From 5b1a219b8bca77c1aa3a0a187e2e8101f80c9681 Mon Sep 17 00:00:00 2001
From: krahets <krahets@163.com>
Date: Fri, 27 Oct 2023 01:01:21 +0800
Subject: [PATCH] Fine-tune code and texts.

---
 codes/cpp/chapter_tree/array_binary_tree.cpp   | 6 +++---
 codes/cpp/utils/tree_node.hpp                  | 3 +--
 codes/python/chapter_tree/array_binary_tree.py | 4 ++--
 docs/chapter_sorting/merge_sort.md             | 5 +----
 4 files changed, 7 insertions(+), 11 deletions(-)

diff --git a/codes/cpp/chapter_tree/array_binary_tree.cpp b/codes/cpp/chapter_tree/array_binary_tree.cpp
index 0ca7ff799..ce07ecda9 100644
--- a/codes/cpp/chapter_tree/array_binary_tree.cpp
+++ b/codes/cpp/chapter_tree/array_binary_tree.cpp
@@ -115,9 +115,9 @@ int main() {
     int i = 1;
     int l = abt.left(i), r = abt.right(i), p = abt.parent(i);
     cout << "\n当前节点的索引为 " << i << "，值为 " << abt.val(i) << "\n";
-    cout << "其左子节点的索引为 " << l << "，值为 " << (l != INT_MAX ? to_string(abt.val(l)) : "None") << "\n";
-    cout << "其右子节点的索引为 " << r << "，值为 " << (r != INT_MAX ? to_string(abt.val(r)) : "None") << "\n";
-    cout << "其父节点的索引为 " << p << "，值为 " << (p != INT_MAX ? to_string(abt.val(p)) : "None") << "\n";
+    cout << "其左子节点的索引为 " << l << "，值为 " << (l != INT_MAX ? to_string(abt.val(l)) : "nullptr") << "\n";
+    cout << "其右子节点的索引为 " << r << "，值为 " << (r != INT_MAX ? to_string(abt.val(r)) : "nullptr") << "\n";
+    cout << "其父节点的索引为 " << p << "，值为 " << (p != INT_MAX ? to_string(abt.val(p)) : "nullptr") << "\n";
 
     // 遍历树
     vector<int> res = abt.levelOrder();
diff --git a/codes/cpp/utils/tree_node.hpp b/codes/cpp/utils/tree_node.hpp
index 055c673dd..0c0b5ee5e 100644
--- a/codes/cpp/utils/tree_node.hpp
+++ b/codes/cpp/utils/tree_node.hpp
@@ -74,12 +74,11 @@ vector<int> treeToVecor(TreeNode *root) {
     return res;
 }
 
-/* Free the memory allocated to a tree */
+/* 释放二叉树内存 */
 void freeMemoryTree(TreeNode *root) {
     if (root == nullptr)
         return;
     freeMemoryTree(root->left);
     freeMemoryTree(root->right);
-    // 释放内存
     delete root;
 }
diff --git a/codes/python/chapter_tree/array_binary_tree.py b/codes/python/chapter_tree/array_binary_tree.py
index 0073a51aa..dd556ff06 100644
--- a/codes/python/chapter_tree/array_binary_tree.py
+++ b/codes/python/chapter_tree/array_binary_tree.py
@@ -92,9 +92,9 @@ if __name__ == "__main__":
     arr = [1, 2, 3, 4, None, 6, 7, 8, 9, None, None, 12, None, None, 15]
     root = list_to_tree(arr)
     print("\n初始化二叉树\n")
-    print(f"二叉树的数组表示：")
+    print("二叉树的数组表示：")
     print(arr)
-    print(f"二叉树的链表表示：")
+    print("二叉树的链表表示：")
     print_tree(root)
 
     # 数组表示下的二叉树类
diff --git a/docs/chapter_sorting/merge_sort.md b/docs/chapter_sorting/merge_sort.md
index 7a596fa30..3ab4201cb 100755
--- a/docs/chapter_sorting/merge_sort.md
+++ b/docs/chapter_sorting/merge_sort.md
@@ -55,10 +55,7 @@
 [file]{merge_sort}-[class]{}-[func]{merge_sort}
 ```
 
-实现合并函数 `merge()` 存在以下难点。
-
-- **需要特别注意各个变量的含义**。`nums` 的待合并区间为 `[left, right]` ，但由于 `tmp` 仅复制了 `nums` 该区间的元素，因此 `tmp` 对应区间为 `[0, right - left]` 。
-- 在比较 `tmp[i]` 和 `tmp[j]` 的大小时，**还需考虑子数组遍历完成后的索引越界问题**，即 `i > leftEnd` 和 `j > rightEnd` 的情况。索引越界的优先级是最高的，如果左子数组已经被合并完了，那么不需要继续比较，直接合并右子数组元素即可。
+值得注意的是，`nums` 的待合并区间为 `[left, right]` ，而 `tmp` 的对应区间为 `[0, right - left]` 。
 
 ## 算法特性