Translation

Translation of binary search tree

src/data-structures/tree/README.zh-CN.md

@@ -1,26 +1,26 @@
 # 树
 
-* [二叉搜索树](binary-search-tree)
+- [二叉搜索树](binary-search-tree/README.zh-CN.md)
-* [AVL树](avl-tree)
+- [AVL 树](avl-tree)
-* [红黑树](red-black-tree)
+- [红黑树](red-black-tree)
-* [线段树](segment-tree) - with min/max/sum range queries examples
+- [线段树](segment-tree) - with min/max/sum range queries examples
-* [芬威克树/Fenwick Tree](fenwick-tree) (Binary Indexed Tree)
+- [芬威克树/Fenwick Tree](fenwick-tree) (Binary Indexed Tree)
 
-在计算机科学中, **树(tree)** 是一种广泛使用的抽象数据类型(ADT)— 或实现此ADT的数据结构 — 模拟分层树结构, 具有根节点和有父节点的子树,表示为一组链接节点。
+在计算机科学中, **树(tree)** 是一种广泛使用的抽象数据类型(ADT)— 或实现此 ADT 的数据结构 — 模拟分层树结构, 具有根节点和有父节点的子树,表示为一组链接节点。
 
 树可以被(本地地)递归定义为一个(始于一个根节点的)节点集, 每个节点都是一个包含了值的数据结构, 除了值,还有该节点的节点引用列表(子节点)一起。
 树的节点之间没有引用重复的约束。
 
 一棵简单的无序树; 在下图中:
 
-标记为7的节点具有两个子节点, 标记为2和6;
+标记为 7 的节点具有两个子节点, 标记为 2 和 6;
-一个父节点,标记为2,作为根节点, 在顶部,没有父节点。
+一个父节点,标记为 2,作为根节点, 在顶部,没有父节点。
 
 ![Tree](./images/tree.jpeg)
 
-*Made with [okso.app](https://okso.app)*
+_Made with [okso.app](https://okso.app)_
 
 ## 参考
 
-- [Wikipedia](https://en.wikipedia.org/wiki/Tree_(data_structure))
+- [Wikipedia](<https://en.wikipedia.org/wiki/Tree_(data_structure)>)
 - [YouTube](https://www.youtube.com/watch?v=oSWTXtMglKE&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8&index=8)

src/data-structures/tree/binary-search-tree/README.md

@@ -1,7 +1,7 @@
 # Binary Search Tree
 
 _Read this in other languages:_
-[_Português_](README.pt-BR.md)
+[_Português_](README.pt-BR.md),[_简体中文_](README.zh-CN.md)
 
 In computer science, **binary search trees** (BST), sometimes called
 ordered or sorted binary trees, are a particular type of container:
@@ -30,7 +30,7 @@ The leaves are not drawn.
 
 ![Trie](./images/binary-search-tree.jpg)
 
-*Made with [okso.app](https://okso.app)*
+_Made with [okso.app](https://okso.app)_
 
 ## Pseudocode for Basic Operations
 
@@ -87,7 +87,6 @@ contains(root, value)
 end contains
 ```
 
-
 ### Deletion
 
 ```text
@@ -265,7 +264,7 @@ end postorder
 
 ### Time Complexity
 
-| Access    | Search    | Insertion | Deletion  |
+|  Access   |  Search   | Insertion | Deletion  |
 | :-------: | :-------: | :-------: | :-------: |
 | O(log(n)) | O(log(n)) | O(log(n)) | O(log(n)) |
 

src/data-structures/tree/binary-search-tree/README.zh-CN.md

@@ -0,0 +1,268 @@
+# 二叉搜索树
+
+_Read this in other languages:_
+[_Português_](README.pt-BR.md)
+
+在计算机科学中, **二叉搜索树** (BST), 也称为有序二叉树或排序二叉树, 是一种特殊的容器:
+在内存中存储“元素”的数据结构（如数字，名称等）。二叉搜索树可以快速查找，添加和删除元素，也可用于
+构建动态元素集或在表中根据键查找元素值 （例：通过某人姓名找到某人的手机号）。
+
+二叉搜索树为有序序列，所以在进行查找或其他操作时可以使用二分查找原理：
+在树中寻找键（或插入新键的位置）时，查找过程为: 从根到叶遍历树，通过比较
+存储在树的节点中的键来判断继续向左或向右搜索子树。 平均而言，这意味着每次
+比较都允许跳过大约一半的操作，这样每个查找、插入或删除所花费的时间为
+树中存储的项目数的对数。 这是比按键在（未排序的）数组中查找元素所需的
+线性时间要好得多，但比在哈希表中相应的操作慢。
+
+下图为一个大小为 9，深度为 3，8 为根结点的二叉搜索树。
+叶子节点没有被绘制。
+
+![Trie](./images/binary-search-tree.jpg)
+
+_Made with [okso.app](https://okso.app)_
+
+## 基础操作的伪代码
+
+### 插入
+
+```text
+insert(value)
+  Pre: value has passed custom type checks for type T
+  Post: value has been placed in the correct location in the tree
+  if root = ø
+    root ← node(value)
+  else
+    insertNode(root, value)
+  end if
+end insert
+```
+
+```text
+insertNode(current, value)
+  Pre: current is the node to start from
+  Post: value has been placed in the correct location in the tree
+  if value < current.value
+    if current.left = ø
+      current.left ← node(value)
+    else
+      InsertNode(current.left, value)
+    end if
+  else
+    if current.right = ø
+      current.right ← node(value)
+    else
+      InsertNode(current.right, value)
+    end if
+  end if
+end insertNode
+```
+
+### 查找
+
+```text
+contains(root, value)
+  Pre: root is the root node of the tree, value is what we would like to locate
+  Post: value is either located or not
+  if root = ø
+    return false
+  end if
+  if root.value = value
+    return true
+  else if value < root.value
+    return contains(root.left, value)
+  else
+    return contains(root.right, value)
+  end if
+end contains
+```
+
+### 删除
+
+```text
+remove(value)
+  Pre: value is the value of the node to remove, root is the node of the BST
+      count is the number of items in the BST
+  Post: node with value is removed if found in which case yields true, otherwise false
+  nodeToRemove ← findNode(value)
+  if nodeToRemove = ø
+    return false
+  end if
+  parent ← findParent(value)
+  if count = 1
+    root ← ø
+  else if nodeToRemove.left = ø and nodeToRemove.right = ø
+    if nodeToRemove.value < parent.value
+      parent.left ←  nodeToRemove.right
+    else
+      parent.right ← nodeToRemove.right
+    end if
+  else if nodeToRemove.left != ø and nodeToRemove.right != ø
+    next ← nodeToRemove.right
+    while next.left != ø
+      next ← next.left
+    end while
+    if next != nodeToRemove.right
+      remove(next.value)
+      nodeToRemove.value ← next.value
+    else
+      nodeToRemove.value ← next.value
+      nodeToRemove.right ← nodeToRemove.right.right
+    end if
+  else
+    if nodeToRemove.left = ø
+      next ← nodeToRemove.right
+    else
+      next ← nodeToRemove.left
+    end if
+    if root = nodeToRemove
+      root = next
+    else if parent.left = nodeToRemove
+      parent.left = next
+    else if parent.right = nodeToRemove
+      parent.right = next
+    end if
+  end if
+  count ← count - 1
+  return true
+end remove
+```
+
+### 查找某个节点的父节点
+
+```text
+findParent(value, root)
+  Pre: value is the value of the node we want to find the parent of
+       root is the root node of the BST and is != ø
+  Post: a reference to the prent node of value if found; otherwise ø
+  if value = root.value
+    return ø
+  end if
+  if value < root.value
+    if root.left = ø
+      return ø
+    else if root.left.value = value
+      return root
+    else
+      return findParent(value, root.left)
+    end if
+  else
+    if root.right = ø
+      return ø
+    else if root.right.value = value
+      return root
+    else
+      return findParent(value, root.right)
+    end if
+  end if
+end findParent
+```
+
+### 查找节点
+
+```text
+findNode(root, value)
+  Pre: value is the value of the node we want to find the parent of
+       root is the root node of the BST
+  Post: a reference to the node of value if found; otherwise ø
+  if root = ø
+    return ø
+  end if
+  if root.value = value
+    return root
+  else if value < root.value
+    return findNode(root.left, value)
+  else
+    return findNode(root.right, value)
+  end if
+end findNode
+```
+
+### 查找最小值
+
+```text
+findMin(root)
+  Pre: root is the root node of the BST
+    root = ø
+  Post: the smallest value in the BST is located
+  if root.left = ø
+    return root.value
+  end if
+  findMin(root.left)
+end findMin
+```
+
+### 查找最大值
+
+```text
+findMax(root)
+  Pre: root is the root node of the BST
+    root = ø
+  Post: the largest value in the BST is located
+  if root.right = ø
+    return root.value
+  end if
+  findMax(root.right)
+end findMax
+```
+
+### 遍历
+
+#### 中序遍历
+
+```text
+inorder(root)
+  Pre: root is the root node of the BST
+  Post: the nodes in the BST have been visited in inorder
+  if root != ø
+    inorder(root.left)
+    yield root.value
+    inorder(root.right)
+  end if
+end inorder
+```
+
+#### 前序遍历
+
+```text
+preorder(root)
+  Pre: root is the root node of the BST
+  Post: the nodes in the BST have been visited in preorder
+  if root != ø
+    yield root.value
+    preorder(root.left)
+    preorder(root.right)
+  end if
+end preorder
+```
+
+#### 后序遍历
+
+```text
+postorder(root)
+  Pre: root is the root node of the BST
+  Post: the nodes in the BST have been visited in postorder
+  if root != ø
+    postorder(root.left)
+    postorder(root.right)
+    yield root.value
+  end if
+end postorder
+```
+
+## 复杂度
+
+### 时间复杂度
+
+|  Access   |  Search   | Insertion | Deletion  |
+| :-------: | :-------: | :-------: | :-------: |
+| O(log(n)) | O(log(n)) | O(log(n)) | O(log(n)) |
+
+### 空间复杂度
+
+O(n)
+
+## 参考资料
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Binary_search_tree)
+- [Inserting to BST on YouTube](https://www.youtube.com/watch?v=wcIRPqTR3Kc&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8&index=9&t=0s)
+- [BST Interactive Visualisations](https://www.cs.usfca.edu/~galles/visualization/BST.html)