add binary_tree and avl_tree python code

docs/chapter_tree/avl_tree.md

@@ -48,7 +48,24 @@ G. M. Adelson-Velsky 和 E. M. Landis 在其 1962 年发表的论文 "An algorit
 === "Python"
 
     ```python title="avl_tree.py"
-    
+    class AVLTreeNode:
+        def __init__(
+                self,
+                val=None,
+                height: int = 0,
+                left: typing.Optional["AVLTreeNode"] = None,
+                right: typing.Optional["AVLTreeNode"] = None
+        ):
+            self.val = val
+            self.height = height
+            self.left = left
+            self.right = right
+
+        def __str__(self):
+            val = self.val
+            left_val = self.left.val if self.left else None
+            right_val = self.right.val if self.right else None
+            return "<AVLTreeNode: {}, leftAVLTreeNode: {}, rightAVLTreeNode: {}>".format(val, left_val, right_val)
     ```
 
 === "Go"
@@ -108,7 +125,31 @@ G. M. Adelson-Velsky 和 E. M. Landis 在其 1962 年发表的论文 "An algorit
 === "Python"
 
     ```python title="avl_tree.py"
-    
+    def height(node: typing.Optional[AVLTreeNode]) -> int:
+        """
+        获取结点高度
+        Args:
+            node:起始结点 
+
+        Returns: 高度 or -1
+
+        """
+        # 空结点高度为 -1 ，叶结点高度为 0
+        if node is not None:
+            return node.height
+        return -1
+
+    def update_height(node: AVLTreeNode):
+        """
+        更新结点高度
+        Args:
+            node: 要更新高度的结点
+
+        Returns: None
+
+        """
+        # 结点高度等于最高子树高度 + 1
+        node.height = max([height(node.left), height(node.right)]) + 1
     ```
 
 === "Go"
@@ -166,7 +207,20 @@ G. M. Adelson-Velsky 和 E. M. Landis 在其 1962 年发表的论文 "An algorit
 === "Python"
 
     ```python title="avl_tree.py"
-    
+    def balance_factor(node: AVLTreeNode) -> int:
+        """
+        获取结点平衡因子
+        Args:
+            node: 要获取平衡因子的结点
+
+        Returns: 平衡因子
+
+        """
+        # 空结点平衡因子为 0
+        if node is None:
+            return 0
+        # 结点平衡因子 = 左子树高度 - 右子树高度
+        return height(node.left) - height(node.right)
     ```
 
 === "Go"
@@ -255,7 +309,17 @@ AVL 树的独特之处在于「旋转 Rotation」的操作，其可 **在不影
 === "Python"
 
     ```python title="avl_tree.py"
-    
+    def rightRotate(node: AVLTreeNode):
+        child = node.left
+        grand_child = child.right
+        # 以 child 为原点，将 node 向右旋转
+        child.right = node
+        node.left = grand_child
+        # 更新结点高度
+        update_height(node)
+        update_height(child)
+        # 返回旋转后子树的根节点
+        return child
     ```
 
 === "Go"
@@ -323,7 +387,17 @@ AVL 树的独特之处在于「旋转 Rotation」的操作，其可 **在不影
 === "Python"
 
     ```python title="avl_tree.py"
-    
+    def leftRotate(node: AVLTreeNode):
+        child = node.right
+        grand_child = child.left
+        # 以 child 为原点，将 node 向左旋转
+        child.left = node
+        node.right = grand_child
+        # 更新结点高度
+        update_height(node)
+        update_height(child)
+        # 返回旋转后子树的根节点
+        return child
     ```
 
 === "Go"
@@ -432,7 +506,37 @@ AVL 树的独特之处在于「旋转 Rotation」的操作，其可 **在不影
 === "Python"
 
     ```python title="avl_tree.py"
-    
+    def rotate(node: AVLTreeNode):
+        """
+        执行旋转操作，使该子树重新恢复平衡
+        Args:
+            node: 要旋转的根结点
+
+        Returns: 旋转后的根结点
+
+        """
+        # 获取结点 node 的平衡因子
+        factor = balance_factor(node)
+        # 左偏树
+        if factor > 1:
+            if balance_factor(node.left) >= 0:
+                # 右旋
+                return right_rotate(node)
+            else:
+                # 先左旋后右旋
+                node.left = left_rotate(node.left)
+                return right_rotate(node)
+        # 右偏树
+        elif factor < -1:
+            if balance_factor(node.right) <= 0:
+                # 左旋
+                return left_rotate(node)
+            else:
+                # 先右旋后左旋
+                node.right = right_rotate(node.right)
+                return left_rotate(node)
+        # 平衡树，无需旋转，直接返回
+        return node
     ```
 
 === "Go"
@@ -507,7 +611,42 @@ AVL 树的独特之处在于「旋转 Rotation」的操作，其可 **在不影
 === "Python"
 
     ```python title="avl_tree.py"
-    
+    def insert(val) -> AVLTreeNode:
+        """
+        插入结点
+        Args:
+            val: 结点的值 
+
+        Returns:
+            node: 插入结点后的根结点
+        """
+        root = insert_helper(root, val)
+        return root
+
+    def insert_helper(node: typing.Optional[AVLTreeNode], val: int) -> AVLTreeNode:
+        """
+        递归插入结点（辅助函数）
+        Args:
+            node: 要插入的根结点
+            val: 要插入的结点的值
+
+        Returns: 插入结点后的根结点
+
+        """
+        if node is None:
+            return AVLTreeNode(val)
+        # 1. 查找插入位置，并插入结点
+        if val < node.val:
+            node.left = insert_helper(node.left, val)
+        elif val > node.val:
+            node.right = insert_helper(node.right, val)
+        else:
+            # 重复结点不插入，直接返回
+            return node
+        # 更新结点高度
+        update_height(node)
+        # 2. 执行旋转操作，使该子树重新恢复平衡
+        return rotate(node)
     ```
 
 === "Go"
@@ -604,7 +743,62 @@ AVL 树的独特之处在于「旋转 Rotation」的操作，其可 **在不影
 === "Python"
 
     ```python title="avl_tree.py"
-    
+    def remove(val: int):
+        """
+        删除结点
+        Args:
+            val: 要删除的结点的值
+
+        Returns:
+
+        """
+        root = remove_helper(root, val)
+        return root
+
+    def remove_helper(node: typing.Optional[AVLTreeNode], val: int) -> typing.Optional[AVLTreeNode]:
+        """
+        递归删除结点（辅助函数）
+        Args:
+            node:  删除的起始结点
+            val: 要删除的结点的值
+
+        Returns: 删除目标结点后的起始结点
+
+        """
+        if node is None:
+            return None
+        # 1. 查找结点，并删除之
+        if val < node.val:
+            node.left = remove_helper(node.left, val)
+        elif val > node.val:
+            node.right = remove_helper(node.right, val)
+        else:
+            if node.left is None or node.right is None:
+                child = node.left or node.right
+                # 子结点数量 = 0 ，直接删除 node 并返回
+                if child is None:
+                    return None
+                # 子结点数量 = 1 ，直接删除 node
+                else:
+                    node = child
+            else: # 子结点数量 = 2 ，则将中序遍历的下个结点删除，并用该结点替换当前结点
+                temp = min_node(node.right)
+                node.right = remove_helper(node.right, temp.val)
+                node.val = temp.val
+        # 更新结点高度
+        update_height(node)
+        # 2. 执行旋转操作，使该子树重新恢复平衡
+        return rotate(node)
+
+
+    def min_node(node: typing.Optional[AVLTreeNode]) -> typing.Optional[AVLTreeNode]:
+        # 获取最小结点
+        if node is None:
+            return None
+        # 循环访问左子结点，直到叶结点时为最小结点，跳出
+        while node.left is not None:
+            node = node.left
+        return node
     ```
 
 === "Go"

docs/chapter_tree/binary_search_tree.md

@@ -82,6 +82,23 @@ comments: true
 === "Python"
 
     ```python title="binary_search_tree.py"
+    def search(self, num):
+        """
+        查找结点
+        """
+        cur = self.get_root()
+        # 循环查找，越过叶结点后跳出
+        while cur is not None:
+            # 目标结点在 root 的右子树中
+            if cur.val < num:
+                cur = cur.right
+            # 目标结点在 root 的左子树中
+            elif cur.val > num:
+                cur = cur.left
+            # 找到目标结点，跳出循环
+            else:
+                break
+        return cur
 
     ```
 
@@ -228,7 +245,37 @@ comments: true
 === "Python"
 
     ```python title="binary_search_tree.py"
+    def insert(self, num):
+        """
+        插入结点
+        """
+        root = self.get_root()
+        # 若树为空，直接提前返回
+        if root is None:
+            return None
 
+        cur = root
+        pre = None
+
+        # 循环查找，越过叶结点后跳出
+        while cur is not None:
+            # 找到重复结点，直接返回
+            if cur.val == num:
+                return None
+            pre = cur
+
+            if cur.val < num:  # 插入位置在 root 的右子树中
+                cur = cur.right
+            else:  # 插入位置在 root 的左子树中
+                cur = cur.left
+
+        # 插入结点 val
+        node = TreeNode(num)
+        if pre.val < num:
+            pre.right = node
+        else:
+            pre.left = node
+        return node
     ```
 
 === "Go"
@@ -483,7 +530,64 @@ comments: true
 === "Python"
 
     ```python title="binary_search_tree.py"
+    def remove(self, num):
+        """
+        删除结点
+        """
+        root = self.get_root()
+        # 若树为空，直接提前返回
+        if root is None:
+            return None
+        
+        cur = root
+        pre = None
 
+        # 循环查找，越过叶结点后跳出
+        while cur is not None:
+            # 找到待删除结点，跳出循环
+            if cur.val == num:
+                break
+            pre = cur
+            if cur.val < num:  # 待删除结点在 root 的右子树中
+                cur = cur.right
+            else:  # 待删除结点在 root 的左子树中
+                cur = cur.left
+
+        # 若无待删除结点，则直接返回
+        if cur is None:
+            return None
+
+        # 子结点数量 = 0 or 1
+        if cur.left is None or cur.right is None:
+            # 当子结点数量 = 0 / 1 时， child = null / 该子结点
+            child = cur.left or cur.right
+            # 删除结点 cur
+            if pre.left == cur:
+                pre.left = child
+            else:
+                pre.right = child
+        # 子结点数量 = 2
+        else:
+            # 获取中序遍历中 cur 的下一个结点
+            nex = self.min(cur.right)
+            tmp = nex.val
+            # 递归删除结点 nex
+            self.remove(nex.val)
+            # 将 nex 的值复制给 cur
+            cur.val =  tmp
+        return cur
+
+    def min(self, root):
+        """
+        获取最小结点
+        """
+        if root is None:
+            return root
+
+        # 循环访问左子结点，直到叶结点时为最小结点，跳出
+        while root.left is not None:
+            root = root.left
+        return root
     ```
 
 === "Go"

docs/chapter_tree/binary_tree.md

@@ -33,9 +33,9 @@ comments: true
 === "Python"
 
     ```python title=""
-    """ 链表结点类 """
     class TreeNode:
-        def __init__(self, val=0, left=None, right=None):
+        """ 链表结点类 """
+        def __init__(self, val=None, left=None, right=None):
             self.val = val      # 结点值
             self.left = left    # 左子结点指针
             self.right = right  # 右子结点指针
@@ -190,7 +190,18 @@ comments: true
 === "Python"
 
     ```python title="binary_tree.py"
-
+    # 初始化二叉树
+    # 初始化节点
+    n1 = TreeNode(val=1)
+    n2 = TreeNode(val=2)
+    n3 = TreeNode(val=3)
+    n4 = TreeNode(val=4)
+    n5 = TreeNode(val=5)
+    # 构建引用指向（即指针）
+    n1.left = n2
+    n1.right = n3
+    n2.left = n4
+    n2.right = n5
     ```
 
 === "Go"
@@ -288,7 +299,13 @@ comments: true
 === "Python"
 
     ```python title="binary_tree.py"
-
+    # 插入与删除结点
+    p = TreeNode(0)
+    # 在 n1 -> n2 中间插入结点 P
+    n1.left = p
+    p.left = n2
+    # 删除节点 P
+    n1.left = n2
     ```
 
 === "Go"
@@ -406,7 +423,24 @@ comments: true
 === "Python"
 
     ```python title="binary_tree_bfs.py"
-
+    def hierOrder(root):
+        # 初始化队列，加入根结点
+        queue = collections.deque()
+        queue.append(root)
+        # 初始化一个列表，用于保存遍历序列
+        result = []
+        while queue:
+            # 队列出队
+            node = queue.popleft()
+            # 保存节点值
+            result.append(node.val)
+            if node.left is not None:
+                # 左子结点入队
+                queue.append(node.left)
+            if node.right is not None:
+                # 右子结点入队
+                queue.append(node.right)
+        return result
     ```
 
 === "Go"
@@ -578,7 +612,43 @@ comments: true
 === "Python"
 
     ```python title="binary_tree_dfs.py"
+    def preOrder(root):
+        """
+        前序遍历二叉树
+        """
+        if root is None:
+            return
+        
+        # 访问优先级：根结点 -> 左子树 -> 右子树
+        result.append(root.val)
+        preOrder(root=root.left)
+        preOrder(root=root.right)
 
+
+    def inOrder(root):
+        """
+        中序遍历二叉树
+        """
+        if root is None:
+            return
+
+        # 访问优先级：左子树 -> 根结点 -> 右子树
+        inOrder(root=root.left)
+        result.append(root.val)
+        inOrder(root=root.right)
+
+
+    def postOrder(root):
+        """
+        后序遍历二叉树
+        """
+        if root is None:
+            return
+        
+        # 访问优先级：左子树 -> 右子树 -> 根结点
+        postOrder(root=root.left)
+        postOrder(root=root.right)
+        result.append(root.val)
     ```
 
 === "Go"