build

docs/chapter_array_and_linkedlist/linked_list.md

@@ -813,6 +813,7 @@ comments: true
     fun remove(n0: ListNode?) {
         if (n0?.next == null)
             return
+        // n0 -> P -> n1
         val p = n0.next
         val n1 = p?.next
         n0.next = n1

docs/chapter_array_and_linkedlist/list.md

@@ -385,10 +385,10 @@ comments: true
     nums.Add(4);
 
     /* 在中间插入元素 */
-    nums.Insert(3, 6);
+    nums.Insert(3, 6);  // 在索引 3 处插入数字 6
 
     /* 删除元素 */
-    nums.RemoveAt(3);
+    nums.RemoveAt(3);  // 删除索引 3 处的元素
     ```
 
 === "Go"
@@ -445,10 +445,10 @@ comments: true
     nums.push(4);
 
     /* 在中间插入元素 */
-    nums.splice(3, 0, 6);
+    nums.splice(3, 0, 6); // 在索引 3 处插入数字 6
 
     /* 删除元素 */
-    nums.splice(3, 1);
+    nums.splice(3, 1);  // 删除索引 3 处的元素
     ```
 
 === "TS"
@@ -465,10 +465,10 @@ comments: true
     nums.push(4);
 
     /* 在中间插入元素 */
-    nums.splice(3, 0, 6);
+    nums.splice(3, 0, 6); // 在索引 3 处插入数字 6
 
     /* 删除元素 */
-    nums.splice(3, 1);
+    nums.splice(3, 1);  // 删除索引 3 处的元素
     ```
 
 === "Dart"

docs/chapter_computational_complexity/iteration_and_recursion.md

@@ -1992,6 +1992,7 @@ comments: true
         var res = 0
         // 递: 递归调用
         for (i in n downTo 0) {
+            // 通过“入栈操作”模拟“递”
             stack.push(i)
         }
         // 归: 返回结果

docs/chapter_computational_complexity/time_complexity.md

@@ -1431,7 +1431,6 @@ $$
     /* 线性阶 */
     fun linear(n: Int): Int {
         var count = 0
-        // 循环次数与数组长度成正比
         for (i in 0..<n)
             count++
         return count
@@ -2175,7 +2174,9 @@ $$
             for (j in 0..<i) {
                 if (nums[j] > nums[j + 1]) {
                     // 交换 nums[j] 与 nums[j + 1]
-                    nums[j] = nums[j + 1].also { nums[j + 1] = nums[j] }
+                    val temp = nums[j]
+                    nums[j] = nums[j + 1]
+                    nums[j + 1] = temp
                     count += 3 // 元素交换包含 3 个单元操作
                 }
             }
@@ -2452,8 +2453,8 @@ $$
     /* 指数阶（循环实现） */
     fun exponential(n: Int): Int {
         var count = 0
-        // 细胞每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1)
         var base = 1
+        // 细胞每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1)
         for (i in 0..<n) {
             for (j in 0..<base) {
                 count++
@@ -3859,12 +3860,11 @@ $$
         for (i in 0..<n) {
             nums[i] = i + 1
         }
-        val mutableList = nums.toMutableList()
         // 随机打乱数组元素
-        mutableList.shuffle()
+        nums.shuffle()
         val res = arrayOfNulls<Int>(n)
         for (i in 0..<n) {
-            res[i] = mutableList[i]
+            res[i] = nums[i]
         }
         return res
     }

docs/chapter_dynamic_programming/intro_to_dynamic_programming.md

@@ -184,7 +184,9 @@ comments: true
             if state + choice > n {
                 continue
             }
+            // 尝试：做出选择，更新状态
             backtrack(choices: choices, state: state + choice, n: n, res: &res)
+            // 回退
         }
     }
 
@@ -1597,7 +1599,9 @@ $$
         var a = 1
         var b = 2
         for (i in 3..n) {
-            b += a.also { a = b }
+            val temp = b
+            b += a
+            a = temp
         }
         return b
     }

docs/chapter_dynamic_programming/knapsack_problem.md

@@ -1036,11 +1036,7 @@ $$
 
     ```kotlin title="knapsack.kt"
     /* 0-1 背包：动态规划 */
-    fun knapsackDP(
-        wgt: IntArray,
-        _val: IntArray,
-        cap: Int
-    ): Int {
+    fun knapsackDP(wgt: IntArray, _val: IntArray, cap: Int): Int {
         val n = wgt.size
         // 初始化 dp 表
         val dp = Array(n + 1) { IntArray(cap + 1) }
@@ -1429,11 +1425,7 @@ $$
 
     ```kotlin title="knapsack.kt"
     /* 0-1 背包：空间优化后的动态规划 */
-    fun knapsackDPComp(
-        wgt: IntArray,
-        _val: IntArray,
-        cap: Int
-    ): Int {
+    fun knapsackDPComp(wgt: IntArray, _val: IntArray, cap: Int): Int {
         val n = wgt.size
         // 初始化 dp 表
         val dp = IntArray(cap + 1)
@@ -1443,8 +1435,7 @@ $$
             for (c in cap downTo 1) {
                 if (wgt[i - 1] <= c) {
                     // 不选和选物品 i 这两种方案的较大值
-                    dp[c] =
-                        max(dp[c], dp[c - wgt[i - 1]] + _val[i - 1])
+                    dp[c] = max(dp[c], dp[c - wgt[i - 1]] + _val[i - 1])
                 }
             }
         }

docs/chapter_graph/graph_operations.md

@@ -1103,8 +1103,8 @@ comments: true
             if (i < 0 || j < 0 || i >= size() || j >= size() || i == j)
                 throw IndexOutOfBoundsException()
             // 在无向图中，邻接矩阵关于主对角线对称，即满足 (i, j) == (j, i)
-            adjMat[i][j] = 1;
-            adjMat[j][i] = 1;
+            adjMat[i][j] = 1
+            adjMat[j][i] = 1
         }
 
         /* 删除边 */
@@ -1113,15 +1113,15 @@ comments: true
             // 索引越界与相等处理
             if (i < 0 || j < 0 || i >= size() || j >= size() || i == j)
                 throw IndexOutOfBoundsException()
-            adjMat[i][j] = 0;
-            adjMat[j][i] = 0;
+            adjMat[i][j] = 0
+            adjMat[j][i] = 0
         }
 
         /* 打印邻接矩阵 */
         fun print() {
             print("顶点列表 = ")
-            println(vertices);
-            println("邻接矩阵 =");
+            println(vertices)
+            println("邻接矩阵 =")
             printMatrix(adjMat)
         }
     }
@@ -2167,9 +2167,9 @@ comments: true
         init {
             // 添加所有顶点和边
             for (edge in edges) {
-                addVertex(edge[0]!!);
-                addVertex(edge[1]!!);
-                addEdge(edge[0]!!, edge[1]!!);
+                addVertex(edge[0]!!)
+                addVertex(edge[1]!!)
+                addEdge(edge[0]!!, edge[1]!!)
             }
         }
 
@@ -2184,7 +2184,7 @@ comments: true
                 throw IllegalArgumentException()
             // 添加边 vet1 - vet2
             adjList[vet1]?.add(vet2)
-            adjList[vet2]?.add(vet1);
+            adjList[vet2]?.add(vet1)
         }
 
         /* 删除边 */
@@ -2192,8 +2192,8 @@ comments: true
             if (!adjList.containsKey(vet1) || !adjList.containsKey(vet2) || vet1 == vet2)
                 throw IllegalArgumentException()
             // 删除边 vet1 - vet2
-            adjList[vet1]?.remove(vet2);
-            adjList[vet2]?.remove(vet1);
+            adjList[vet1]?.remove(vet2)
+            adjList[vet2]?.remove(vet1)
         }
 
         /* 添加顶点 */
@@ -2209,7 +2209,7 @@ comments: true
             if (!adjList.containsKey(vet))
                 throw IllegalArgumentException()
             // 在邻接表中删除顶点 vet 对应的链表
-            adjList.remove(vet);
+            adjList.remove(vet)
             // 遍历其他顶点的链表，删除所有包含 vet 的边
             for (list in adjList.values) {
                 list.remove(vet)

docs/chapter_hashing/hash_algorithm.md

@@ -560,6 +560,7 @@ index = hash(key) % capacity
     /* 加法哈希 */
     fun addHash(key: String): Int {
         var hash = 0L
+        val MODULUS = 1000000007
         for (c in key.toCharArray()) {
             hash = (hash + c.code) % MODULUS
         }
@@ -569,6 +570,7 @@ index = hash(key) % capacity
     /* 乘法哈希 */
     fun mulHash(key: String): Int {
         var hash = 0L
+        val MODULUS = 1000000007
         for (c in key.toCharArray()) {
             hash = (31 * hash + c.code) % MODULUS
         }
@@ -578,6 +580,7 @@ index = hash(key) % capacity
     /* 异或哈希 */
     fun xorHash(key: String): Int {
         var hash = 0
+        val MODULUS = 1000000007
         for (c in key.toCharArray()) {
             hash = hash xor c.code
         }
@@ -587,6 +590,7 @@ index = hash(key) % capacity
     /* 旋转哈希 */
     fun rotHash(key: String): Int {
         var hash = 0L
+        val MODULUS = 1000000007
         for (c in key.toCharArray()) {
             hash = ((hash shl 4) xor (hash shr 28) xor c.code.toLong()) % MODULUS
         }

docs/chapter_hashing/hash_collision.md

@@ -1312,7 +1312,7 @@ comments: true
 
     ```kotlin title="hash_map_chaining.kt"
     /* 链式地址哈希表 */
-    class HashMapChaining() {
+    class HashMapChaining {
         var size: Int // 键值对数量
         var capacity: Int // 哈希表容量
         val loadThres: Double // 触发扩容的负载因子阈值

docs/chapter_hashing/hash_map.md

@@ -1646,7 +1646,8 @@ index = hash(key) % capacity
         fun valueSet(): MutableList<String> {
             val valueSet = mutableListOf<String>()
             for (pair in buckets) {
-                pair?.let { valueSet.add(it._val) }
+                if (pair != null)
+                    valueSet.add(pair._val)
             }
             return valueSet
         }
@@ -1656,7 +1657,7 @@ index = hash(key) % capacity
             for (kv in pairSet()) {
                 val key = kv.key
                 val _val = kv._val
-                println("${key} -> ${_val}")
+                println("$key -> $_val")
             }
         }
     }

docs/chapter_heap/build_heap.md

@@ -220,7 +220,9 @@ comments: true
 
         /* 交换元素 */
         private fun swap(i: Int, j: Int) {
-            maxHeap[i] = maxHeap[j].also { maxHeap[j] = maxHeap[i] }
+            val temp = maxHeap[i]
+            maxHeap[i] = maxHeap[j]
+            maxHeap[j] = temp
         }
 
         /* 获取堆大小 */

docs/chapter_heap/heap.md

@@ -650,7 +650,7 @@ comments: true
 
     /* 获取父节点的索引 */
     int parent(MaxHeap *maxHeap, int i) {
-        return (i - 1) / 2;
+        return (i - 1) / 2; // 向下取整
     }
     ```
 

docs/chapter_sorting/bubble_sort.md

@@ -264,7 +264,9 @@ comments: true
             for (j in 0..<i) {
                 if (nums[j] > nums[j + 1]) {
                     // 交换 nums[j] 与 nums[j + 1]
-                    nums[j] = nums[j + 1].also { nums[j + 1] = nums[j] }
+                    val temp = nums[j]
+                    nums[j] = nums[j + 1]
+                    nums[j + 1] = temp
                 }
             }
         }
@@ -571,7 +573,9 @@ comments: true
             for (j in 0..<i) {
                 if (nums[j] > nums[j + 1]) {
                     // 交换 nums[j] 与 nums[j + 1]
-                    nums[j] = nums[j + 1].also { nums[j] = nums[j + 1] }
+                    val temp = nums[j]
+                    nums[j] = nums[j + 1]
+                    nums[j + 1] = temp
                     flag = true // 记录交换元素
                 }
             }

docs/chapter_sorting/heap_sort.md

@@ -553,7 +553,9 @@ comments: true
             if (ma == i) 
                 break
             // 交换两节点
-            nums[i] = nums[ma].also { nums[ma] = nums[i] }
+            val temp = nums[i]
+            nums[i] = nums[ma]
+            nums[ma] = temp
             // 循环向下堆化
             i = ma
         }
@@ -568,7 +570,9 @@ comments: true
         // 从堆中提取最大元素，循环 n-1 轮
         for (i in nums.size - 1 downTo 1) {
             // 交换根节点与最右叶节点（交换首元素与尾元素）
-            nums[0] = nums[i].also { nums[i] = nums[0] }
+            val temp = nums[0]
+            nums[0] = nums[i]
+            nums[i] = temp
             // 以根节点为起点，从顶至底进行堆化
             siftDown(nums, i, 0)
         }

docs/chapter_sorting/quick_sort.md

@@ -328,7 +328,9 @@ comments: true
     ```kotlin title="quick_sort.kt"
     /* 元素交换 */
     fun swap(nums: IntArray, i: Int, j: Int) {
-        nums[i] = nums[j].also { nums[j] = nums[i] }
+        val temp = nums[i]
+        nums[i] = nums[j]
+        nums[j] = temp
     }
 
     /* 哨兵划分 */

docs/chapter_sorting/selection_sort.md

@@ -296,7 +296,9 @@ comments: true
                     k = j // 记录最小元素的索引
             }
             // 将该最小元素与未排序区间的首个元素交换
-            nums[i] = nums[k].also { nums[k] = nums[i] }
+            val temp = nums[i]
+            nums[i] = nums[k]
+            nums[k] = temp
         }
     }
     ```

docs/chapter_stack_and_queue/stack.md

@@ -1092,7 +1092,7 @@ comments: true
         fun pop(): Int? {
             val num = peek()
             stackPeek = stackPeek?.next
-            stkSize--;
+            stkSize--
             return num
         }
 

docs/chapter_tree/array_representation_of_tree.md

@@ -125,7 +125,7 @@ comments: true
     ```kotlin title=""
     /* 二叉树的数组表示 */
     // 使用 null 来表示空位
-    val tree = mutableListOf( 1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15 )
+    val tree = arrayOf( 1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15 )
     ```
 
 === "Ruby"
@@ -1172,7 +1172,7 @@ comments: true
 === "Kotlin"
 
     ```kotlin title="array_binary_tree.kt"
-    /* 构造方法 */
+    /* 数组表示下的二叉树类 */
     class ArrayBinaryTree(val tree: MutableList<Int?>) {
         /* 列表容量 */
         fun size(): Int {

en/docs/chapter_array_and_linkedlist/linked_list.md

@@ -760,6 +760,7 @@ It's important to note that even though node `P` continues to point to `n1` afte
     fun remove(n0: ListNode?) {
         if (n0?.next == null)
             return
+        // n0 -> P -> n1
         val p = n0.next
         val n1 = p?.next
         n0.next = n1

en/docs/chapter_computational_complexity/iteration_and_recursion.md

@@ -1992,6 +1992,7 @@ Therefore, **we can use an explicit stack to simulate the behavior of the call s
         var res = 0
         // 递: 递归调用
         for (i in n downTo 0) {
+            // 通过“入栈操作”模拟“递”
             stack.push(i)
         }
         // 归: 返回结果

en/docs/chapter_computational_complexity/time_complexity.md

@@ -1319,7 +1319,6 @@ Linear order indicates the number of operations grows linearly with the input da
     /* 线性阶 */
     fun linear(n: Int): Int {
         var count = 0
-        // 循环次数与数组长度成正比
         for (i in 0..<n)
             count++
         return count
@@ -2063,7 +2062,9 @@ For instance, in bubble sort, the outer loop runs $n - 1$ times, and the inner l
             for (j in 0..<i) {
                 if (nums[j] > nums[j + 1]) {
                     // 交换 nums[j] 与 nums[j + 1]
-                    nums[j] = nums[j + 1].also { nums[j + 1] = nums[j] }
+                    val temp = nums[j]
+                    nums[j] = nums[j + 1]
+                    nums[j + 1] = temp
                     count += 3 // 元素交换包含 3 个单元操作
                 }
             }
@@ -2340,8 +2341,8 @@ The following image and code simulate the cell division process, with a time com
     /* 指数阶（循环实现） */
     fun exponential(n: Int): Int {
         var count = 0
-        // 细胞每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1)
         var base = 1
+        // 细胞每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1)
         for (i in 0..<n) {
             for (j in 0..<base) {
                 count++
@@ -3747,12 +3748,11 @@ The "worst-case time complexity" corresponds to the asymptotic upper bound, deno
         for (i in 0..<n) {
             nums[i] = i + 1
         }
-        val mutableList = nums.toMutableList()
         // 随机打乱数组元素
-        mutableList.shuffle()
+        nums.shuffle()
         val res = arrayOfNulls<Int>(n)
         for (i in 0..<n) {
-            res[i] = mutableList[i]
+            res[i] = nums[i]
         }
         return res
     }

en/docs/chapter_graph/graph_operations.md

@@ -1103,8 +1103,8 @@ Below is the implementation code for graphs represented using an adjacency matri
             if (i < 0 || j < 0 || i >= size() || j >= size() || i == j)
                 throw IndexOutOfBoundsException()
             // 在无向图中，邻接矩阵关于主对角线对称，即满足 (i, j) == (j, i)
-            adjMat[i][j] = 1;
-            adjMat[j][i] = 1;
+            adjMat[i][j] = 1
+            adjMat[j][i] = 1
         }
 
         /* 删除边 */
@@ -1113,15 +1113,15 @@ Below is the implementation code for graphs represented using an adjacency matri
             // 索引越界与相等处理
             if (i < 0 || j < 0 || i >= size() || j >= size() || i == j)
                 throw IndexOutOfBoundsException()
-            adjMat[i][j] = 0;
-            adjMat[j][i] = 0;
+            adjMat[i][j] = 0
+            adjMat[j][i] = 0
         }
 
         /* 打印邻接矩阵 */
         fun print() {
             print("顶点列表 = ")
-            println(vertices);
-            println("邻接矩阵 =");
+            println(vertices)
+            println("邻接矩阵 =")
             printMatrix(adjMat)
         }
     }
@@ -2167,9 +2167,9 @@ Additionally, we use the `Vertex` class to represent vertices in the adjacency l
         init {
             // 添加所有顶点和边
             for (edge in edges) {
-                addVertex(edge[0]!!);
-                addVertex(edge[1]!!);
-                addEdge(edge[0]!!, edge[1]!!);
+                addVertex(edge[0]!!)
+                addVertex(edge[1]!!)
+                addEdge(edge[0]!!, edge[1]!!)
             }
         }
 
@@ -2184,7 +2184,7 @@ Additionally, we use the `Vertex` class to represent vertices in the adjacency l
                 throw IllegalArgumentException()
             // 添加边 vet1 - vet2
             adjList[vet1]?.add(vet2)
-            adjList[vet2]?.add(vet1);
+            adjList[vet2]?.add(vet1)
         }
 
         /* 删除边 */
@@ -2192,8 +2192,8 @@ Additionally, we use the `Vertex` class to represent vertices in the adjacency l
             if (!adjList.containsKey(vet1) || !adjList.containsKey(vet2) || vet1 == vet2)
                 throw IllegalArgumentException()
             // 删除边 vet1 - vet2
-            adjList[vet1]?.remove(vet2);
-            adjList[vet2]?.remove(vet1);
+            adjList[vet1]?.remove(vet2)
+            adjList[vet2]?.remove(vet1)
         }
 
         /* 添加顶点 */
@@ -2209,7 +2209,7 @@ Additionally, we use the `Vertex` class to represent vertices in the adjacency l
             if (!adjList.containsKey(vet))
                 throw IllegalArgumentException()
             // 在邻接表中删除顶点 vet 对应的链表
-            adjList.remove(vet);
+            adjList.remove(vet)
             // 遍历其他顶点的链表，删除所有包含 vet 的边
             for (list in adjList.values) {
                 list.remove(vet)

en/docs/chapter_hashing/hash_algorithm.md

@@ -560,6 +560,7 @@ The design of hash algorithms is a complex issue that requires consideration of
     /* 加法哈希 */
     fun addHash(key: String): Int {
         var hash = 0L
+        val MODULUS = 1000000007
         for (c in key.toCharArray()) {
             hash = (hash + c.code) % MODULUS
         }
@@ -569,6 +570,7 @@ The design of hash algorithms is a complex issue that requires consideration of
     /* 乘法哈希 */
     fun mulHash(key: String): Int {
         var hash = 0L
+        val MODULUS = 1000000007
         for (c in key.toCharArray()) {
             hash = (31 * hash + c.code) % MODULUS
         }
@@ -578,6 +580,7 @@ The design of hash algorithms is a complex issue that requires consideration of
     /* 异或哈希 */
     fun xorHash(key: String): Int {
         var hash = 0
+        val MODULUS = 1000000007
         for (c in key.toCharArray()) {
             hash = hash xor c.code
         }
@@ -587,6 +590,7 @@ The design of hash algorithms is a complex issue that requires consideration of
     /* 旋转哈希 */
     fun rotHash(key: String): Int {
         var hash = 0L
+        val MODULUS = 1000000007
         for (c in key.toCharArray()) {
             hash = ((hash shl 4) xor (hash shr 28) xor c.code.toLong()) % MODULUS
         }

en/docs/chapter_hashing/hash_collision.md

@@ -1312,7 +1312,7 @@ The code below provides a simple implementation of a separate chaining hash tabl
 
     ```kotlin title="hash_map_chaining.kt"
     /* 链式地址哈希表 */
-    class HashMapChaining() {
+    class HashMapChaining {
         var size: Int // 键值对数量
         var capacity: Int // 哈希表容量
         val loadThres: Double // 触发扩容的负载因子阈值

en/docs/chapter_hashing/hash_map.md

@@ -1605,7 +1605,8 @@ The following code implements a simple hash table. Here, we encapsulate `key` an
         fun valueSet(): MutableList<String> {
             val valueSet = mutableListOf<String>()
             for (pair in buckets) {
-                pair?.let { valueSet.add(it._val) }
+                if (pair != null)
+                    valueSet.add(pair._val)
             }
             return valueSet
         }
@@ -1615,7 +1616,7 @@ The following code implements a simple hash table. Here, we encapsulate `key` an
             for (kv in pairSet()) {
                 val key = kv.key
                 val _val = kv._val
-                println("${key} -> ${_val}")
+                println("$key -> $_val")
             }
         }
     }

en/docs/chapter_heap/build_heap.md

@@ -220,7 +220,9 @@ It's worth mentioning that **since leaf nodes have no children, they naturally f
 
         /* 交换元素 */
         private fun swap(i: Int, j: Int) {
-            maxHeap[i] = maxHeap[j].also { maxHeap[j] = maxHeap[i] }
+            val temp = maxHeap[i]
+            maxHeap[i] = maxHeap[j]
+            maxHeap[j] = temp
         }
 
         /* 获取堆大小 */

en/docs/chapter_heap/heap.md

@@ -649,7 +649,7 @@ We can encapsulate the index mapping formula into functions for convenient later
 
     /* 获取父节点的索引 */
     int parent(MaxHeap *maxHeap, int i) {
-        return (i - 1) / 2;
+        return (i - 1) / 2; // 向下取整
     }
     ```
 

en/docs/chapter_stack_and_queue/stack.md

@@ -1045,7 +1045,7 @@ Below is an example code for implementing a stack based on a linked list:
         fun pop(): Int? {
             val num = peek()
             stackPeek = stackPeek?.next
-            stkSize--;
+            stkSize--
             return num
         }
 

en/docs/chapter_tree/array_representation_of_tree.md

@@ -1172,7 +1172,7 @@ The following code implements a binary tree based on array representation, inclu
 === "Kotlin"
 
     ```kotlin title="array_binary_tree.kt"
-    /* 构造方法 */
+    /* 数组表示下的二叉树类 */
     class ArrayBinaryTree(val tree: MutableList<Int?>) {
         /* 列表容量 */
         fun size(): Int {

zh-Hant/docs/chapter_array_and_linkedlist/linked_list.md

@@ -813,6 +813,7 @@ comments: true
     fun remove(n0: ListNode?) {
         if (n0?.next == null)
             return
+        // n0 -> P -> n1
         val p = n0.next
         val n1 = p?.next
         n0.next = n1

zh-Hant/docs/chapter_array_and_linkedlist/list.md

@@ -385,10 +385,10 @@ comments: true
     nums.Add(4);
 
     /* 在中間插入元素 */
-    nums.Insert(3, 6);
+    nums.Insert(3, 6);  // 在索引 3 處插入數字 6
 
     /* 刪除元素 */
-    nums.RemoveAt(3);
+    nums.RemoveAt(3);  // 刪除索引 3 處的元素
     ```
 
 === "Go"
@@ -445,10 +445,10 @@ comments: true
     nums.push(4);
 
     /* 在中間插入元素 */
-    nums.splice(3, 0, 6);
+    nums.splice(3, 0, 6); // 在索引 3 處插入數字 6
 
     /* 刪除元素 */
-    nums.splice(3, 1);
+    nums.splice(3, 1);  // 刪除索引 3 處的元素
     ```
 
 === "TS"
@@ -465,10 +465,10 @@ comments: true
     nums.push(4);
 
     /* 在中間插入元素 */
-    nums.splice(3, 0, 6);
+    nums.splice(3, 0, 6); // 在索引 3 處插入數字 6
 
     /* 刪除元素 */
-    nums.splice(3, 1);
+    nums.splice(3, 1);  // 刪除索引 3 處的元素
     ```
 
 === "Dart"

zh-Hant/docs/chapter_computational_complexity/iteration_and_recursion.md

@@ -1992,6 +1992,7 @@ comments: true
         var res = 0
         // 遞: 遞迴呼叫
         for (i in n downTo 0) {
+            // 透過“入堆疊操作”模擬“遞”
             stack.push(i)
         }
         // 迴: 返回結果

zh-Hant/docs/chapter_computational_complexity/time_complexity.md

@@ -1431,7 +1431,6 @@ $$
     /* 線性階 */
     fun linear(n: Int): Int {
         var count = 0
-        // 迴圈次數與陣列長度成正比
         for (i in 0..<n)
             count++
         return count
@@ -2175,7 +2174,9 @@ $$
             for (j in 0..<i) {
                 if (nums[j] > nums[j + 1]) {
                     // 交換 nums[j] 與 nums[j + 1]
-                    nums[j] = nums[j + 1].also { nums[j + 1] = nums[j] }
+                    val temp = nums[j]
+                    nums[j] = nums[j + 1]
+                    nums[j + 1] = temp
                     count += 3 // 元素交換包含 3 個單元操作
                 }
             }
@@ -2452,8 +2453,8 @@ $$
     /* 指數階（迴圈實現） */
     fun exponential(n: Int): Int {
         var count = 0
-        // 細胞每輪一分為二，形成數列 1, 2, 4, 8, ..., 2^(n-1)
         var base = 1
+        // 細胞每輪一分為二，形成數列 1, 2, 4, 8, ..., 2^(n-1)
         for (i in 0..<n) {
             for (j in 0..<base) {
                 count++
@@ -3859,12 +3860,11 @@ $$
         for (i in 0..<n) {
             nums[i] = i + 1
         }
-        val mutableList = nums.toMutableList()
         // 隨機打亂陣列元素
-        mutableList.shuffle()
+        nums.shuffle()
         val res = arrayOfNulls<Int>(n)
         for (i in 0..<n) {
-            res[i] = mutableList[i]
+            res[i] = nums[i]
         }
         return res
     }

zh-Hant/docs/chapter_dynamic_programming/intro_to_dynamic_programming.md

@@ -184,7 +184,9 @@ comments: true
             if state + choice > n {
                 continue
             }
+            // 嘗試：做出選擇，更新狀態
             backtrack(choices: choices, state: state + choice, n: n, res: &res)
+            // 回退
         }
     }
 
@@ -1597,7 +1599,9 @@ $$
         var a = 1
         var b = 2
         for (i in 3..n) {
-            b += a.also { a = b }
+            val temp = b
+            b += a
+            a = temp
         }
         return b
     }

zh-Hant/docs/chapter_dynamic_programming/knapsack_problem.md

@@ -1036,11 +1036,7 @@ $$
 
     ```kotlin title="knapsack.kt"
     /* 0-1 背包：動態規劃 */
-    fun knapsackDP(
-        wgt: IntArray,
-        _val: IntArray,
-        cap: Int
-    ): Int {
+    fun knapsackDP(wgt: IntArray, _val: IntArray, cap: Int): Int {
         val n = wgt.size
         // 初始化 dp 表
         val dp = Array(n + 1) { IntArray(cap + 1) }
@@ -1429,11 +1425,7 @@ $$
 
     ```kotlin title="knapsack.kt"
     /* 0-1 背包：空間最佳化後的動態規劃 */
-    fun knapsackDPComp(
-        wgt: IntArray,
-        _val: IntArray,
-        cap: Int
-    ): Int {
+    fun knapsackDPComp(wgt: IntArray, _val: IntArray, cap: Int): Int {
         val n = wgt.size
         // 初始化 dp 表
         val dp = IntArray(cap + 1)
@@ -1443,8 +1435,7 @@ $$
             for (c in cap downTo 1) {
                 if (wgt[i - 1] <= c) {
                     // 不選和選物品 i 這兩種方案的較大值
-                    dp[c] =
-                        max(dp[c], dp[c - wgt[i - 1]] + _val[i - 1])
+                    dp[c] = max(dp[c], dp[c - wgt[i - 1]] + _val[i - 1])
                 }
             }
         }

zh-Hant/docs/chapter_graph/graph_operations.md

@@ -1103,8 +1103,8 @@ comments: true
             if (i < 0 || j < 0 || i >= size() || j >= size() || i == j)
                 throw IndexOutOfBoundsException()
             // 在無向圖中，鄰接矩陣關於主對角線對稱，即滿足 (i, j) == (j, i)
-            adjMat[i][j] = 1;
-            adjMat[j][i] = 1;
+            adjMat[i][j] = 1
+            adjMat[j][i] = 1
         }
 
         /* 刪除邊 */
@@ -1113,15 +1113,15 @@ comments: true
             // 索引越界與相等處理
             if (i < 0 || j < 0 || i >= size() || j >= size() || i == j)
                 throw IndexOutOfBoundsException()
-            adjMat[i][j] = 0;
-            adjMat[j][i] = 0;
+            adjMat[i][j] = 0
+            adjMat[j][i] = 0
         }
 
         /* 列印鄰接矩陣 */
         fun print() {
             print("頂點串列 = ")
-            println(vertices);
-            println("鄰接矩陣 =");
+            println(vertices)
+            println("鄰接矩陣 =")
             printMatrix(adjMat)
         }
     }
@@ -2167,9 +2167,9 @@ comments: true
         init {
             // 新增所有頂點和邊
             for (edge in edges) {
-                addVertex(edge[0]!!);
-                addVertex(edge[1]!!);
-                addEdge(edge[0]!!, edge[1]!!);
+                addVertex(edge[0]!!)
+                addVertex(edge[1]!!)
+                addEdge(edge[0]!!, edge[1]!!)
             }
         }
 
@@ -2184,7 +2184,7 @@ comments: true
                 throw IllegalArgumentException()
             // 新增邊 vet1 - vet2
             adjList[vet1]?.add(vet2)
-            adjList[vet2]?.add(vet1);
+            adjList[vet2]?.add(vet1)
         }
 
         /* 刪除邊 */
@@ -2192,8 +2192,8 @@ comments: true
             if (!adjList.containsKey(vet1) || !adjList.containsKey(vet2) || vet1 == vet2)
                 throw IllegalArgumentException()
             // 刪除邊 vet1 - vet2
-            adjList[vet1]?.remove(vet2);
-            adjList[vet2]?.remove(vet1);
+            adjList[vet1]?.remove(vet2)
+            adjList[vet2]?.remove(vet1)
         }
 
         /* 新增頂點 */
@@ -2209,7 +2209,7 @@ comments: true
             if (!adjList.containsKey(vet))
                 throw IllegalArgumentException()
             // 在鄰接表中刪除頂點 vet 對應的鏈結串列
-            adjList.remove(vet);
+            adjList.remove(vet)
             // 走訪其他頂點的鏈結串列，刪除所有包含 vet 的邊
             for (list in adjList.values) {
                 list.remove(vet)

zh-Hant/docs/chapter_hashing/hash_algorithm.md

@@ -560,6 +560,7 @@ index = hash(key) % capacity
     /* 加法雜湊 */
     fun addHash(key: String): Int {
         var hash = 0L
+        val MODULUS = 1000000007
         for (c in key.toCharArray()) {
             hash = (hash + c.code) % MODULUS
         }
@@ -569,6 +570,7 @@ index = hash(key) % capacity
     /* 乘法雜湊 */
     fun mulHash(key: String): Int {
         var hash = 0L
+        val MODULUS = 1000000007
         for (c in key.toCharArray()) {
             hash = (31 * hash + c.code) % MODULUS
         }
@@ -578,6 +580,7 @@ index = hash(key) % capacity
     /* 互斥或雜湊 */
     fun xorHash(key: String): Int {
         var hash = 0
+        val MODULUS = 1000000007
         for (c in key.toCharArray()) {
             hash = hash xor c.code
         }
@@ -587,6 +590,7 @@ index = hash(key) % capacity
     /* 旋轉雜湊 */
     fun rotHash(key: String): Int {
         var hash = 0L
+        val MODULUS = 1000000007
         for (c in key.toCharArray()) {
             hash = ((hash shl 4) xor (hash shr 28) xor c.code.toLong()) % MODULUS
         }

zh-Hant/docs/chapter_hashing/hash_collision.md

@@ -1312,7 +1312,7 @@ comments: true
 
     ```kotlin title="hash_map_chaining.kt"
     /* 鏈式位址雜湊表 */
-    class HashMapChaining() {
+    class HashMapChaining {
         var size: Int // 鍵值對數量
         var capacity: Int // 雜湊表容量
         val loadThres: Double // 觸發擴容的負載因子閾值

zh-Hant/docs/chapter_hashing/hash_map.md

@@ -1646,7 +1646,8 @@ index = hash(key) % capacity
         fun valueSet(): MutableList<String> {
             val valueSet = mutableListOf<String>()
             for (pair in buckets) {
-                pair?.let { valueSet.add(it._val) }
+                if (pair != null)
+                    valueSet.add(pair._val)
             }
             return valueSet
         }
@@ -1656,7 +1657,7 @@ index = hash(key) % capacity
             for (kv in pairSet()) {
                 val key = kv.key
                 val _val = kv._val
-                println("${key} -> ${_val}")
+                println("$key -> $_val")
             }
         }
     }

zh-Hant/docs/chapter_heap/build_heap.md

@@ -220,7 +220,9 @@ comments: true
 
         /* 交換元素 */
         private fun swap(i: Int, j: Int) {
-            maxHeap[i] = maxHeap[j].also { maxHeap[j] = maxHeap[i] }
+            val temp = maxHeap[i]
+            maxHeap[i] = maxHeap[j]
+            maxHeap[j] = temp
         }
 
         /* 獲取堆積大小 */

zh-Hant/docs/chapter_heap/heap.md

@@ -650,7 +650,7 @@ comments: true
 
     /* 獲取父節點的索引 */
     int parent(MaxHeap *maxHeap, int i) {
-        return (i - 1) / 2;
+        return (i - 1) / 2; // 向下取整
     }
     ```
 

zh-Hant/docs/chapter_searching/binary_search.md

@@ -339,7 +339,27 @@ comments: true
 === "Ruby"
 
     ```ruby title="binary_search.rb"
-    [class]{}-[func]{binary_search}
+    ### 二分搜尋（雙閉區間） ###
+    def binary_search(nums, target)
+      # 初始化雙閉區間 [0, n-1] ，即 i, j 分別指向陣列首元素、尾元素
+      i, j = 0, nums.length - 1
+
+      # 迴圈，當搜尋區間為空時跳出（當 i > j 時為空）
+      while i <= j
+        # 理論上 Ruby 的數字可以無限大（取決於記憶體大小），無須考慮大數越界問題
+        m = (i + j) / 2   # 計算中點索引 m
+      
+        if nums[m] < target
+          i = m + 1 # 此情況說明 target 在區間 [m+1, j] 中
+        elsif nums[m] > target
+          j = m - 1 # 此情況說明 target 在區間 [i, m-1] 中
+        else
+          return m  # 找到目標元素，返回其索引
+        end
+      end
+
+      -1  # 未找到目標元素，返回 -1
+    end
     ```
 
 === "Zig"
@@ -667,7 +687,27 @@ comments: true
 === "Ruby"
 
     ```ruby title="binary_search.rb"
-    [class]{}-[func]{binary_search_lcro}
+    ### 二分搜尋（左閉右開區間） ###
+    def binary_search_lcro(nums, target)
+      # 初始化左閉右開區間 [0, n) ，即 i, j 分別指向陣列首元素、尾元素+1
+      i, j = 0, nums.length
+
+      # 迴圈，當搜尋區間為空時跳出（當 i = j 時為空）
+      while i < j
+        # 計算中點索引 m
+        m = (i + j) / 2
+
+        if nums[m] < target
+          i = m + 1 # 此情況說明 target 在區間 [m+1, j) 中
+        elsif nums[m] > target
+          j = m - 1 # 此情況說明 target 在區間 [i, m) 中
+        else
+          return m  # 找到目標元素，返回其索引
+        end
+      end
+
+      -1  # 未找到目標元素，返回 -1
+    end
     ```
 
 === "Zig"

zh-Hant/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}
+    ### 二分搜尋最左一個 target ###
+    def binary_search_left_edge(nums, target)
+      # 等價於查詢 target 的插入點
+      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}
+    ### 二分搜尋最右一個 target ###
+    def binary_search_right_edge(nums, target)
+      # 轉化為查詢最左一個 target + 1
+      i = binary_search_insertion(nums, target + 1)
+
+      # j 指向最右一個 target ，i 指向首個大於 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"

zh-Hant/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}
+    ### 二分搜尋插入點（無重複元素） ###
+    def binary_search_insertion_simple(nums, target)
+      # 初始化雙閉區間 [0, n-1]
+      i, j = 0, nums.length - 1
+
+      while i <= j
+        # 計算中點索引 m
+        m = (i + j) / 2
+
+        if nums[m] < target
+          i = m + 1 # target 在區間 [m+1, j] 中
+        elsif nums[m] > target
+          j = m - 1 # target 在區間 [i, m-1] 中
+        else
+          return m  # 找到 target ，返回插入點 m
+        end
+      end
+
+      i # 未找到 target ，返回插入點 i
+    end
     ```
 
 === "Zig"
@@ -625,7 +644,26 @@ comments: true
 === "Ruby"
 
     ```ruby title="binary_search_insertion.rb"
-    [class]{}-[func]{binary_search_insertion}
+    ### 二分搜尋插入點（存在重複元素） ###
+    def binary_search_insertion(nums, target)
+      # 初始化雙閉區間 [0, n-1]
+      i, j = 0, nums.length - 1
+
+      while i <= j
+        # 計算中點索引 m
+        m = (i + j) / 2
+
+        if nums[m] < target
+          i = m + 1 # target 在區間 [m+1, j] 中
+        elsif nums[m] > target
+          j = m - 1 # target 在區間 [i, m-1] 中
+        else
+          j = m - 1 # 首個小於 target 的元素在區間 [i, m-1] 中
+        end
+      end
+
+      i # 返回插入點 i
+    end
     ```
 
 === "Zig"

zh-Hant/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：暴力列舉 ###
+    def two_sum_brute_force(nums, target)
+      # 兩層迴圈，時間複雜度為 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：輔助雜湊表 ###
+    def two_sum_hash_table(nums, target)
+      # 輔助雜湊表，空間複雜度為 O(n)
+      dic = {}
+      # 單層迴圈，時間複雜度為 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"

zh-Hant/docs/chapter_sorting/bubble_sort.md

@@ -264,7 +264,9 @@ comments: true
             for (j in 0..<i) {
                 if (nums[j] > nums[j + 1]) {
                     // 交換 nums[j] 與 nums[j + 1]
-                    nums[j] = nums[j + 1].also { nums[j + 1] = nums[j] }
+                    val temp = nums[j]
+                    nums[j] = nums[j + 1]
+                    nums[j + 1] = temp
                 }
             }
         }
@@ -571,7 +573,9 @@ comments: true
             for (j in 0..<i) {
                 if (nums[j] > nums[j + 1]) {
                     // 交換 nums[j] 與 nums[j + 1]
-                    nums[j] = nums[j + 1].also { nums[j] = nums[j + 1] }
+                    val temp = nums[j]
+                    nums[j] = nums[j + 1]
+                    nums[j + 1] = temp
                     flag = true // 記錄交換元素
                 }
             }

zh-Hant/docs/chapter_sorting/heap_sort.md

@@ -553,7 +553,9 @@ comments: true
             if (ma == i) 
                 break
             // 交換兩節點
-            nums[i] = nums[ma].also { nums[ma] = nums[i] }
+            val temp = nums[i]
+            nums[i] = nums[ma]
+            nums[ma] = temp
             // 迴圈向下堆積化
             i = ma
         }
@@ -568,7 +570,9 @@ comments: true
         // 從堆積中提取最大元素，迴圈 n-1 輪
         for (i in nums.size - 1 downTo 1) {
             // 交換根節點與最右葉節點（交換首元素與尾元素）
-            nums[0] = nums[i].also { nums[i] = nums[0] }
+            val temp = nums[0]
+            nums[0] = nums[i]
+            nums[i] = temp
             // 以根節點為起點，從頂至底進行堆積化
             siftDown(nums, i, 0)
         }

zh-Hant/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
+      # 外迴圈：已排序區間為 [0, i-1]
+      for i in 1...n
+        base = nums[i]
+        j = i - 1
+        # 內迴圈：將 base 插入到已排序區間 [0, i-1] 中的正確位置
+        while j >= 0 && nums[j] > base
+          nums[j + 1] = nums[j] # 將 nums[j] 向右移動一位
+          j -= 1
+        end
+        nums[j + 1] = base # 將 base 賦值到正確位置
+      end
+    end
     ```
 
 === "Zig"

zh-Hant/docs/chapter_sorting/quick_sort.md

@@ -302,19 +302,16 @@ comments: true
         nums[j] = tmp;
     }
 
-    /* 快速排序類別 */
-    // 快速排序類別-哨兵劃分
+    /* 哨兵劃分 */
     int partition(int nums[], int left, int right) {
         // 以 nums[left] 為基準數
         int i = left, j = right;
         while (i < j) {
             while (i < j && nums[j] >= nums[left]) {
-                // 從右向左找首個小於基準數的元素
-                j--;
+                j--; // 從右向左找首個小於基準數的元素
             }
             while (i < j && nums[i] <= nums[left]) {
-                // 從左向右找首個大於基準數的元素
-                i++;
+                i++; // 從左向右找首個大於基準數的元素
             }
             // 交換這兩個元素
             swap(nums, i, j);
@@ -331,7 +328,9 @@ comments: true
     ```kotlin title="quick_sort.kt"
     /* 元素交換 */
     fun swap(nums: IntArray, i: Int, j: Int) {
-        nums[i] = nums[j].also { nums[j] = nums[i] }
+        val temp = nums[i]
+        nums[i] = nums[j]
+        nums[j] = temp
     }
 
     /* 哨兵劃分 */
@@ -563,30 +562,7 @@ comments: true
 === "C"
 
     ```c title="quick_sort.c"
-    /* 快速排序類別 */
-    // 快速排序類別-哨兵劃分
-    int partition(int nums[], int left, int right) {
-        // 以 nums[left] 為基準數
-        int i = left, j = right;
-        while (i < j) {
-            while (i < j && nums[j] >= nums[left]) {
-                // 從右向左找首個小於基準數的元素
-                j--;
-            }
-            while (i < j && nums[i] <= nums[left]) {
-                // 從左向右找首個大於基準數的元素
-                i++;
-            }
-            // 交換這兩個元素
-            swap(nums, i, j);
-        }
-        // 將基準數交換至兩子陣列的分界線
-        swap(nums, i, left);
-        // 返回基準數的索引
-        return i;
-    }
-
-    // 快速排序類別-快速排序
+    /* 快速排序 */
     void quickSort(int nums[], int left, int right) {
         // 子陣列長度為 1 時終止遞迴
         if (left >= right) {
@@ -1022,8 +998,7 @@ comments: true
 === "C"
 
     ```c title="quick_sort.c"
-    /* 快速排序類別（中位基準數最佳化） */
-    // 選取三個候選元素的中位數
+    /* 選取三個候選元素的中位數 */
     int medianThree(int nums[], int left, int mid, int right) {
         int l = nums[left], m = nums[mid], r = nums[right];
         if ((l <= m && m <= r) || (r <= m && m <= l))
@@ -1354,8 +1329,7 @@ comments: true
 === "C"
 
     ```c title="quick_sort.c"
-    /* 快速排序類別（尾遞迴最佳化） */
-    // 快速排序（尾遞迴最佳化）
+    /* 快速排序（尾遞迴最佳化） */
     void quickSortTailCall(int nums[], int left, int right) {
         // 子陣列長度為 1 時終止
         while (left < right) {
@@ -1363,11 +1337,15 @@ comments: true
             int pivot = partition(nums, left, right);
             // 對兩個子陣列中較短的那個執行快速排序
             if (pivot - left < right - pivot) {
-                quickSortTailCall(nums, left, pivot - 1); // 遞迴排序左子陣列
-                left = pivot + 1;                         // 剩餘未排序區間為 [pivot + 1, right]
+                // 遞迴排序左子陣列
+                quickSortTailCall(nums, left, pivot - 1);
+                // 剩餘未排序區間為 [pivot + 1, right]
+                left = pivot + 1;
             } else {
-                quickSortTailCall(nums, pivot + 1, right); // 遞迴排序右子陣列
-                right = pivot - 1;                         // 剩餘未排序區間為 [left, pivot - 1]
+                // 遞迴排序右子陣列
+                quickSortTailCall(nums, pivot + 1, right);
+                // 剩餘未排序區間為 [left, pivot - 1]
+                right = pivot - 1;
             }
         }
     }

zh-Hant/docs/chapter_sorting/selection_sort.md

@@ -296,7 +296,9 @@ comments: true
                     k = j // 記錄最小元素的索引
             }
             // 將該最小元素與未排序區間的首個元素交換
-            nums[i] = nums[k].also { nums[k] = nums[i] }
+            val temp = nums[i]
+            nums[i] = nums[k]
+            nums[k] = temp
         }
     }
     ```

zh-Hant/docs/chapter_stack_and_queue/stack.md

@@ -1092,7 +1092,7 @@ comments: true
         fun pop(): Int? {
             val num = peek()
             stackPeek = stackPeek?.next
-            stkSize--;
+            stkSize--
             return num
         }
 

zh-Hant/docs/chapter_tree/array_representation_of_tree.md

@@ -125,7 +125,7 @@ comments: true
     ```kotlin title=""
     /* 二元樹的陣列表示 */
     // 使用 null 來表示空位
-    val tree = mutableListOf( 1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15 )
+    val tree = arrayOf( 1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15 )
     ```
 
 === "Ruby"
@@ -1172,7 +1172,7 @@ comments: true
 === "Kotlin"
 
     ```kotlin title="array_binary_tree.kt"
-    /* 建構子 */
+    /* 陣列表示下的二元樹類別 */
     class ArrayBinaryTree(val tree: MutableList<Int?>) {
         /* 串列容量 */
         fun size(): Int {