diff --git a/docs/chapter_backtracking/backtracking_algorithm.md b/docs/chapter_backtracking/backtracking_algorithm.md
index 1466c5370..04e9d672a 100644
--- a/docs/chapter_backtracking/backtracking_algorithm.md
+++ b/docs/chapter_backtracking/backtracking_algorithm.md
@@ -317,7 +317,7 @@ comments: true
         *path = append(*path, root)
         if root.Val.(int) == 7 {
             // 记录解
-            *res = append(*res, *path)
+            *res = append(*res, append([]*TreeNode{}, *path...))
         }
         preOrderII(root.Left, res, path)
         preOrderII(root.Right, res, path)
diff --git a/docs/chapter_hashing/hash_collision.md b/docs/chapter_hashing/hash_collision.md
index a227bb496..5ea302570 100644
--- a/docs/chapter_hashing/hash_collision.md
+++ b/docs/chapter_hashing/hash_collision.md
@@ -498,7 +498,7 @@ comments: true
 
     /* 负载因子 */
     func (m *hashMapChaining) loadFactor() float64 {
-        return float64(m.size / m.capacity)
+        return float64(m.size) / float64(m.capacity)
     }
 
     /* 查询操作 */
@@ -523,9 +523,9 @@ comments: true
         }
         idx := m.hashFunc(key)
         // 遍历桶，若遇到指定 key ，则更新对应 val 并返回
-        for _, p := range m.buckets[idx] {
-            if p.key == key {
-                p.val = val
+        for i := range m.buckets[idx] {
+            if m.buckets[idx][i].key == key {
+                m.buckets[idx][i].val = val
                 return
             }
         }
@@ -1931,6 +1931,7 @@ comments: true
             // 若遇到指定 key ，则更新对应 val
             if m.buckets[j].key == key {
                 m.buckets[j].val = val
+                return
             }
         }
     }
diff --git a/docs/chapter_preface/about_the_book.md b/docs/chapter_preface/about_the_book.md
index 1fbc3d5a0..b1f3b2b25 100644
--- a/docs/chapter_preface/about_the_book.md
+++ b/docs/chapter_preface/about_the_book.md
@@ -49,4 +49,4 @@ comments: true
 
 本书倡导手脑并用的学习方式，在这一点上深受[《动手学深度学习》](https://github.com/d2l-ai/d2l-zh)的启发。在此向各位读者强烈推荐这本优秀的著作。
 
-衷心感谢我的父母，正是你们一直以来的支持与鼓励，让我有机会做这件富有趣味的事。
+**衷心感谢我的父母，正是你们一直以来的支持与鼓励，让我有机会做这件富有趣味的事**。
diff --git a/docs/chapter_sorting/bubble_sort.md b/docs/chapter_sorting/bubble_sort.md
index a4e1c627b..68d08b4d5 100755
--- a/docs/chapter_sorting/bubble_sort.md
+++ b/docs/chapter_sorting/bubble_sort.md
@@ -244,7 +244,7 @@ comments: true
         // 外循环：未排序区间为 [0, i]
         for (int i = size - 1; i > 0; i--) {
             // 内循环：将未排序区间 [0, i] 中的最大元素交换至该区间的最右端
-            for (int j = 0; j < size - 1 - i; j++) {
+            for (int j = 0; j < i; j++) {
                 if (nums[j] > nums[j + 1]) {
                     int temp = nums[j];
                     nums[j] = nums[j + 1];
@@ -518,7 +518,7 @@ comments: true
         for (int i = size - 1; i > 0; i--) {
             bool flag = false;
             // 内循环：将未排序区间 [0, i] 中的最大元素交换至该区间的最右端
-            for (int j = 0; j < size - 1 - i; j++) {
+            for (int j = 0; j < i; j++) {
                 if (nums[j] > nums[j + 1]) {
                     int temp = nums[j];
                     nums[j] = nums[j + 1];