diff --git a/docs/chapter_hashing/hash_map.md b/docs/chapter_hashing/hash_map.md
index e65eeefce..7167dd21f 100755
--- a/docs/chapter_hashing/hash_map.md
+++ b/docs/chapter_hashing/hash_map.md
@@ -1458,18 +1458,21 @@ index = hash(key) % capacity
 
     /* 基于数组实现的哈希表 */
     typedef struct {
-        Pair *buckets[HASHTABLE_CAPACITY];
+        Pair *buckets[MAX_SIZE];
     } ArrayHashMap;
 
     /* 构造函数 */
     ArrayHashMap *newArrayHashMap() {
         ArrayHashMap *hmap = malloc(sizeof(ArrayHashMap));
+        for (int i=0; i < MAX_SIZE; i++) {
+            hmap->buckets[i] = NULL;
+        }
         return hmap;
     }
 
     /* 析构函数 */
     void delArrayHashMap(ArrayHashMap *hmap) {
-        for (int i = 0; i < HASHTABLE_CAPACITY; i++) {
+        for (int i = 0; i < MAX_SIZE; i++) {
             if (hmap->buckets[i] != NULL) {
                 free(hmap->buckets[i]->val);
                 free(hmap->buckets[i]);
@@ -1503,13 +1506,13 @@ index = hash(key) % capacity
         int i = 0, index = 0;
         int total = 0;
         /* 统计有效键值对数量 */
-        for (i = 0; i < HASHTABLE_CAPACITY; i++) {
+        for (i = 0; i < MAX_SIZE; i++) {
             if (hmap->buckets[i] != NULL) {
                 total++;
             }
         }
         entries = malloc(sizeof(Pair) * total);
-        for (i = 0; i < HASHTABLE_CAPACITY; i++) {
+        for (i = 0; i < MAX_SIZE; i++) {
             if (hmap->buckets[i] != NULL) {
                 entries[index].key = hmap->buckets[i]->key;
                 entries[index].val = malloc(strlen(hmap->buckets[i]->val) + 1);
@@ -1527,13 +1530,13 @@ index = hash(key) % capacity
         int i = 0, index = 0;
         int total = 0;
         /* 统计有效键值对数量 */
-        for (i = 0; i < HASHTABLE_CAPACITY; i++) {
+        for (i = 0; i < MAX_SIZE; i++) {
             if (hmap->buckets[i] != NULL) {
                 total++;
             }
         }
         keys = malloc(total * sizeof(int));
-        for (i = 0; i < HASHTABLE_CAPACITY; i++) {
+        for (i = 0; i < MAX_SIZE; i++) {
             if (hmap->buckets[i] != NULL) {
                 keys[index] = hmap->buckets[i]->key;
                 index++;
@@ -1549,13 +1552,13 @@ index = hash(key) % capacity
         int i = 0, index = 0;
         int total = 0;
         /* 统计有效键值对数量 */
-        for (i = 0; i < HASHTABLE_CAPACITY; i++) {
+        for (i = 0; i < MAX_SIZE; i++) {
             if (hmap->buckets[i] != NULL) {
                 total++;
             }
         }
         vals = malloc(total * sizeof(char *));
-        for (i = 0; i < HASHTABLE_CAPACITY; i++) {
+        for (i = 0; i < MAX_SIZE; i++) {
             if (hmap->buckets[i] != NULL) {
                 vals[index] = hmap->buckets[i]->val;
                 index++;
diff --git a/docs/chapter_searching/binary_search.md b/docs/chapter_searching/binary_search.md
index be5d33fad..ed755432b 100755
--- a/docs/chapter_searching/binary_search.md
+++ b/docs/chapter_searching/binary_search.md
@@ -339,7 +339,27 @@ comments: true
 === "Ruby"
 
     ```ruby title="binary_search.rb"
-    [class]{}-[func]{binary_search}
+    ### 二分查找（双闭区间） ###
+    def binary_search(nums, target)
+      # 初始化双闭区间 [0, n-1] ，即 i, j 分别指向数组首元素、尾元素
+      i, j = 0, nums.length - 1
+
+      # 循环，当搜索区间为空时跳出（当 i > j 时为空）
+      while i <= j
+        # 理论上 Ruby 的数字可以无限大（取决于内存大小），无须考虑大数越界问题
+        m = (i + j) / 2   # 计算中点索引 m
+      
+        if nums[m] < target
+          i = m + 1 # 此情况说明 target 在区间 [m+1, j] 中
+        elsif nums[m] > target
+          j = m - 1 # 此情况说明 target 在区间 [i, m-1] 中
+        else
+          return m  # 找到目标元素，返回其索引
+        end
+      end
+
+      -1  # 未找到目标元素，返回 -1
+    end
     ```
 
 === "Zig"
@@ -667,7 +687,27 @@ comments: true
 === "Ruby"
 
     ```ruby title="binary_search.rb"
-    [class]{}-[func]{binary_search_lcro}
+    ### 二分查找（左闭右开区间） ###
+    def binary_search_lcro(nums, target)
+      # 初始化左闭右开区间 [0, n) ，即 i, j 分别指向数组首元素、尾元素+1
+      i, j = 0, nums.length
+
+      # 循环，当搜索区间为空时跳出（当 i = j 时为空）
+      while i < j
+        # 计算中点索引 m
+        m = (i + j) / 2
+
+        if nums[m] < target
+          i = m + 1 # 此情况说明 target 在区间 [m+1, j) 中
+        elsif nums[m] > target
+          j = m - 1 # 此情况说明 target 在区间 [i, m) 中
+        else
+          return m  # 找到目标元素，返回其索引
+        end
+      end
+
+      -1  # 未找到目标元素，返回 -1
+    end
     ```
 
 === "Zig"
diff --git a/docs/chapter_searching/binary_search_edge.md b/docs/chapter_searching/binary_search_edge.md
index 8cd9c96c5..7213e300a 100644
--- a/docs/chapter_searching/binary_search_edge.md
+++ b/docs/chapter_searching/binary_search_edge.md
@@ -212,7 +212,16 @@ comments: true
 === "Ruby"
 
     ```ruby title="binary_search_edge.rb"
-    [class]{}-[func]{binary_search_left_edge}
+    ### 二分查找最左一个 target ###
+    def binary_search_left_edge(nums, target)
+      # 等价于查找 target 的插入点
+      i = binary_search_insertion(nums, target)
+
+      # 未找到 target ，返回 -1
+      return -1 if i == nums.length || nums[i] != target
+
+      i # 找到 target ，返回索引 i
+    end
     ```
 
 === "Zig"
@@ -461,7 +470,19 @@ comments: true
 === "Ruby"
 
     ```ruby title="binary_search_edge.rb"
-    [class]{}-[func]{binary_search_right_edge}
+    ### 二分查找最右一个 target ###
+    def binary_search_right_edge(nums, target)
+      # 转化为查找最左一个 target + 1
+      i = binary_search_insertion(nums, target + 1)
+
+      # j 指向最右一个 target ，i 指向首个大于 target 的元素
+      j = i - 1
+
+      # 未找到 target ，返回 -1
+      return -1 if j == -1 || nums[j] != target
+
+      j # 找到 target ，返回索引 j
+    end
     ```
 
 === "Zig"
diff --git a/docs/chapter_searching/binary_search_insertion.md b/docs/chapter_searching/binary_search_insertion.md
index 0d14a0eec..e8f466343 100644
--- a/docs/chapter_searching/binary_search_insertion.md
+++ b/docs/chapter_searching/binary_search_insertion.md
@@ -293,7 +293,26 @@ comments: true
 === "Ruby"
 
     ```ruby title="binary_search_insertion.rb"
-    [class]{}-[func]{binary_search_insertion_simple}
+    ### 二分查找插入点（无重复元素） ###
+    def binary_search_insertion_simple(nums, target)
+      # 初始化双闭区间 [0, n-1]
+      i, j = 0, nums.length - 1
+
+      while i <= j
+        # 计算中点索引 m
+        m = (i + j) / 2
+
+        if nums[m] < target
+          i = m + 1 # target 在区间 [m+1, j] 中
+        elsif nums[m] > target
+          j = m - 1 # target 在区间 [i, m-1] 中
+        else
+          return m  # 找到 target ，返回插入点 m
+        end
+      end
+
+      i # 未找到 target ，返回插入点 i
+    end
     ```
 
 === "Zig"
@@ -625,7 +644,26 @@ comments: true
 === "Ruby"
 
     ```ruby title="binary_search_insertion.rb"
-    [class]{}-[func]{binary_search_insertion}
+    ### 二分查找插入点（存在重复元素） ###
+    def binary_search_insertion(nums, target)
+      # 初始化双闭区间 [0, n-1]
+      i, j = 0, nums.length - 1
+
+      while i <= j
+        # 计算中点索引 m
+        m = (i + j) / 2
+
+        if nums[m] < target
+          i = m + 1 # target 在区间 [m+1, j] 中
+        elsif nums[m] > target
+          j = m - 1 # target 在区间 [i, m-1] 中
+        else
+          j = m - 1 # 首个小于 target 的元素在区间 [i, m-1] 中
+        end
+      end
+
+      i # 返回插入点 i
+    end
     ```
 
 === "Zig"
diff --git a/docs/chapter_searching/replace_linear_by_hashing.md b/docs/chapter_searching/replace_linear_by_hashing.md
index a06d95962..3db51f347 100755
--- a/docs/chapter_searching/replace_linear_by_hashing.md
+++ b/docs/chapter_searching/replace_linear_by_hashing.md
@@ -228,7 +228,17 @@ comments: true
 === "Ruby"
 
     ```ruby title="two_sum.rb"
-    [class]{}-[func]{two_sum_brute_force}
+    ### 方法一：暴力枚举 ###
+    def two_sum_brute_force(nums, target)
+      # 两层循环，时间复杂度为 O(n^2)
+      for i in 0...(nums.length - 1)
+        for j in (i + 1)...nums.length
+          return [i, j] if nums[i] + nums[j] == target
+        end
+      end
+
+      []
+    end
     ```
 
 === "Zig"
@@ -531,7 +541,19 @@ comments: true
 === "Ruby"
 
     ```ruby title="two_sum.rb"
-    [class]{}-[func]{two_sum_hash_table}
+    ### 方法二：辅助哈希表 ###
+    def two_sum_hash_table(nums, target)
+      # 辅助哈希表，空间复杂度为 O(n)
+      dic = {}
+      # 单层循环，时间复杂度为 O(n)
+      for i in 0...nums.length
+        return [dic[target - nums[i]], i] if dic.has_key?(target - nums[i])
+
+        dic[nums[i]] = i
+      end
+
+      []
+    end
     ```
 
 === "Zig"
diff --git a/docs/chapter_sorting/bucket_sort.md b/docs/chapter_sorting/bucket_sort.md
index fa030145b..4a9270947 100644
--- a/docs/chapter_sorting/bucket_sort.md
+++ b/docs/chapter_sorting/bucket_sort.md
@@ -340,51 +340,37 @@ comments: true
 
     ```c title="bucket_sort.c"
     /* 桶排序 */
-    void bucketSort(float nums[], int size) {
-        // 初始化 k = n/2 个桶，预期向每个桶分配 2 个元素
-        int k = size / 2;
-        float **buckets = calloc(k, sizeof(float *));
-        for (int i = 0; i < k; i++) {
-            // 每个桶最多可以分配 size 个元素
-            buckets[i] = calloc(size, sizeof(float));
+    void bucketSort(float nums[], int n) {
+        int k = n / 2;                                 // 初始化 k = n/2 个桶
+        int *sizes = malloc(k * sizeof(int));          // 记录每个桶的大小
+        float **buckets = malloc(k * sizeof(float *)); // 动态数组的数组（桶）
+
+        for (int i = 0; i < k; ++i) {
+            // 为每个桶预分配足够的空间
+            buckets[i] = (float *)malloc(n * sizeof(float));
+            sizes[i] = 0;
         }
 
         // 1. 将数组元素分配到各个桶中
-        for (int i = 0; i < size; i++) {
-            // 输入数据范围为 [0, 1)，使用 num * k 映射到索引范围 [0, k-1]
-            int bucket_idx = nums[i] * k;
-            int j = 0;
-            // 如果桶中有数据且数据小于当前值 nums[i], 要将其放到当前桶的后面，相当于 cpp 中的 push_back
-            while (buckets[bucket_idx][j] > 0 && buckets[bucket_idx][j] < nums[i]) {
-                j++;
-            }
-            float temp = nums[i];
-            while (j < size && buckets[bucket_idx][j] > 0) {
-                swap(&temp, &buckets[bucket_idx][j]);
-                j++;
-            }
-            buckets[bucket_idx][j] = temp;
+        for (int i = 0; i < n; ++i) {
+            int idx = (int)(nums[i] * k);
+            buckets[idx][sizes[idx]++] = nums[i];
         }
 
         // 2. 对各个桶执行排序
-        for (int i = 0; i < k; i++) {
-            qsort(buckets[i], size, sizeof(float), compare_float);
+        for (int i = 0; i < k; ++i) {
+            qsort(buckets[i], sizes[i], sizeof(float), compare);
         }
 
-        // 3. 遍历桶合并结果
-        for (int i = 0, j = 0; j < k; j++) {
-            for (int l = 0; l < size; l++) {
-                if (buckets[j][l] > 0) {
-                    nums[i++] = buckets[j][l];
-                }
+        // 3. 合并排序后的桶
+        int idx = 0;
+        for (int i = 0; i < k; ++i) {
+            for (int j = 0; j < sizes[i]; ++j) {
+                nums[idx++] = buckets[i][j];
             }
-        }
-
-        // 释放上述分配的内存
-        for (int i = 0; i < k; i++) {
+            // 释放内存
             free(buckets[i]);
         }
-        free(buckets);
     }
     ```
 
diff --git a/docs/chapter_sorting/insertion_sort.md b/docs/chapter_sorting/insertion_sort.md
index 40ed3d4ed..1dee1b995 100755
--- a/docs/chapter_sorting/insertion_sort.md
+++ b/docs/chapter_sorting/insertion_sort.md
@@ -253,7 +253,21 @@ comments: true
 === "Ruby"
 
     ```ruby title="insertion_sort.rb"
-    [class]{}-[func]{insertion_sort}
+    ### 插入排序 ###
+    def insertion_sort(nums)
+      n = nums.length
+      # 外循环：已排序区间为 [0, i-1]
+      for i in 1...n
+        base = nums[i]
+        j = i - 1
+        # 内循环：将 base 插入到已排序区间 [0, i-1] 中的正确位置
+        while j >= 0 && nums[j] > base
+          nums[j + 1] = nums[j] # 将 nums[j] 向右移动一位
+          j -= 1
+        end
+        nums[j + 1] = base # 将 base 赋值到正确位置
+      end
+    end
     ```
 
 === "Zig"
diff --git a/en/docs/chapter_hashing/hash_map.md b/en/docs/chapter_hashing/hash_map.md
index 922eb15c2..0937369d7 100755
--- a/en/docs/chapter_hashing/hash_map.md
+++ b/en/docs/chapter_hashing/hash_map.md
@@ -1417,18 +1417,21 @@ The following code implements a simple hash table. Here, we encapsulate `key` an
 
     /* 基于数组实现的哈希表 */
     typedef struct {
-        Pair *buckets[HASHTABLE_CAPACITY];
+        Pair *buckets[MAX_SIZE];
     } ArrayHashMap;
 
     /* 构造函数 */
     ArrayHashMap *newArrayHashMap() {
         ArrayHashMap *hmap = malloc(sizeof(ArrayHashMap));
+        for (int i=0; i < MAX_SIZE; i++) {
+            hmap->buckets[i] = NULL;
+        }
         return hmap;
     }
 
     /* 析构函数 */
     void delArrayHashMap(ArrayHashMap *hmap) {
-        for (int i = 0; i < HASHTABLE_CAPACITY; i++) {
+        for (int i = 0; i < MAX_SIZE; i++) {
             if (hmap->buckets[i] != NULL) {
                 free(hmap->buckets[i]->val);
                 free(hmap->buckets[i]);
@@ -1462,13 +1465,13 @@ The following code implements a simple hash table. Here, we encapsulate `key` an
         int i = 0, index = 0;
         int total = 0;
         /* 统计有效键值对数量 */
-        for (i = 0; i < HASHTABLE_CAPACITY; i++) {
+        for (i = 0; i < MAX_SIZE; i++) {
             if (hmap->buckets[i] != NULL) {
                 total++;
             }
         }
         entries = malloc(sizeof(Pair) * total);
-        for (i = 0; i < HASHTABLE_CAPACITY; i++) {
+        for (i = 0; i < MAX_SIZE; i++) {
             if (hmap->buckets[i] != NULL) {
                 entries[index].key = hmap->buckets[i]->key;
                 entries[index].val = malloc(strlen(hmap->buckets[i]->val) + 1);
@@ -1486,13 +1489,13 @@ The following code implements a simple hash table. Here, we encapsulate `key` an
         int i = 0, index = 0;
         int total = 0;
         /* 统计有效键值对数量 */
-        for (i = 0; i < HASHTABLE_CAPACITY; i++) {
+        for (i = 0; i < MAX_SIZE; i++) {
             if (hmap->buckets[i] != NULL) {
                 total++;
             }
         }
         keys = malloc(total * sizeof(int));
-        for (i = 0; i < HASHTABLE_CAPACITY; i++) {
+        for (i = 0; i < MAX_SIZE; i++) {
             if (hmap->buckets[i] != NULL) {
                 keys[index] = hmap->buckets[i]->key;
                 index++;
@@ -1508,13 +1511,13 @@ The following code implements a simple hash table. Here, we encapsulate `key` an
         int i = 0, index = 0;
         int total = 0;
         /* 统计有效键值对数量 */
-        for (i = 0; i < HASHTABLE_CAPACITY; i++) {
+        for (i = 0; i < MAX_SIZE; i++) {
             if (hmap->buckets[i] != NULL) {
                 total++;
             }
         }
         vals = malloc(total * sizeof(char *));
-        for (i = 0; i < HASHTABLE_CAPACITY; i++) {
+        for (i = 0; i < MAX_SIZE; i++) {
             if (hmap->buckets[i] != NULL) {
                 vals[index] = hmap->buckets[i]->val;
                 index++;
diff --git a/zh-Hant/docs/chapter_hashing/hash_map.md b/zh-Hant/docs/chapter_hashing/hash_map.md
index 77c69317f..9c7aea2d1 100755
--- a/zh-Hant/docs/chapter_hashing/hash_map.md
+++ b/zh-Hant/docs/chapter_hashing/hash_map.md
@@ -1458,18 +1458,21 @@ index = hash(key) % capacity
 
     /* 基於陣列實現的雜湊表 */
     typedef struct {
-        Pair *buckets[HASHTABLE_CAPACITY];
+        Pair *buckets[MAX_SIZE];
     } ArrayHashMap;
 
     /* 建構子 */
     ArrayHashMap *newArrayHashMap() {
         ArrayHashMap *hmap = malloc(sizeof(ArrayHashMap));
+        for (int i = 0; i < MAX_SIZE; i++) {
+            hmap->buckets[i] = NULL;
+        }
         return hmap;
     }
 
     /* 析構函式 */
     void delArrayHashMap(ArrayHashMap *hmap) {
-        for (int i = 0; i < HASHTABLE_CAPACITY; i++) {
+        for (int i = 0; i < MAX_SIZE; i++) {
             if (hmap->buckets[i] != NULL) {
                 free(hmap->buckets[i]->val);
                 free(hmap->buckets[i]);
@@ -1503,13 +1506,13 @@ index = hash(key) % capacity
         int i = 0, index = 0;
         int total = 0;
         /* 統計有效鍵值對數量 */
-        for (i = 0; i < HASHTABLE_CAPACITY; i++) {
+        for (i = 0; i < MAX_SIZE; i++) {
             if (hmap->buckets[i] != NULL) {
                 total++;
             }
         }
         entries = malloc(sizeof(Pair) * total);
-        for (i = 0; i < HASHTABLE_CAPACITY; i++) {
+        for (i = 0; i < MAX_SIZE; i++) {
             if (hmap->buckets[i] != NULL) {
                 entries[index].key = hmap->buckets[i]->key;
                 entries[index].val = malloc(strlen(hmap->buckets[i]->val) + 1);
@@ -1527,13 +1530,13 @@ index = hash(key) % capacity
         int i = 0, index = 0;
         int total = 0;
         /* 統計有效鍵值對數量 */
-        for (i = 0; i < HASHTABLE_CAPACITY; i++) {
+        for (i = 0; i < MAX_SIZE; i++) {
             if (hmap->buckets[i] != NULL) {
                 total++;
             }
         }
         keys = malloc(total * sizeof(int));
-        for (i = 0; i < HASHTABLE_CAPACITY; i++) {
+        for (i = 0; i < MAX_SIZE; i++) {
             if (hmap->buckets[i] != NULL) {
                 keys[index] = hmap->buckets[i]->key;
                 index++;
@@ -1549,13 +1552,13 @@ index = hash(key) % capacity
         int i = 0, index = 0;
         int total = 0;
         /* 統計有效鍵值對數量 */
-        for (i = 0; i < HASHTABLE_CAPACITY; i++) {
+        for (i = 0; i < MAX_SIZE; i++) {
             if (hmap->buckets[i] != NULL) {
                 total++;
             }
         }
         vals = malloc(total * sizeof(char *));
-        for (i = 0; i < HASHTABLE_CAPACITY; i++) {
+        for (i = 0; i < MAX_SIZE; i++) {
             if (hmap->buckets[i] != NULL) {
                 vals[index] = hmap->buckets[i]->val;
                 index++;
diff --git a/zh-Hant/docs/chapter_sorting/bucket_sort.md b/zh-Hant/docs/chapter_sorting/bucket_sort.md
index bd49cc67f..d7c4eea25 100644
--- a/zh-Hant/docs/chapter_sorting/bucket_sort.md
+++ b/zh-Hant/docs/chapter_sorting/bucket_sort.md
@@ -340,51 +340,37 @@ comments: true
 
     ```c title="bucket_sort.c"
     /* 桶排序 */
-    void bucketSort(float nums[], int size) {
-        // 初始化 k = n/2 個桶，預期向每個桶分配 2 個元素
-        int k = size / 2;
-        float **buckets = calloc(k, sizeof(float *));
-        for (int i = 0; i < k; i++) {
-            // 每個桶最多可以分配 size 個元素
-            buckets[i] = calloc(size, sizeof(float));
+    void bucketSort(float nums[], int n) {
+        int k = n / 2;                                 // 初始化 k = n/2 個桶
+        int *sizes = malloc(k * sizeof(int));          // 記錄每個桶的大小
+        float **buckets = malloc(k * sizeof(float *)); // 動態陣列的陣列（桶）
+
+        for (int i = 0; i < k; ++i) {
+            // 為每個桶預分配足夠的空間
+            buckets[i] = (float *)malloc(n * sizeof(float));
+            sizes[i] = 0;
         }
 
         // 1. 將陣列元素分配到各個桶中
-        for (int i = 0; i < size; i++) {
-            // 輸入資料範圍為 [0, 1)，使用 num * k 對映到索引範圍 [0, k-1]
-            int bucket_idx = nums[i] * k;
-            int j = 0;
-            // 如果桶中有資料且資料小於當前值 nums[i], 要將其放到當前桶的後面，相當於 cpp 中的 push_back
-            while (buckets[bucket_idx][j] > 0 && buckets[bucket_idx][j] < nums[i]) {
-                j++;
-            }
-            float temp = nums[i];
-            while (j < size && buckets[bucket_idx][j] > 0) {
-                swap(&temp, &buckets[bucket_idx][j]);
-                j++;
-            }
-            buckets[bucket_idx][j] = temp;
+        for (int i = 0; i < n; ++i) {
+            int idx = (int)(nums[i] * k);
+            buckets[idx][sizes[idx]++] = nums[i];
         }
 
         // 2. 對各個桶執行排序
-        for (int i = 0; i < k; i++) {
-            qsort(buckets[i], size, sizeof(float), compare_float);
+        for (int i = 0; i < k; ++i) {
+            qsort(buckets[i], sizes[i], sizeof(float), compare);
         }
 
-        // 3. 走訪桶合併結果
-        for (int i = 0, j = 0; j < k; j++) {
-            for (int l = 0; l < size; l++) {
-                if (buckets[j][l] > 0) {
-                    nums[i++] = buckets[j][l];
-                }
+        // 3. 合併排序後的桶
+        int idx = 0;
+        for (int i = 0; i < k; ++i) {
+            for (int j = 0; j < sizes[i]; ++j) {
+                nums[idx++] = buckets[i][j];
             }
-        }
-
-        // 釋放上述分配的記憶體
-        for (int i = 0; i < k; i++) {
+            // 釋放記憶體
             free(buckets[i]);
         }
-        free(buckets);
     }
     ```