------
 codes/swift/chapter_tree/avl_tree.swift       | 24 +++-------
 .../chapter_tree/binary_search_tree.swift     | 43 +++++++-----------
 codes/typescript/chapter_tree/avl_tree.ts     | 21 +++------
 .../chapter_tree/binary_search_tree.ts        | 42 +++++++-----------
 codes/zig/chapter_tree/avl_tree.zig           | 25 +++--------
 codes/zig/chapter_tree/binary_search_tree.zig | 41 +++++++----------
 docs/chapter_tree/binary_search_tree.md       |  6 +--
 24 files changed, 247 insertions(+), 451 deletions(-)

diff --git a/codes/c/chapter_tree/avl_tree.c b/codes/c/chapter_tree/avl_tree.c
index 432cd5d7..3a148c3a 100644
--- a/codes/c/chapter_tree/avl_tree.c
+++ b/codes/c/chapter_tree/avl_tree.c
@@ -15,7 +15,7 @@ typedef struct avlTree avlTree;
 
 /* 构建 AVL 树 */
 avlTree *newAVLTree() {
-    avlTree *tree = (avlTree *) malloc(sizeof(avlTree));
+    avlTree *tree = (avlTree *)malloc(sizeof(avlTree));
     tree->root = NULL;
     return tree;
 }
@@ -132,11 +132,9 @@ TreeNode *insertHelper(TreeNode *node, int val) {
     return node;
 }
 
-
 /* 插入节点 */
-TreeNode *insert(avlTree *tree, int val) {
+void insert(avlTree *tree, int val) {
     tree->root = insertHelper(tree->root, val);
-    return tree->root;
 }
 
 /* 获取中序遍历中的下一个节点（仅适用于 root 有左子节点的情况） */
@@ -153,7 +151,7 @@ TreeNode *getInOrderNext(TreeNode *node) {
 
 /* 递归删除节点（辅助方法） */
 TreeNode *removeHelper(TreeNode *node, int val) {
-    TreeNode *child, *grandChild, *temp;
+    TreeNode *child, *grandChild;
     if (node == NULL) {
         return NULL;
     }
@@ -177,9 +175,13 @@ TreeNode *removeHelper(TreeNode *node, int val) {
             }
         } else {
             // 子节点数量 = 2 ，则将中序遍历的下个节点删除，并用该节点替换当前节点
-            temp = getInOrderNext(node->right);
+            TreeNode *temp = node->right;
+            while (temp->left != NULL) {
+                temp = temp->left;
+            }
+            int tempVal = temp->val;
             node->right = removeHelper(node->right, temp->val);
-            node->val = temp->val;
+            node->val = tempVal;
         }
     }
     // 更新节点高度
@@ -192,9 +194,8 @@ TreeNode *removeHelper(TreeNode *node, int val) {
 
 /* 删除节点 */
 // 由于引入了 stdio.h ，此处无法使用 remove 关键词
-TreeNode *removeNode(avlTree *tree, int val) {
+void removeNode(avlTree *tree, int val) {
     TreeNode *root = removeHelper(tree->root, val);
-    return root;
 }
 
 /* 查找节点 */
@@ -232,7 +233,7 @@ void testRemove(avlTree *tree, int val) {
 /* Driver Code */
 int main() {
     /* 初始化空 AVL 树 */
-    avlTree *tree = (avlTree *) newAVLTree();
+    avlTree *tree = (avlTree *)newAVLTree();
     /* 插入节点 */
     // 请关注插入节点后，AVL 树是如何保持平衡的
     testInsert(tree, 1);
diff --git a/codes/c/chapter_tree/binary_search_tree.c b/codes/c/chapter_tree/binary_search_tree.c
index 1039c24f..c207ddd3 100644
--- a/codes/c/chapter_tree/binary_search_tree.c
+++ b/codes/c/chapter_tree/binary_search_tree.c
@@ -69,15 +69,16 @@ TreeNode *search(binarySearchTree *bst, int num) {
 }
 
 /* 插入节点 */
-TreeNode *insert(binarySearchTree *bst, int num) {
+void insert(binarySearchTree *bst, int num) {
     // 若树为空，直接提前返回
-    if (bst->root == NULL) return NULL;
+    if (bst->root == NULL)
+        return;
     TreeNode *cur = bst->root, *pre = NULL;
     // 循环查找，越过叶节点后跳出
     while (cur != NULL) {
         // 找到重复节点，直接返回
         if (cur->val == num) {
-            return NULL;
+            return;
         }
         pre = cur;
         if (cur->val < num) {
@@ -95,24 +96,14 @@ TreeNode *insert(binarySearchTree *bst, int num) {
     } else {
         pre->left = node;
     }
-    return node;
-}
-
-/* 获取中序遍历中的下一个节点（仅适用于 root 有左子节点的情况） */
-TreeNode *getInOrderNext(TreeNode *root) {
-    if (root == NULL) return root;
-    // 循环访问左子节点，直到叶节点时为最小节点，跳出
-    while (root->left != NULL) {
-        root = root->left;
-    }
-    return root;
 }
 
 /* 删除节点 */
 // 由于引入了 stdio.h ，此处无法使用 remove 关键词
-TreeNode *removeNode(binarySearchTree *bst, int num) {
+void removeNode(binarySearchTree *bst, int num) {
     // 若树为空，直接提前返回
-    if (bst->root == NULL) return NULL;
+    if (bst->root == NULL)
+        return;
     TreeNode *cur = bst->root, *pre = NULL;
     // 循环查找，越过叶节点后跳出
     while (cur != NULL) {
@@ -128,9 +119,8 @@ TreeNode *removeNode(binarySearchTree *bst, int num) {
         }
     }
     // 若无待删除节点，则直接返回
-    if (cur == NULL) {
-        return NULL;
-    }
+    if (cur == NULL)
+        return;
     // 判断待删除节点是否存在子节点
     if (cur->left == NULL || cur->right == NULL) {
         /* 子节点数量 = 0 or 1 */
@@ -145,14 +135,16 @@ TreeNode *removeNode(binarySearchTree *bst, int num) {
     } else {
         /* 子节点数量 = 2 */
         // 获取中序遍历中 cur 的下一个节点
-        TreeNode *nex = getInOrderNext(cur->right);
-        int tmp = nex->val;
-        // 递归删除节点 nex
-        removeNode(bst, nex->val);
-        // 将 nex 的值复制给 cur
-        cur->val = tmp;
+        TreeNode *tmp = cur->right;
+        while (tmp->left != NULL) {
+            tmp = tmp->left;
+        }
+        int tmpVal = tmp->val;
+        // 递归删除节点 tmp
+        removeNode(bst, tmp->val);
+        // 用 tmp 覆盖 cur
+        cur->val = tmpVal;
     }
-    return cur;
 }
 
 /* Driver Code */
diff --git a/codes/cpp/chapter_tree/avl_tree.cpp b/codes/cpp/chapter_tree/avl_tree.cpp
index 2cc89459..82e01d44 100644
--- a/codes/cpp/chapter_tree/avl_tree.cpp
+++ b/codes/cpp/chapter_tree/avl_tree.cpp
@@ -93,17 +93,6 @@ class AVLTree {
         return node;
     }
 
-    /* 获取中序遍历中的下一个节点（仅适用于 root 有左子节点的情况） */
-    TreeNode *getInOrderNext(TreeNode *node) {
-        if (node == nullptr)
-            return node;
-        // 循环访问左子节点，直到叶节点时为最小节点，跳出
-        while (node->left != nullptr) {
-            node = node->left;
-        }
-        return node;
-    }
-
     /* 递归删除节点（辅助方法） */
     TreeNode *removeHelper(TreeNode *node, int val) {
         if (node == nullptr)
@@ -128,7 +117,10 @@ class AVLTree {
                 }
             } else {
                 // 子节点数量 = 2 ，则将中序遍历的下个节点删除，并用该节点替换当前节点
-                TreeNode *temp = getInOrderNext(node->right);
+                TreeNode *temp = node->right;
+                while (temp->left != nullptr) {
+                    temp = temp->left;
+                }
                 int tempVal = temp->val;
                 node->right = removeHelper(node->right, temp->val);
                 node->val = tempVal;
@@ -158,15 +150,13 @@ class AVLTree {
     }
 
     /* 插入节点 */
-    TreeNode *insert(int val) {
+    void insert(int val) {
         root = insertHelper(root, val);
-        return root;
     }
 
     /* 删除节点 */
-    TreeNode *remove(int val) {
+    void remove(int val) {
         root = removeHelper(root, val);
-        return root;
     }
 
     /* 查找节点 */
@@ -209,6 +199,8 @@ void testRemove(AVLTree &tree, int val) {
     cout << "\n删除节点 " << val << " 后，AVL 树为" << endl;
     printTree(tree.root);
 }
+
+/* Driver Code */
 int main() {
     /* 初始化空 AVL 树 */
     AVLTree avlTree;
diff --git a/codes/cpp/chapter_tree/binary_search_tree.cpp b/codes/cpp/chapter_tree/binary_search_tree.cpp
index 08bedbef..022afeca 100644
--- a/codes/cpp/chapter_tree/binary_search_tree.cpp
+++ b/codes/cpp/chapter_tree/binary_search_tree.cpp
@@ -59,16 +59,16 @@ class BinarySearchTree {
     }
 
     /* 插入节点 */
-    TreeNode *insert(int num) {
+    void insert(int num) {
         // 若树为空，直接提前返回
         if (root == nullptr)
-            return nullptr;
+            return;
         TreeNode *cur = root, *pre = nullptr;
         // 循环查找，越过叶节点后跳出
         while (cur != nullptr) {
             // 找到重复节点，直接返回
             if (cur->val == num)
-                return nullptr;
+                return;
             pre = cur;
             // 插入位置在 cur 的右子树中
             if (cur->val < num)
@@ -83,14 +83,13 @@ class BinarySearchTree {
             pre->right = node;
         else
             pre->left = node;
-        return node;
     }
 
     /* 删除节点 */
-    TreeNode *remove(int num) {
+    void remove(int num) {
         // 若树为空，直接提前返回
         if (root == nullptr)
-            return nullptr;
+            return;
         TreeNode *cur = root, *pre = nullptr;
         // 循环查找，越过叶节点后跳出
         while (cur != nullptr) {
@@ -107,7 +106,7 @@ class BinarySearchTree {
         }
         // 若无待删除节点，则直接返回
         if (cur == nullptr)
-            return nullptr;
+            return;
         // 子节点数量 = 0 or 1
         if (cur->left == nullptr || cur->right == nullptr) {
             // 当子节点数量 = 0 / 1 时， child = nullptr / 该子节点
@@ -123,25 +122,16 @@ class BinarySearchTree {
         // 子节点数量 = 2
         else {
             // 获取中序遍历中 cur 的下一个节点
-            TreeNode *nex = getInOrderNext(cur->right);
-            int tmp = nex->val;
-            // 递归删除节点 nex
-            remove(nex->val);
-            // 将 nex 的值复制给 cur
-            cur->val = tmp;
+            TreeNode *tmp = cur->right;
+            while (tmp->left != nullptr) {
+                tmp = tmp->left;
+            }
+            int tmpVal = tmp->val;
+            // 递归删除节点 tmp
+            remove(tmp->val);
+            // 用 tmp 覆盖 cur
+            cur->val = tmpVal;
         }
-        return cur;
-    }
-
-    /* 获取中序遍历中的下一个节点（仅适用于 root 有左子节点的情况） */
-    TreeNode *getInOrderNext(TreeNode *root) {
-        if (root == nullptr)
-            return root;
-        // 循环访问左子节点，直到叶节点时为最小节点，跳出
-        while (root->left != nullptr) {
-            root = root->left;
-        }
-        return root;
     }
 };
 
@@ -158,7 +148,7 @@ int main() {
     cout << endl << "查找到的节点对象为 " << node << "，节点值 = " << node->val << endl;
 
     /* 插入节点 */
-    node = bst->insert(16);
+    bst->insert(16);
     cout << endl << "插入节点 16 后，二叉树为\n" << endl;
     printTree(bst->getRoot());
 
diff --git a/codes/csharp/chapter_tree/avl_tree.cs b/codes/csharp/chapter_tree/avl_tree.cs
index 70d3282a..64b7cf37 100644
--- a/codes/csharp/chapter_tree/avl_tree.cs
+++ b/codes/csharp/chapter_tree/avl_tree.cs
@@ -107,10 +107,9 @@ class AVLTree
     }
 
     /* 插入节点 */
-    public TreeNode? insert(int val)
+    public void insert(int val)
     {
         root = insertHelper(root, val);
-        return root;
     }
 
     /* 递归插入节点（辅助方法） */
@@ -132,10 +131,9 @@ class AVLTree
     }
 
     /* 删除节点 */
-    public TreeNode? remove(int val)
+    public void remove(int val)
     {
         root = removeHelper(root, val);
-        return root;
     }
 
     /* 递归删除节点（辅助方法） */
@@ -162,7 +160,11 @@ class AVLTree
             else
             {
                 // 子节点数量 = 2 ，则将中序遍历的下个节点删除，并用该节点替换当前节点
-                TreeNode? temp = getInOrderNext(node.right);
+                TreeNode? temp = node.right;
+                while (temp.left != null)
+                {
+                    temp = temp.left;
+                }
                 node.right = removeHelper(node.right, temp.val);
                 node.val = temp.val;
             }
@@ -174,18 +176,6 @@ class AVLTree
         return node;
     }
 
-    /* 获取中序遍历中的下一个节点（仅适用于 root 有左子节点的情况） */
-    private TreeNode? getInOrderNext(TreeNode? node)
-    {
-        if (node == null) return node;
-        // 循环访问左子节点，直到叶节点时为最小节点，跳出
-        while (node.left != null)
-        {
-            node = node.left;
-        }
-        return node;
-    }
-
     /* 查找节点 */
     public TreeNode? search(int val)
     {
diff --git a/codes/csharp/chapter_tree/binary_search_tree.cs b/codes/csharp/chapter_tree/binary_search_tree.cs
index b4eae044..f3a56d3f 100644
--- a/codes/csharp/chapter_tree/binary_search_tree.cs
+++ b/codes/csharp/chapter_tree/binary_search_tree.cs
@@ -57,16 +57,16 @@ class BinarySearchTree
     }
 
     /* 插入节点 */
-    public TreeNode? insert(int num)
+    public void insert(int num)
     {
         // 若树为空，直接提前返回
-        if (root == null) return null;
+        if (root == null) return;
         TreeNode? cur = root, pre = null;
         // 循环查找，越过叶节点后跳出
         while (cur != null)
         {
             // 找到重复节点，直接返回
-            if (cur.val == num) return null;
+            if (cur.val == num) return;
             pre = cur;
             // 插入位置在 cur 的右子树中
             if (cur.val < num) cur = cur.right;
@@ -81,15 +81,14 @@ class BinarySearchTree
             if (pre.val < num) pre.right = node;
             else pre.left = node;
         }
-        return node;
     }
 
 
     /* 删除节点 */
-    public TreeNode? remove(int num)
+    public void remove(int num)
     {
         // 若树为空，直接提前返回
-        if (root == null) return null;
+        if (root == null) return;
         TreeNode? cur = root, pre = null;
         // 循环查找，越过叶节点后跳出
         while (cur != null)
@@ -103,7 +102,7 @@ class BinarySearchTree
             else cur = cur.left;
         }
         // 若无待删除节点，则直接返回
-        if (cur == null || pre == null) return null;
+        if (cur == null || pre == null) return;
         // 子节点数量 = 0 or 1
         if (cur.left == null || cur.right == null)
         {
@@ -123,29 +122,16 @@ class BinarySearchTree
         else
         {
             // 获取中序遍历中 cur 的下一个节点
-            TreeNode? nex = getInOrderNext(cur.right);
-            if (nex != null)
+            TreeNode? tmp = cur.right;
+            while (tmp.left != null)
             {
-                int tmp = nex.val;
-                // 递归删除节点 nex
-                remove(nex.val);
-                // 将 nex 的值复制给 cur
-                cur.val = tmp;
+                tmp = tmp.left;
             }
+            // 递归删除节点 tmp
+            remove(tmp.val);
+            // 用 tmp 覆盖 cur
+            cur.val = tmp.val;
         }
-        return cur;
-    }
-
-    /* 获取中序遍历中的下一个节点（仅适用于 root 有左子节点的情况） */
-    private TreeNode? getInOrderNext(TreeNode? root)
-    {
-        if (root == null) return root;
-        // 循环访问左子节点，直到叶节点时为最小节点，跳出
-        while (root.left != null)
-        {
-            root = root.left;
-        }
-        return root;
     }
 }
 
@@ -165,7 +151,7 @@ public class binary_search_tree
         Console.WriteLine("\n查找到的节点对象为 " + node + "，节点值 = " + node.val);
 
         /* 插入节点 */
-        node = bst.insert(16);
+        bst.insert(16);
         Console.WriteLine("\n插入节点 16 后，二叉树为\n");
         PrintUtil.PrintTree(bst.getRoot());
 
diff --git a/codes/dart/chapter_tree/avl_tree.dart b/codes/dart/chapter_tree/avl_tree.dart
index 39e7bcb2..379f6868 100644
--- a/codes/dart/chapter_tree/avl_tree.dart
+++ b/codes/dart/chapter_tree/avl_tree.dart
@@ -94,9 +94,8 @@ class AVLTree {
   }
 
   /* 插入节点 */
-  TreeNode? insert(int val) {
+  void insert(int val) {
     root = insertHelper(root, val);
-    return root;
   }
 
   /* 递归插入节点（辅助方法） */
@@ -117,9 +116,8 @@ class AVLTree {
   }
 
   /* 删除节点 */
-  TreeNode? remove(int val) {
+  void remove(int val) {
     root = removeHelper(root, val);
-    return root;
   }
 
   /* 递归删除节点（辅助方法） */
@@ -141,7 +139,10 @@ class AVLTree {
           node = child;
       } else {
         // 子节点数量 = 2 ，则将中序遍历的下个节点删除，并用该节点替换当前节点
-        TreeNode? temp = getInOrderNext(node.right);
+        TreeNode? temp = node.right;
+        while (temp!.left != null) {
+          temp = temp.left;
+        }
         node.right = removeHelper(node.right, temp!.val);
         node.val = temp.val;
       }
@@ -153,16 +154,6 @@ class AVLTree {
     return node;
   }
 
-  /* 获取中序遍历中的下一个节点（仅适用于 root 有左子节点的情况） */
-  TreeNode? getInOrderNext(TreeNode? node) {
-    if (node == null) return node;
-    // 循环访问左子节点，直到叶节点时为最小节点，跳出
-    while (node!.left != null) {
-      node = node.left;
-    }
-    return node;
-  }
-
   /* 查找节点 */
   TreeNode? search(int val) {
     TreeNode? cur = root;
diff --git a/codes/dart/chapter_tree/binary_search_tree.dart b/codes/dart/chapter_tree/binary_search_tree.dart
index a775085c..5c172e54 100644
--- a/codes/dart/chapter_tree/binary_search_tree.dart
+++ b/codes/dart/chapter_tree/binary_search_tree.dart
@@ -53,15 +53,15 @@ TreeNode? search(int num) {
 }
 
 /* 插入节点 */
-TreeNode? insert(int num) {
+void insert(int num) {
   // 若树为空，直接提前返回
-  if (root == null) return null;
+  if (root == null) return;
   TreeNode? cur = root;
   TreeNode? pre = null;
   // 循环查找，越过叶节点后跳出
   while (cur != null) {
     // 找到重复节点，直接返回
-    if (cur.val == num) return null;
+    if (cur.val == num) return;
     pre = cur;
     // 插入位置在 cur 的右子树中
     if (cur.val < num)
@@ -76,13 +76,12 @@ TreeNode? insert(int num) {
     pre.right = node;
   else
     pre.left = node;
-  return node;
 }
 
 /* 删除节点 */
-TreeNode? remove(int num) {
+void remove(int num) {
   // 若树为空，直接提前返回
-  if (root == null) return null;
+  if (root == null) return;
 
   TreeNode? cur = root;
   TreeNode? pre = null;
@@ -99,7 +98,7 @@ TreeNode? remove(int num) {
       cur = cur.left;
   }
   // 若无待删除节点，直接返回
-  if (cur == null) return null;
+  if (cur == null) return;
   // 子节点数量 = 0 or 1
   if (cur.left == null || cur.right == null) {
     // 当子节点数量 = 0 / 1 时， child = null / 该子节点
@@ -112,24 +111,15 @@ TreeNode? remove(int num) {
   } else {
     // 子节点数量 = 2
     // 获取中序遍历中 cur 的下一个节点
-    TreeNode? nex = getInOrderNext(cur.right);
-    int tem = nex!.val;
-    // 递归删除节点 nex
-    remove(nex.val);
-    // 将 nex 的值复制给 cur
-    cur.val = tem;
+    TreeNode? tmp = cur.right;
+    while (tmp!.left != null) {
+      tmp = tmp.left;
+    }
+    // 递归删除节点 tmp
+    remove(tmp.val);
+    // 用 tmp 覆盖 cur
+    cur.val = tmp.val;
   }
-  return cur;
-}
-
-/* 获取中序遍历中的下一个节点（仅适用于 root 有左子节点的情况） */
-TreeNode? getInOrderNext(TreeNode? root) {
-  if (root == null) return null;
-  // 循环访问左子节点，直到叶节点时为最小节点，跳出
-  while (root!.left != null) {
-    root = root.left;
-  }
-  return root;
 }
 
 /* Driver Code */
diff --git a/codes/go/chapter_tree/avl_tree.go b/codes/go/chapter_tree/avl_tree.go
index d57cdff1..b6ba06c6 100644
--- a/codes/go/chapter_tree/avl_tree.go
+++ b/codes/go/chapter_tree/avl_tree.go
@@ -107,9 +107,8 @@ func (t *aVLTree) rotate(node *TreeNode) *TreeNode {
 }
 
 /* 插入节点 */
-func (t *aVLTree) insert(val int) *TreeNode {
+func (t *aVLTree) insert(val int) {
 	t.root = t.insertHelper(t.root, val)
-	return t.root
 }
 
 /* 递归插入节点（辅助方法） */
@@ -135,9 +134,8 @@ func (t *aVLTree) insertHelper(node *TreeNode, val int) *TreeNode {
 }
 
 /* 删除节点 */
-func (t *aVLTree) remove(val int) *TreeNode {
-	root := t.removeHelper(t.root, val)
-	return root
+func (t *aVLTree) remove(val int) {
+	t.root = t.removeHelper(t.root, val)
 }
 
 /* 递归删除节点（辅助方法） */
@@ -156,8 +154,8 @@ func (t *aVLTree) removeHelper(node *TreeNode, val int) *TreeNode {
 			if node.Right != nil {
 				child = node.Right
 			}
-			// 子节点数量 = 0 ，直接删除 node 并返回
 			if child == nil {
+				// 子节点数量 = 0 ，直接删除 node 并返回
 				return nil
 			} else {
 				// 子节点数量 = 1 ，直接删除 node
@@ -165,7 +163,10 @@ func (t *aVLTree) removeHelper(node *TreeNode, val int) *TreeNode {
 			}
 		} else {
 			// 子节点数量 = 2 ，则将中序遍历的下个节点删除，并用该节点替换当前节点
-			temp := t.getInOrderNext(node.Right)
+			temp := node.Right
+			for temp.Left != nil {
+				temp = temp.Left
+			}
 			node.Right = t.removeHelper(node.Right, temp.Val)
 			node.Val = temp.Val
 		}
@@ -178,18 +179,6 @@ func (t *aVLTree) removeHelper(node *TreeNode, val int) *TreeNode {
 	return node
 }
 
-/* 获取中序遍历中的下一个节点（仅适用于 root 有左子节点的情况） */
-func (t *aVLTree) getInOrderNext(node *TreeNode) *TreeNode {
-	if node == nil {
-		return node
-	}
-	// 循环访问左子节点，直到叶节点时为最小节点，跳出
-	for node.Left != nil {
-		node = node.Left
-	}
-	return node
-}
-
 /* 查找节点 */
 func (t *aVLTree) search(val int) *TreeNode {
 	cur := t.root
diff --git a/codes/go/chapter_tree/binary_search_tree.go b/codes/go/chapter_tree/binary_search_tree.go
index a4cb8596..6cb6554e 100644
--- a/codes/go/chapter_tree/binary_search_tree.go
+++ b/codes/go/chapter_tree/binary_search_tree.go
@@ -42,18 +42,6 @@ func (bst *binarySearchTree) getRoot() *TreeNode {
 	return bst.root
 }
 
-/* 获取中序遍历的下一个节点（仅适用于 root 有左子节点的情况） */
-func (bst *binarySearchTree) getInOrderNext(node *TreeNode) *TreeNode {
-	if node == nil {
-		return node
-	}
-	// 循环访问左子节点，直到叶节点时为最小节点，跳出
-	for node.Left != nil {
-		node = node.Left
-	}
-	return node
-}
-
 /* 查找节点 */
 func (bst *binarySearchTree) search(num int) *TreeNode {
 	node := bst.root
@@ -75,18 +63,18 @@ func (bst *binarySearchTree) search(num int) *TreeNode {
 }
 
 /* 插入节点 */
-func (bst *binarySearchTree) insert(num int) *TreeNode {
+func (bst *binarySearchTree) insert(num int) {
 	cur := bst.root
 	// 若树为空，直接提前返回
 	if cur == nil {
-		return nil
+		return
 	}
 	// 待插入节点之前的节点位置
 	var pre *TreeNode = nil
 	// 循环查找，越过叶节点后跳出
 	for cur != nil {
 		if cur.Val == num {
-			return nil
+			return
 		}
 		pre = cur
 		if cur.Val < num {
@@ -102,15 +90,14 @@ func (bst *binarySearchTree) insert(num int) *TreeNode {
 	} else {
 		pre.Left = node
 	}
-	return cur
 }
 
 /* 删除节点 */
-func (bst *binarySearchTree) remove(num int) *TreeNode {
+func (bst *binarySearchTree) remove(num int) {
 	cur := bst.root
 	// 若树为空，直接提前返回
 	if cur == nil {
-		return nil
+		return
 	}
 	// 待删除节点之前的节点位置
 	var pre *TreeNode = nil
@@ -130,7 +117,7 @@ func (bst *binarySearchTree) remove(num int) *TreeNode {
 	}
 	// 若无待删除节点，则直接返回
 	if cur == nil {
-		return nil
+		return
 	}
 	// 子节点数为 0 或 1
 	if cur.Left == nil || cur.Right == nil {
@@ -150,14 +137,15 @@ func (bst *binarySearchTree) remove(num int) *TreeNode {
 		// 子节点数为 2
 	} else {
 		// 获取中序遍历中待删除节点 cur 的下一个节点
-		next := bst.getInOrderNext(cur)
-		temp := next.Val
-		// 递归删除节点 next
-		bst.remove(next.Val)
-		// 将 next 的值复制给 cur
-		cur.Val = temp
+		tmp := cur.Right
+		for tmp.Left != nil {
+			tmp = tmp.Left
+		}
+		// 递归删除节点 tmp
+		bst.remove(tmp.Val)
+		// 用 tmp 覆盖 cur
+		cur.Val = tmp.Val
 	}
-	return cur
 }
 
 /* 打印二叉搜索树 */
diff --git a/codes/go/chapter_tree/binary_search_tree_test.go b/codes/go/chapter_tree/binary_search_tree_test.go
index 4f87ee7a..2733adb1 100644
--- a/codes/go/chapter_tree/binary_search_tree_test.go
+++ b/codes/go/chapter_tree/binary_search_tree_test.go
@@ -24,7 +24,7 @@ func TestBinarySearchTree(t *testing.T) {
 	fmt.Println("查找到的节点对象为", node, "，节点值 =", node.Val)
 
 	// 插入节点
-	node = bst.insert(16)
+	bst.insert(16)
 	fmt.Println("\n插入节点后 16 的二叉树为:")
 	bst.print()
 
diff --git a/codes/java/chapter_tree/avl_tree.java b/codes/java/chapter_tree/avl_tree.java
index 70a5340b..aea19fa5 100644
--- a/codes/java/chapter_tree/avl_tree.java
+++ b/codes/java/chapter_tree/avl_tree.java
@@ -92,9 +92,8 @@ class AVLTree {
     }
 
     /* 插入节点 */
-    public TreeNode insert(int val) {
+    public void insert(int val) {
         root = insertHelper(root, val);
-        return root;
     }
 
     /* 递归插入节点（辅助方法） */
@@ -116,9 +115,8 @@ class AVLTree {
     }
 
     /* 删除节点 */
-    public TreeNode remove(int val) {
+    public void remove(int val) {
         root = removeHelper(root, val);
-        return root;
     }
 
     /* 递归删除节点（辅助方法） */
@@ -141,7 +139,10 @@ class AVLTree {
                     node = child;
             } else {
                 // 子节点数量 = 2 ，则将中序遍历的下个节点删除，并用该节点替换当前节点
-                TreeNode temp = getInOrderNext(node.right);
+                TreeNode temp = node.right;
+                while (temp.left != null) {
+                    temp = temp.left;
+                }
                 node.right = removeHelper(node.right, temp.val);
                 node.val = temp.val;
             }
@@ -153,17 +154,6 @@ class AVLTree {
         return node;
     }
 
-    /* 获取中序遍历中的下一个节点（仅适用于 root 有左子节点的情况） */
-    private TreeNode getInOrderNext(TreeNode node) {
-        if (node == null)
-            return node;
-        // 循环访问左子节点，直到叶节点时为最小节点，跳出
-        while (node.left != null) {
-            node = node.left;
-        }
-        return node;
-    }
-
     /* 查找节点 */
     public TreeNode search(int val) {
         TreeNode cur = root;
diff --git a/codes/java/chapter_tree/binary_search_tree.java b/codes/java/chapter_tree/binary_search_tree.java
index 0f81d409..8565b7be 100644
--- a/codes/java/chapter_tree/binary_search_tree.java
+++ b/codes/java/chapter_tree/binary_search_tree.java
@@ -56,16 +56,16 @@ class BinarySearchTree {
     }
 
     /* 插入节点 */
-    public TreeNode insert(int num) {
+    public void insert(int num) {
         // 若树为空，直接提前返回
         if (root == null)
-            return null;
+            return;
         TreeNode cur = root, pre = null;
         // 循环查找，越过叶节点后跳出
         while (cur != null) {
             // 找到重复节点，直接返回
             if (cur.val == num)
-                return null;
+                return;
             pre = cur;
             // 插入位置在 cur 的右子树中
             if (cur.val < num)
@@ -80,14 +80,13 @@ class BinarySearchTree {
             pre.right = node;
         else
             pre.left = node;
-        return node;
     }
 
     /* 删除节点 */
-    public TreeNode remove(int num) {
+    public void remove(int num) {
         // 若树为空，直接提前返回
         if (root == null)
-            return null;
+            return;
         TreeNode cur = root, pre = null;
         // 循环查找，越过叶节点后跳出
         while (cur != null) {
@@ -104,7 +103,7 @@ class BinarySearchTree {
         }
         // 若无待删除节点，则直接返回
         if (cur == null)
-            return null;
+            return;
         // 子节点数量 = 0 or 1
         if (cur.left == null || cur.right == null) {
             // 当子节点数量 = 0 / 1 时， child = null / 该子节点
@@ -118,14 +117,15 @@ class BinarySearchTree {
         // 子节点数量 = 2
         else {
             // 获取中序遍历中 cur 的下一个节点
-            TreeNode nex = getInOrderNext(cur.right);
-            int tmp = nex.val;
-            // 递归删除节点 nex
-            remove(nex.val);
-            // 将 nex 的值复制给 cur
-            cur.val = tmp;
+            TreeNode tmp = cur.right;
+            while (tmp.left != null) {
+                tmp = tmp.left;
+            }
+            // 递归删除节点 tmp
+            remove(tmp.val);
+            // 用 tmp 覆盖 cur
+            cur.val = tmp.val;
         }
-        return cur;
     }
 
     /* 获取中序遍历中的下一个节点（仅适用于 root 有左子节点的情况） */
@@ -153,7 +153,7 @@ public class binary_search_tree {
         System.out.println("\n查找到的节点对象为 " + node + "，节点值 = " + node.val);
 
         /* 插入节点 */
-        node = bst.insert(16);
+        bst.insert(16);
         System.out.println("\n插入节点 16 后，二叉树为\n");
         PrintUtil.printTree(bst.getRoot());
 
diff --git a/codes/javascript/chapter_tree/avl_tree.js b/codes/javascript/chapter_tree/avl_tree.js
index 13a9d6ee..0648c2e7 100644
--- a/codes/javascript/chapter_tree/avl_tree.js
+++ b/codes/javascript/chapter_tree/avl_tree.js
@@ -95,7 +95,6 @@ class AVLTree {
     /* 插入节点 */
     insert(val) {
         this.root = this.#insertHelper(this.root, val);
-        return this.root;
     }
 
     /* 递归插入节点（辅助方法） */
@@ -115,7 +114,6 @@ class AVLTree {
     /* 删除节点 */
     remove(val) {
         this.root = this.#removeHelper(this.root, val);
-        return this.root;
     }
 
     /* 递归删除节点（辅助方法） */
@@ -133,7 +131,10 @@ class AVLTree {
                 else node = child;
             } else {
                 // 子节点数量 = 2 ，则将中序遍历的下个节点删除，并用该节点替换当前节点
-                const temp = this.#getInOrderNext(node.right);
+                let temp = node.right;
+                while (temp.left !== null) {
+                    temp = temp.left;
+                }
                 node.right = this.#removeHelper(node.right, temp.val);
                 node.val = temp.val;
             }
@@ -145,16 +146,6 @@ class AVLTree {
         return node;
     }
 
-    /* 获取中序遍历中的下一个节点（仅适用于 root 有左子节点的情况） */
-    #getInOrderNext(node) {
-        if (node === null) return node;
-        // 循环访问左子节点，直到叶节点时为最小节点，跳出
-        while (node.left !== null) {
-            node = node.left;
-        }
-        return node;
-    }
-
     /* 查找节点 */
     search(val) {
         let cur = this.root;
diff --git a/codes/javascript/chapter_tree/binary_search_tree.js b/codes/javascript/chapter_tree/binary_search_tree.js
index 2ed342d7..15847953 100644
--- a/codes/javascript/chapter_tree/binary_search_tree.js
+++ b/codes/javascript/chapter_tree/binary_search_tree.js
@@ -51,12 +51,12 @@ function search(num) {
 /* 插入节点 */
 function insert(num) {
     // 若树为空，直接提前返回
-    if (root === null) return null;
+    if (root === null) return;
     let cur = root, pre = null;
     // 循环查找，越过叶节点后跳出
     while (cur !== null) {
         // 找到重复节点，直接返回
-        if (cur.val === num) return null;
+        if (cur.val === num) return;
         pre = cur;
         // 插入位置在 cur 的右子树中
         if (cur.val < num) cur = cur.right;
@@ -67,13 +67,12 @@ function insert(num) {
     let node = new TreeNode(num);
     if (pre.val < num) pre.right = node;
     else pre.left = node;
-    return node;
 }
 
 /* 删除节点 */
 function remove(num) {
     // 若树为空，直接提前返回
-    if (root === null) return null;
+    if (root === null) return;
     let cur = root, pre = null;
     // 循环查找，越过叶节点后跳出
     while (cur !== null) {
@@ -86,7 +85,7 @@ function remove(num) {
         else cur = cur.left;
     }
     // 若无待删除节点，则直接返回
-    if (cur === null) return null;
+    if (cur === null) return;
     // 子节点数量 = 0 or 1
     if (cur.left === null || cur.right === null) {
         // 当子节点数量 = 0 / 1 时， child = null / 该子节点
@@ -98,24 +97,15 @@ function remove(num) {
     // 子节点数量 = 2
     else {
         // 获取中序遍历中 cur 的下一个节点
-        let nex = getInOrderNext(cur.right);
-        let tmp = nex.val;
-        // 递归删除节点 nex
-        remove(nex.val);
-        // 将 nex 的值复制给 cur
-        cur.val = tmp;
+        let tmp = cur.right;
+        while (tmp.left !== null) {
+            tmp = tmp.left;
+        }
+        // 递归删除节点 tmp
+        remove(tmp.val);
+        // 用 tmp 覆盖 cur
+        cur.val = tmp.val;
     }
-    return cur;
-}
-
-/* 获取中序遍历中的下一个节点（仅适用于 root 有左子节点的情况） */
-function getInOrderNext(root) {
-    if (root === null) return root;
-    // 循环访问左子节点，直到叶节点时为最小节点，跳出
-    while (root.left !== null) {
-        root = root.left;
-    }
-    return root;
 }
 
 /* Driver Code */
@@ -130,7 +120,7 @@ let node = search(7);
 console.log("\n查找到的节点对象为 " + node + "，节点值 = " + node.val);
 
 /* 插入节点 */
-node = insert(16);
+insert(16);
 console.log("\n插入节点 16 后，二叉树为\n");
 printTree(getRoot());
 
diff --git a/codes/python/chapter_tree/avl_tree.py b/codes/python/chapter_tree/avl_tree.py
index e439eaff..6fe4676f 100644
--- a/codes/python/chapter_tree/avl_tree.py
+++ b/codes/python/chapter_tree/avl_tree.py
@@ -92,10 +92,9 @@ class AVLTree:
         # 平衡树，无需旋转，直接返回
         return node
 
-    def insert(self, val) -> TreeNode:
+    def insert(self, val) -> None:
         """插入节点"""
         self.__root = self.__insert_helper(self.__root, val)
-        return self.__root
 
     def __insert_helper(self, node: TreeNode | None, val: int) -> TreeNode:
         """递归插入节点（辅助方法）"""
@@ -114,10 +113,9 @@ class AVLTree:
         # 2. 执行旋转操作，使该子树重新恢复平衡
         return self.__rotate(node)
 
-    def remove(self, val: int) -> TreeNode | None:
+    def remove(self, val: int) -> None:
         """删除节点"""
         self.__root = self.__remove_helper(self.__root, val)
-        return self.__root
 
     def __remove_helper(self, node: TreeNode | None, val: int) -> TreeNode | None:
         """递归删除节点（辅助方法）"""
@@ -137,8 +135,11 @@ class AVLTree:
                 # 子节点数量 = 1 ，直接删除 node
                 else:
                     node = child
-            else:  # 子节点数量 = 2 ，则将中序遍历的下个节点删除，并用该节点替换当前节点
-                temp = self.__get_inorder_next(node.right)
+            else:
+                # 子节点数量 = 2 ，则将中序遍历的下个节点删除，并用该节点替换当前节点
+                temp = node.right
+                while temp.left is not None:
+                    temp = temp.left
                 node.right = self.__remove_helper(node.right, temp.val)
                 node.val = temp.val
         # 更新节点高度
@@ -146,15 +147,6 @@ class AVLTree:
         # 2. 执行旋转操作，使该子树重新恢复平衡
         return self.__rotate(node)
 
-    def __get_inorder_next(self, node: TreeNode | None) -> TreeNode | None:
-        """获取中序遍历中的下一个节点（仅适用于 root 有左子节点的情况）"""
-        if node is None:
-            return None
-        # 循环访问左子节点，直到叶节点时为最小节点，跳出
-        while node.left is not None:
-            node = node.left
-        return node
-
     def search(self, val: int) -> TreeNode | None:
         """查找节点"""
         cur = self.__root
diff --git a/codes/python/chapter_tree/binary_search_tree.py b/codes/python/chapter_tree/binary_search_tree.py
index 4ae45d69..fc9b98cc 100644
--- a/codes/python/chapter_tree/binary_search_tree.py
+++ b/codes/python/chapter_tree/binary_search_tree.py
@@ -57,18 +57,18 @@ class BinarySearchTree:
                 break
         return cur
 
-    def insert(self, num: int) -> TreeNode | None:
+    def insert(self, num: int) -> None:
         """插入节点"""
         # 若树为空，直接提前返回
         if self.__root is None:
-            return None
+            return
 
         # 循环查找，越过叶节点后跳出
         cur, pre = self.__root, None
         while cur is not None:
             # 找到重复节点，直接返回
             if cur.val == num:
-                return None
+                return
             pre = cur
             # 插入位置在 cur 的右子树中
             if cur.val < num:
@@ -83,13 +83,12 @@ class BinarySearchTree:
             pre.right = node
         else:
             pre.left = node
-        return node
 
-    def remove(self, num: int) -> TreeNode | None:
+    def remove(self, num: int) -> None:
         """删除节点"""
         # 若树为空，直接提前返回
         if self.__root is None:
-            return None
+            return
 
         # 循环查找，越过叶节点后跳出
         cur, pre = self.__root, None
@@ -98,13 +97,15 @@ class BinarySearchTree:
             if cur.val == num:
                 break
             pre = cur
-            if cur.val < num:  # 待删除节点在 cur 的右子树中
+            # 待删除节点在 cur 的右子树中
+            if cur.val < num:
                 cur = cur.right
-            else:  # 待删除节点在 cur 的左子树中
+            # 待删除节点在 cur 的左子树中
+            else:
                 cur = cur.left
         # 若无待删除节点，则直接返回
         if cur is None:
-            return None
+            return
 
         # 子节点数量 = 0 or 1
         if cur.left is None or cur.right is None:
@@ -118,22 +119,13 @@ class BinarySearchTree:
         # 子节点数量 = 2
         else:
             # 获取中序遍历中 cur 的下一个节点
-            nex: TreeNode = self.get_inorder_next(cur.right)
-            tmp: int = nex.val
-            # 递归删除节点 nex
-            self.remove(nex.val)
-            # 将 nex 的值复制给 cur
-            cur.val = tmp
-        return cur
-
-    def get_inorder_next(self, root: TreeNode | None) -> TreeNode | None:
-        """获取中序遍历中的下一个节点（仅适用于 root 有左子节点的情况）"""
-        if root is None:
-            return root
-        # 循环访问左子节点，直到叶节点时为最小节点，跳出
-        while root.left is not None:
-            root = root.left
-        return root
+            tmp: TreeNode = cur.right
+            while tmp.left is not None:
+                tmp = tmp.left
+            # 递归删除节点 tmp
+            self.remove(tmp.val)
+            # 用 tmp 覆盖 cur
+            cur.val = tmp.val
 
 
 """Driver Code"""
@@ -149,7 +141,7 @@ if __name__ == "__main__":
     print("\n查找到的节点对象为: {}，节点值 = {}".format(node, node.val))
 
     # 插入节点
-    node = bst.insert(16)
+    bst.insert(16)
     print("\n插入节点 16 后，二叉树为\n")
     print_tree(bst.root)
 
diff --git a/codes/swift/chapter_tree/avl_tree.swift b/codes/swift/chapter_tree/avl_tree.swift
index 0fb41976..087b5975 100644
--- a/codes/swift/chapter_tree/avl_tree.swift
+++ b/codes/swift/chapter_tree/avl_tree.swift
@@ -90,9 +90,8 @@ class AVLTree {
 
     /* 插入节点 */
     @discardableResult
-    func insert(val: Int) -> TreeNode? {
+    func insert(val: Int) {
         root = insertHelper(node: root, val: val)
-        return root
     }
 
     /* 递归插入节点（辅助方法） */
@@ -118,9 +117,8 @@ class AVLTree {
 
     /* 删除节点 */
     @discardableResult
-    func remove(val: Int) -> TreeNode? {
+    func remove(val: Int) {
         root = removeHelper(node: root, val: val)
-        return root
     }
 
     /* 递归删除节点（辅助方法） */
@@ -147,7 +145,10 @@ class AVLTree {
                 }
             } else {
                 // 子节点数量 = 2 ，则将中序遍历的下个节点删除，并用该节点替换当前节点
-                let temp = getInOrderNext(node: node?.right)
+                let temp = node?.right
+                while temp?.left != nil {
+                    temp = temp?.left
+                }
                 node?.right = removeHelper(node: node?.right, val: temp!.val)
                 node?.val = temp!.val
             }
@@ -159,19 +160,6 @@ class AVLTree {
         return node
     }
 
-    /* 获取中序遍历中的下一个节点（仅适用于 root 有左子节点的情况） */
-    private func getInOrderNext(node: TreeNode?) -> TreeNode? {
-        var node = node
-        if node == nil {
-            return node
-        }
-        // 循环访问左子节点，直到叶节点时为最小节点，跳出
-        while node?.left != nil {
-            node = node?.left
-        }
-        return node
-    }
-
     /* 查找节点 */
     func search(val: Int) -> TreeNode? {
         var cur = root
diff --git a/codes/swift/chapter_tree/binary_search_tree.swift b/codes/swift/chapter_tree/binary_search_tree.swift
index 5cb4b134..3ea129a1 100644
--- a/codes/swift/chapter_tree/binary_search_tree.swift
+++ b/codes/swift/chapter_tree/binary_search_tree.swift
@@ -57,10 +57,10 @@ class BinarySearchTree {
     }
 
     /* 插入节点 */
-    func insert(num: Int) -> TreeNode? {
+    func insert(num: Int) {
         // 若树为空，直接提前返回
         if root == nil {
-            return nil
+            return
         }
         var cur = root
         var pre: TreeNode?
@@ -68,7 +68,7 @@ class BinarySearchTree {
         while cur != nil {
             // 找到重复节点，直接返回
             if cur!.val == num {
-                return nil
+                return
             }
             pre = cur
             // 插入位置在 cur 的右子树中
@@ -87,15 +87,14 @@ class BinarySearchTree {
         } else {
             pre?.left = node
         }
-        return node
     }
 
     /* 删除节点 */
     @discardableResult
-    func remove(num: Int) -> TreeNode? {
+    func remove(num: Int) {
         // 若树为空，直接提前返回
         if root == nil {
-            return nil
+            return
         }
         var cur = root
         var pre: TreeNode?
@@ -117,7 +116,7 @@ class BinarySearchTree {
         }
         // 若无待删除节点，则直接返回
         if cur == nil {
-            return nil
+            return
         }
         // 子节点数量 = 0 or 1
         if cur?.left == nil || cur?.right == nil {
@@ -133,27 +132,15 @@ class BinarySearchTree {
         // 子节点数量 = 2
         else {
             // 获取中序遍历中 cur 的下一个节点
-            let nex = getInOrderNext(root: cur?.right)
-            let tmp = nex!.val
-            // 递归删除节点 nex
-            remove(num: nex!.val)
-            // 将 nex 的值复制给 cur
-            cur?.val = tmp
+            let tmp = cur?.right
+            while tmp?.left != nil {
+                tmp = tmp?.left
+            }
+            // 递归删除节点 tmp
+            remove(num: tmp!.val)
+            // 用 tmp 覆盖 cur
+            cur?.val = tmp!.val
         }
-        return cur
-    }
-
-    /* 获取中序遍历中的下一个节点（仅适用于 root 有左子节点的情况） */
-    func getInOrderNext(root: TreeNode?) -> TreeNode? {
-        var root = root
-        if root == nil {
-            return root
-        }
-        // 循环访问左子节点，直到叶节点时为最小节点，跳出
-        while root?.left != nil {
-            root = root?.left
-        }
-        return root
     }
 }
 
@@ -172,7 +159,7 @@ enum _BinarySearchTree {
         print("\n查找到的节点对象为 \(node!)，节点值 = \(node!.val)")
 
         /* 插入节点 */
-        node = bst.insert(num: 16)
+        bst.insert(num: 16)
         print("\n插入节点 16 后，二叉树为\n")
         PrintUtil.printTree(root: bst.getRoot())
 
diff --git a/codes/typescript/chapter_tree/avl_tree.ts b/codes/typescript/chapter_tree/avl_tree.ts
index 7e5951c5..c217491c 100644
--- a/codes/typescript/chapter_tree/avl_tree.ts
+++ b/codes/typescript/chapter_tree/avl_tree.ts
@@ -94,9 +94,8 @@ class AVLTree {
     }
 
     /* 插入节点 */
-    insert(val: number): TreeNode {
+    insert(val: number): void {
         this.root = this.insertHelper(this.root, val);
-        return this.root;
     }
 
     /* 递归插入节点（辅助方法） */
@@ -118,9 +117,8 @@ class AVLTree {
     }
 
     /* 删除节点 */
-    remove(val: number): TreeNode {
+    remove(val: number): void {
         this.root = this.removeHelper(this.root, val);
-        return this.root;
     }
 
     /* 递归删除节点（辅助方法） */
@@ -143,7 +141,10 @@ class AVLTree {
                 }
             } else {
                 // 子节点数量 = 2 ，则将中序遍历的下个节点删除，并用该节点替换当前节点
-                const temp = this.getInOrderNext(node.right);
+                let temp = node.right;
+                while (temp.left !== null) {
+                    temp = temp.left;
+                }
                 node.right = this.removeHelper(node.right, temp.val);
                 node.val = temp.val;
             }
@@ -155,16 +156,6 @@ class AVLTree {
         return node;
     }
 
-    /* 获取中序遍历中的下一个节点（仅适用于 root 有左子节点的情况） */
-    private getInOrderNext(node: TreeNode): TreeNode {
-        if (node === null) return node;
-        // 循环访问左子节点，直到叶节点时为最小节点，跳出
-        while (node.left !== null) {
-            node = node.left;
-        }
-        return node;
-    }
-
     /* 查找节点 */
     search(val: number): TreeNode {
         let cur = this.root;
diff --git a/codes/typescript/chapter_tree/binary_search_tree.ts b/codes/typescript/chapter_tree/binary_search_tree.ts
index 51508a86..fa40a0ca 100644
--- a/codes/typescript/chapter_tree/binary_search_tree.ts
+++ b/codes/typescript/chapter_tree/binary_search_tree.ts
@@ -52,17 +52,17 @@ function search(num: number): TreeNode | null {
 }
 
 /* 插入节点 */
-function insert(num: number): TreeNode | null {
+function insert(num: number): void {
     // 若树为空，直接提前返回
     if (root === null) {
-        return null;
+        return;
     }
     let cur = root,
         pre: TreeNode | null = null;
     // 循环查找，越过叶节点后跳出
     while (cur !== null) {
         if (cur.val === num) {
-            return null; // 找到重复节点，直接返回
+            return; // 找到重复节点，直接返回
         }
         pre = cur;
         if (cur.val < num) {
@@ -78,14 +78,13 @@ function insert(num: number): TreeNode | null {
     } else {
         pre!.left = node;
     }
-    return node;
 }
 
 /* 删除节点 */
-function remove(num: number): TreeNode | null {
+function remove(num: number): void {
     // 若树为空，直接提前返回
     if (root === null) {
-        return null;
+        return;
     }
     let cur = root,
         pre: TreeNode | null = null;
@@ -104,7 +103,7 @@ function remove(num: number): TreeNode | null {
     }
     // 若无待删除节点，则直接返回
     if (cur === null) {
-        return null;
+        return;
     }
     // 子节点数量 = 0 or 1
     if (cur.left === null || cur.right === null) {
@@ -120,26 +119,15 @@ function remove(num: number): TreeNode | null {
     // 子节点数量 = 2
     else {
         // 获取中序遍历中 cur 的下一个节点
-        let next = getInOrderNext(cur.right);
-        let tmp = next!.val;
-        // 递归删除节点 nex
-        remove(next!.val);
-        // 将 nex 的值复制给 cur
-        cur.val = tmp;
+        let tmp = cur.right;
+        while (tmp.left !== null) {
+            tmp = tmp.left;
+        }
+        // 递归删除节点 tmp
+        remove(tmp!.val);
+        // 用 tmp 覆盖 cur
+        cur.val = tmp.val;
     }
-    return cur;
-}
-
-/* 获取中序遍历中的下一个节点（仅适用于 root 有左子节点的情况） */
-function getInOrderNext(root: TreeNode | null): TreeNode | null {
-    if (root === null) {
-        return null;
-    }
-    // 循环访问左子节点，直到叶节点时为最小节点，跳出
-    while (root.left !== null) {
-        root = root.left;
-    }
-    return root;
 }
 
 /* Driver Code */
@@ -154,7 +142,7 @@ let node = search(7);
 console.log('\n查找到的节点对象为 ' + node + '，节点值 = ' + node!.val);
 
 /* 插入节点 */
-node = insert(16);
+insert(16);
 console.log('\n插入节点 16 后，二叉树为\n');
 printTree(getRoot());
 
diff --git a/codes/zig/chapter_tree/avl_tree.zig b/codes/zig/chapter_tree/avl_tree.zig
index b6647207..0e6207d4 100644
--- a/codes/zig/chapter_tree/avl_tree.zig
+++ b/codes/zig/chapter_tree/avl_tree.zig
@@ -108,9 +108,8 @@ pub fn AVLTree(comptime T: type) type {
         }
 
         // 插入节点
-        fn insert(self: *Self, val: T) !?*inc.TreeNode(T) {
+        fn insert(self: *Self, val: T) void {
             self.root = try self.insertHelper(self.root, val);
-            return self.root;
         }
 
         // 递归插入节点（辅助方法）
@@ -137,9 +136,8 @@ pub fn AVLTree(comptime T: type) type {
         }
 
         // 删除节点
-        fn remove(self: *Self, val: T) ?*inc.TreeNode(T) {
+        fn remove(self: *Self, val: T) void {
            self.root = self.removeHelper(self.root, val);
-            return self.root;
         }
 
         // 递归删除节点（辅助方法）
@@ -163,30 +161,21 @@ pub fn AVLTree(comptime T: type) type {
                     }
                 } else {
                     // 子节点数量 = 2 ，则将中序遍历的下个节点删除，并用该节点替换当前节点
-                    var temp = self.getInOrderNext(node.?.right);
+                    var temp = node.?.right;
+                    while (temp.?.left != null) {
+                        temp = temp.?.left;
+                    }
                     node.?.right = self.removeHelper(node.?.right, temp.?.val);
                     node.?.val = temp.?.val;
                 }
             }
-            self.updateHeight(node);    // 更新节点高度
+            self.updateHeight(node); // 更新节点高度
             // 2. 执行旋转操作，使该子树重新恢复平衡
             node = self.rotate(node);
             // 返回子树的根节点
             return node;
         }
 
-        // 获取中序遍历中的下一个节点（仅适用于 root 有左子节点的情况）
-        fn getInOrderNext(self: *Self, node_: ?*inc.TreeNode(T)) ?*inc.TreeNode(T) {
-            _ = self;
-            var node = node_;
-            if (node == null) return node;
-            // 循环访问左子节点，直到叶节点时为最小节点，跳出
-            while (node.?.left != null) {
-                node = node.?.left;
-            }
-            return node;
-        }
-
         // 查找节点
         fn search(self: *Self, val: T) ?*inc.TreeNode(T) {
             var cur = self.root;
diff --git a/codes/zig/chapter_tree/binary_search_tree.zig b/codes/zig/chapter_tree/binary_search_tree.zig
index c94cdb6c..ca62cd69 100644
--- a/codes/zig/chapter_tree/binary_search_tree.zig
+++ b/codes/zig/chapter_tree/binary_search_tree.zig
@@ -69,15 +69,15 @@ pub fn BinarySearchTree(comptime T: type) type {
         }
 
         // 插入节点
-        fn insert(self: *Self, num: T) !?*inc.TreeNode(T) {
+        fn insert(self: *Self, num: T) !void {
             // 若树为空，直接提前返回
-            if (self.root == null) return null;
+            if (self.root == null) return;
             var cur = self.root;
             var pre: ?*inc.TreeNode(T) = null;
             // 循环查找，越过叶节点后跳出
             while (cur != null) {
                 // 找到重复节点，直接返回
-                if (cur.?.val == num) return null;
+                if (cur.?.val == num) return;
                 pre = cur;
                 // 插入位置在 cur 的右子树中
                 if (cur.?.val < num) {
@@ -95,13 +95,12 @@ pub fn BinarySearchTree(comptime T: type) type {
             } else {
                 pre.?.left = node;
             }
-            return node;
         }
 
         // 删除节点
-        fn remove(self: *Self, num: T) ?*inc.TreeNode(T) {
+        fn remove(self: *Self, num: T) !void {
             // 若树为空，直接提前返回
-            if (self.root == null) return null;
+            if (self.root == null) return;
             var cur = self.root;
             var pre: ?*inc.TreeNode(T) = null;
             // 循环查找，越过叶节点后跳出
@@ -118,7 +117,7 @@ pub fn BinarySearchTree(comptime T: type) type {
                 }
             }
             // 若无待删除节点，则直接返回
-            if (cur == null) return null;
+            if (cur == null) return;
             // 子节点数量 = 0 or 1
             if (cur.?.left == null or cur.?.right == null) {
                 // 当子节点数量 = 0 / 1 时， child = null / 该子节点
@@ -132,26 +131,16 @@ pub fn BinarySearchTree(comptime T: type) type {
             // 子节点数量 = 2
             } else {
                 // 获取中序遍历中 cur 的下一个节点
-                var nex = self.getInOrderNext(cur.?.right);
-                var tmp = nex.?.val;
-                // 递归删除节点 nex
-                _ = self.remove(nex.?.val);
-                // 将 nex 的值复制给 cur
-                cur.?.val = tmp;
+                var tmp = cur.?.right;
+                while (tmp.?.left != null) {
+                    tmp = tmp.?.left;
+                }
+                var tmpVal = tmp.?.val;
+                // 递归删除节点 tmp
+                _ = self.remove(tmp.?.val);
+                // 用 tmp 覆盖 cur
+                cur.?.val = tmpVal;
             }
-            return cur;
-        }
-
-        // 获取中序遍历中的下一个节点（仅适用于 root 有左子节点的情况）
-        fn getInOrderNext(self: *Self, node: ?*inc.TreeNode(T)) ?*inc.TreeNode(T) {
-            _ = self;
-            var node_tmp = node;
-            if (node_tmp == null) return null;
-            // 循环访问左子节点，直到叶节点时为最小节点，跳出
-            while (node_tmp.?.left != null) {
-                node_tmp = node_tmp.?.left;
-            }
-            return node_tmp;
         }
     };   
 }
diff --git a/docs/chapter_tree/binary_search_tree.md b/docs/chapter_tree/binary_search_tree.md
index 9fa5cb5d..affe026a 100755
--- a/docs/chapter_tree/binary_search_tree.md
+++ b/docs/chapter_tree/binary_search_tree.md
@@ -180,9 +180,9 @@
 
 当待删除节点的子节点数量 $= 2$ 时，删除操作分为三步：
 
-1. 找到待删除节点在“中序遍历序列”中的下一个节点，记为 nex；
-2. 在树中递归删除节点 `nex` ；
-3. 使用 `nex` 替换待删除节点；
+1. 找到待删除节点在“中序遍历序列”中的下一个节点，记为 `tmp` ；
+2. 在树中递归删除节点 `tmp` ；
+3. 用 `tmp` 的值覆盖待删除节点的值；
 
 === "<1>"
     ![bst_remove_case3_step1](binary_search_tree.assets/bst_remove_case3_step1.png)