Merge pull request #2083 from jianghongcheng/master

Update 0106.从中序与后序遍历序列构造二叉树.md

problems/0106.从中序与后序遍历序列构造二叉树.md

@@ -400,8 +400,6 @@ public:
 };
 ```
 
-## Python
-
 
 # 105.从前序与中序遍历序列构造二叉树
 
@@ -692,38 +690,6 @@ class Solution {
 
 ## Python
 
-```python
-class Solution:
-    def buildTree(self, inorder: List[int], postorder: List[int]) -> Optional[TreeNode]:
-        # 第一步: 特殊情况讨论: 树为空. 或者说是递归终止条件
-        if not postorder:
-            return
-
-        # 第二步: 后序遍历的最后一个就是当前的中间节点
-        root_val = postorder[-1]
-        root = TreeNode(root_val)
-
-        # 第三步: 找切割点.
-        root_index = inorder.index(root_val)
-
-        # 第四步: 切割inorder数组. 得到inorder数组的左,右半边.
-        left_inorder = inorder[:root_index]
-        right_inorder = inorder[root_index + 1:]
-
-        # 第五步: 切割postorder数组. 得到postorder数组的左,右半边.
-        # ⭐️ 重点1: 中序数组大小一定跟后序数组大小是相同的.
-        left_postorder = postorder[:len(left_inorder)]
-        right_postorder = postorder[len(left_inorder): len(postorder) - 1]
-
-
-        # 第六步: 递归
-        root.left = self.buildTree(left_inorder, left_postorder)
-        root.right = self.buildTree(right_inorder, right_postorder)
-
-        # 第七步: 返回答案
-        return root
-```
-
 105.从前序与中序遍历序列构造二叉树
 
 ```python
@@ -752,7 +718,7 @@ class Solution:
         # 第六步: 递归
         root.left = self.buildTree(preorder_left, inorder_left)
         root.right = self.buildTree(preorder_right, inorder_right)
-
+        # 第七步: 返回答案
         return root
 ```
 
@@ -784,7 +750,7 @@ class Solution:
         # 第六步: 递归
         root.left = self.buildTree(inorder_left, postorder_left)
         root.right = self.buildTree(inorder_right, postorder_right)
-
+         # 第七步: 返回答案
         return root
 ```
 

problems/0110.平衡二叉树.md

@@ -553,6 +553,52 @@ class Solution:
 
 迭代法：
 
+```python
+class Solution:
+    def getDepth(self, cur):
+        st = []
+        if cur is not None:
+            st.append(cur)
+        depth = 0
+        result = 0
+        while st:
+            node = st[-1]
+            if node is not None:
+                st.pop()
+                st.append(node)                           # 中
+                st.append(None)
+                depth += 1
+                if node.right:
+                    st.append(node.right)                 # 右
+                if node.left:
+                    st.append(node.left)                   # 左
+
+            else:               
+                node = st.pop()
+                st.pop()
+                depth -= 1
+            result = max(result, depth)
+        return result
+
+    def isBalanced(self, root):
+        st = []
+        if root is None:
+            return True
+        st.append(root)
+        while st:
+            node = st.pop()                                 # 中
+            if abs(self.getDepth(node.left) - self.getDepth(node.right)) > 1:
+                return False
+            if node.right:
+                st.append(node.right)                       # 右（空节点不入栈）
+            if node.left:
+                st.append(node.left)                         # 左（空节点不入栈）
+        return True
+
+```
+
+迭代法精简版：
+
 ```python
 class Solution:
     def isBalanced(self, root: Optional[TreeNode]) -> bool:
@@ -576,8 +622,6 @@ class Solution:
                 height_map[real_node] = 1 + max(left, right)
         return True
 ```
-
-
 ### Go
 
 ```Go

problems/0257.二叉树的所有路径.md

@@ -470,38 +470,34 @@ class Solution {
 ## Python:  
 	
 	
-递归法+回溯（版本一）
+递归法+回溯
 ```Python
 # Definition for a binary tree node.
-# class TreeNode:
-#     def __init__(self, val=0, left=None, right=None):
-#         self.val = val
-#         self.left = left
-#         self.right = right
-import copy
-from typing import List, Optional
-
 class Solution:
-    def binaryTreePaths(self, root: Optional[TreeNode]) -> List[str]:
+    def traversal(self, cur, path, result):
-        if not root:
+        path.append(cur.val)  # 中
-            return []
+        if not cur.left and not cur.right:  # 到达叶子节点
+            sPath = '->'.join(map(str, path))
+            result.append(sPath)
+            return
+        if cur.left:  # 左
+            self.traversal(cur.left, path, result)
+            path.pop()  # 回溯
+        if cur.right:  # 右
+            self.traversal(cur.right, path, result)
+            path.pop()  # 回溯
+
+    def binaryTreePaths(self, root):
         result = []
-        self.generate_paths(root, [], result)
+        path = []
+        if not root:
+            return result
+        self.traversal(root, path, result)
         return result
-    
-    def generate_paths(self, node: TreeNode, path: List[int], result: List[str]) -> None:
-        path.append(node.val)
-        if not node.left and not node.right:
-            result.append('->'.join(map(str, path)))
-        if node.left:
-            self.generate_paths(node.left, copy.copy(path), result)
-        if node.right:
-            self.generate_paths(node.right, copy.copy(path), result)
-        path.pop()
 
 
 ```
-递归法+回溯（版本二）
+递归法+隐形回溯（版本一）
 ```Python
 # Definition for a binary tree node.
 # class TreeNode:
@@ -509,7 +505,6 @@ class Solution:
 #         self.val = val
 #         self.left = left
 #         self.right = right
-import copy
 from typing import List, Optional
 
 class Solution:
@@ -517,23 +512,23 @@ class Solution:
         if not root:
             return []
         result = []
-        self.generate_paths(root, [], result)
+        self.traversal(root, [], result)
         return result
     
-    def generate_paths(self, node: TreeNode, path: List[int], result: List[str]) -> None:
+    def traversal(self, cur: TreeNode, path: List[int], result: List[str]) -> None:
-        if not node:
+        if not cur:
             return
-        path.append(node.val)
+        path.append(cur.val)
-        if not node.left and not node.right:
+        if not cur.left and not cur.right:
             result.append('->'.join(map(str, path)))
-        else:
+        if cur.left:
-            self.generate_paths(node.left, copy.copy(path), result)
+            self.traversal(cur.left, path[:], result)
-            self.generate_paths(node.right, copy.copy(path), result)
+        if cur.right:
-        path.pop()
+            self.traversal(cur.right, path[:], result)
 
 ```
 	
-递归法+隐形回溯
+递归法+隐形回溯（版本二）
 ```Python
 # Definition for a binary tree node.
 # class TreeNode:
@@ -566,16 +561,11 @@ class Solution:
 迭代法：
 
 ```Python
-from collections import deque
-
-
 class Solution:
-    """二叉树的所有路径 迭代法"""
 
     def binaryTreePaths(self, root: TreeNode) -> List[str]:
         # 题目中节点数至少为1
-        stack, path_st, result = deque([root]), deque(), []
+        stack, path_st, result = [root], [str(root.val)], []
-        path_st.append(str(root.val))
 
         while stack:
             cur = stack.pop()

problems/0404.左叶子之和.md

@@ -247,8 +247,7 @@ class Solution {
 
 
 ### Python 
-
+递归
-**递归后序遍历**
 ```python
 # Definition for a binary tree node.
 # class TreeNode:
@@ -257,47 +256,64 @@ class Solution {
 #         self.left = left
 #         self.right = right
 class Solution:
-    def sumOfLeftLeaves(self, root: Optional[TreeNode]) -> int:
+    def sumOfLeftLeaves(self, root):
-        if not root:
+        if root is None:
+            return 0
+        if root.left is None and root.right is None:
             return 0
         
-        # 检查根节点的左子节点是否为叶节点
+        leftValue = self.sumOfLeftLeaves(root.left)  # 左
-        if root.left and not root.left.left and not root.left.right:
+        if root.left and not root.left.left and not root.left.right:  # 左子树是左叶子的情况
-            left_val = root.left.val
+            leftValue = root.left.val
-        else:
-            left_val = self.sumOfLeftLeaves(root.left)
             
-        # 递归地计算右子树左叶节点的和
+        rightValue = self.sumOfLeftLeaves(root.right)  # 右
-        right_val = self.sumOfLeftLeaves(root.right)
+
-        
+        sum_val = leftValue + rightValue  # 中
-        return left_val + right_val
+        return sum_val
+```
+递归精简版
+
+```python
+# Definition for a binary tree node.
+# class TreeNode:
+#     def __init__(self, val=0, left=None, right=None):
+#         self.val = val
+#         self.left = left
+#         self.right = right
+class Solution:
+    def sumOfLeftLeaves(self, root):
+        if root is None:
+            return 0
+        leftValue = 0
+        if root.left is not None and root.left.left is None and root.left.right is None:
+            leftValue = root.left.val
+        return leftValue + self.sumOfLeftLeaves(root.left) + self.sumOfLeftLeaves(root.right)
 ```
 
-**迭代**
+迭代法
 ```python
+# Definition for a binary tree node.
+# class TreeNode:
+#     def __init__(self, val=0, left=None, right=None):
+#         self.val = val
+#         self.left = left
+#         self.right = right
 class Solution:
-    def sumOfLeftLeaves(self, root: TreeNode) -> int:
+    def sumOfLeftLeaves(self, root):
-        """
+        if root is None:
-        Idea: Each time check current node's left node. 
+            return 0
-              If current node don't have one, skip it. 
+        st = [root]
-        """
+        result = 0
-        stack = []
+        while st:
-        if root: 
+            node = st.pop()
-            stack.append(root)
+            if node.left and node.left.left is None and node.left.right is None:
-        res = 0
+                result += node.left.val
-        
+            if node.right:
-        while stack: 
+                st.append(node.right)
-            # 每次都把当前节点的左节点加进去. 
+            if node.left:
-            cur_node = stack.pop()
+                st.append(node.left)
-            if cur_node.left and not cur_node.left.left and not cur_node.left.right: 
+        return result
-                res += cur_node.left.val
+
-                
-            if cur_node.left: 
-                stack.append(cur_node.left)
-            if cur_node.right: 
-                stack.append(cur_node.right)
-                
-        return res
 ```
 
 ### Go

problems/0513.找树左下角的值.md

@@ -330,19 +330,24 @@ class Solution:
 #         self.right = right
 from collections import deque
 class Solution:
-    def findBottomLeftValue(self, root: Optional[TreeNode]) -> int:
+    def findBottomLeftValue(self, root):
-        queue = deque([root])
+        if root is None:
+            return 0
+        queue = deque()
+        queue.append(root)
+        result = 0
         while queue:
             size = len(queue)
-            leftmost = queue[0].val
             for i in range(size):
                 node = queue.popleft()
+                if i == 0:
+                    result = node.val
                 if node.left:
                     queue.append(node.left)
                 if node.right:
                     queue.append(node.right)
-            if not queue:
+        return result
-                return leftmost
+
 
 
 ```

problems/0617.合并二叉树.md

@@ -352,8 +352,7 @@ class Solution {
 ```
 
 ### Python 
-
+(版本一) 递归 - 前序 - 修改root1
-**递归法 - 前序遍历**
 ```python
 # Definition for a binary tree node.
 # class TreeNode:
@@ -377,8 +376,33 @@ class Solution:
         return root1 # ⚠️ 注意: 本题我们重复使用了题目给出的节点而不是创建新节点. 节省时间, 空间. 
 
 ```
+(版本二) 递归 - 前序 - 新建root
+```python
+# Definition for a binary tree node.
+# class TreeNode:
+#     def __init__(self, val=0, left=None, right=None):
+#         self.val = val
+#         self.left = left
+#         self.right = right
+class Solution:
+    def mergeTrees(self, root1: TreeNode, root2: TreeNode) -> TreeNode:
+        # 递归终止条件: 
+        #  但凡有一个节点为空, 就立刻返回另外一个. 如果另外一个也为None就直接返回None. 
+        if not root1: 
+            return root2
+        if not root2: 
+            return root1
+        # 上面的递归终止条件保证了代码执行到这里root1, root2都非空. 
+        root = TreeNode() # 创建新节点
+        root.val += root1.val + root2.val# 中
+        root.left = self.mergeTrees(root1.left, root2.left) #左
+        root.right = self.mergeTrees(root1.right, root2.right) # 右
+        
+        return root # ⚠️ 注意: 本题我们创建了新节点. 
 
-**迭代法**
+```
+
+(版本三) 迭代
 ```python
 class Solution:
     def mergeTrees(self, root1: TreeNode, root2: TreeNode) -> TreeNode:
@@ -413,7 +437,44 @@ class Solution:
 
         return root1
 ```
+(版本四) 迭代 + 代码优化
+```python
+# Definition for a binary tree node.
+# class TreeNode:
+#     def __init__(self, val=0, left=None, right=None):
+#         self.val = val
+#         self.left = left
+#         self.right = right
+from collections import deque
 
+class Solution:
+    def mergeTrees(self, root1: TreeNode, root2: TreeNode) -> TreeNode:
+        if not root1:
+            return root2
+        if not root2:
+            return root1
+
+        queue = deque()
+        queue.append((root1, root2))
+
+        while queue:
+            node1, node2 = queue.popleft()
+            node1.val += node2.val
+
+            if node1.left and node2.left:
+                queue.append((node1.left, node2.left))
+            elif not node1.left:
+                node1.left = node2.left
+
+            if node1.right and node2.right:
+                queue.append((node1.right, node2.right))
+            elif not node1.right:
+                node1.right = node2.right
+
+        return root1
+
+
+```
 ### Go 
 
 ```go

problems/0654.最大二叉树.md

@@ -259,52 +259,75 @@ class Solution {
 ```
 
 ### Python 
-
+(版本一) 基础版
 ```python
+# Definition for a binary tree node.
+# class TreeNode:
+#     def __init__(self, val=0, left=None, right=None):
+#         self.val = val
+#         self.left = left
+#         self.right = right
 class Solution:
-    """递归法 更快"""
     def constructMaximumBinaryTree(self, nums: List[int]) -> TreeNode:
-        if not nums:
+        if len(nums) == 1:
-            return None
+            return TreeNode(nums[0])
-        maxvalue = max(nums)
+        node = TreeNode(0)
-        index = nums.index(maxvalue)
+        # 找到数组中最大的值和对应的下标
+        maxValue = 0
+        maxValueIndex = 0
+        for i in range(len(nums)):
+            if nums[i] > maxValue:
+                maxValue = nums[i]
+                maxValueIndex = i
+        node.val = maxValue
+        # 最大值所在的下标左区间 构造左子树
+        if maxValueIndex > 0:
+            new_list = nums[:maxValueIndex]
+            node.left = self.constructMaximumBinaryTree(new_list)
+        # 最大值所在的下标右区间 构造右子树
+        if maxValueIndex < len(nums) - 1:
+            new_list = nums[maxValueIndex+1:]
+            node.right = self.constructMaximumBinaryTree(new_list)
+        return node
         
-        root = TreeNode(maxvalue)
+```
+(版本二) 使用下标 
+```python
 
-        left = nums[:index]
-        right = nums[index + 1:]
-
-        root.left = self.constructMaximumBinaryTree(left)
-        root.right = self.constructMaximumBinaryTree(right)
-        return root
-        
 class Solution:
-    """最大二叉树 递归法"""
+    def traversal(self, nums: List[int], left: int, right: int) -> TreeNode:
+        if left >= right:
+            return None
+        maxValueIndex = left
+        for i in range(left + 1, right):
+            if nums[i] > nums[maxValueIndex]:
+                maxValueIndex = i
+        root = TreeNode(nums[maxValueIndex])
+        root.left = self.traversal(nums, left, maxValueIndex)
+        root.right = self.traversal(nums, maxValueIndex + 1, right)
+        return root
 
     def constructMaximumBinaryTree(self, nums: List[int]) -> TreeNode:
         return self.traversal(nums, 0, len(nums))
-    
-    def traversal(self, nums: List[int], begin: int, end: int) -> TreeNode:
-        # 列表长度为0时返回空节点
-        if begin == end:
-            return None
-        
-        # 找到最大的值和其对应的下标
-        max_index = begin
-        for i in range(begin, end):
-            if nums[i] > nums[max_index]:
-                max_index = i
-        
-        # 构建当前节点
-        root = TreeNode(nums[max_index])
-        
-        # 递归构建左右子树
-        root.left = self.traversal(nums, begin, max_index)
-        root.right = self.traversal(nums, max_index + 1, end)
-        
-        return root
-```
 
+ ```       
+
+(版本三) 使用切片
+
+```python
+
+class Solution:
+    def constructMaximumBinaryTree(self, nums: List[int]) -> TreeNode:
+        if not nums:
+            return None
+        max_val = max(nums)
+        max_index = nums.index(max_val)
+        node = TreeNode(max_val)
+        node.left = self.constructMaximumBinaryTree(nums[:max_index])
+        node.right = self.constructMaximumBinaryTree(nums[max_index+1:])
+        return node
+        
+```
 ### Go
 
 

problems/0700.二叉搜索树中的搜索.md

@@ -230,7 +230,7 @@ class Solution {
 
 ### Python 
 
-递归法：
+（方法一） 递归
 
 ```python
 class Solution:
@@ -250,12 +250,12 @@ class Solution:
 
 ```
 
-迭代法：
+（方法二）迭代
 
 ```python
 class Solution:
     def searchBST(self, root: TreeNode, val: int) -> TreeNode:
-        while root is not None:
+        while root:
             if val < root.val: root = root.left
             elif val > root.val: root = root.right
             else: return root