From c53d6303b5b540b98ac2a54b0ba06ab3a75c0aec Mon Sep 17 00:00:00 2001
From: Sangeeth Sudheer <sangeeth96@users.noreply.github.com>
Date: Thu, 21 Apr 2022 00:22:02 +0530
Subject: [PATCH] balanced-binary-tree: add py3 soln

---
 0110_balanced-binary-tree/README.md           | 32 +++++++++++++
 0110_balanced-binary-tree/python3/solution.py | 47 +++++++++++++++++++
 2 files changed, 79 insertions(+)
 create mode 100644 0110_balanced-binary-tree/README.md
 create mode 100644 0110_balanced-binary-tree/python3/solution.py

diff --git a/0110_balanced-binary-tree/README.md b/0110_balanced-binary-tree/README.md
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+++ b/0110_balanced-binary-tree/README.md
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+Given a binary tree, determine if it is height-balanced.
+
+For this problem, a height-balanced binary tree is defined as:
+
+> a binary tree in which the left and right subtrees of _every_ node differ in height by no more than 1.
+
+**Example 1:**
+
+![](https://assets.leetcode.com/uploads/2020/10/06/balance_1.jpg)
+
+    Input: root = [3,9,20,null,null,15,7]
+    Output: true
+    
+
+**Example 2:**
+
+![](https://assets.leetcode.com/uploads/2020/10/06/balance_2.jpg)
+
+    Input: root = [1,2,2,3,3,null,null,4,4]
+    Output: false
+    
+
+**Example 3:**
+
+    Input: root = []
+    Output: true
+    
+
+**Constraints:**
+
+*   The number of nodes in the tree is in the range `[0, 5000]`.
+*   `-104 <= Node.val <= 104`
\ No newline at end of file
diff --git a/0110_balanced-binary-tree/python3/solution.py b/0110_balanced-binary-tree/python3/solution.py
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+# Time: O(N)
+# Space: O(N)
+
+# 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 namedtuple
+
+class Solution:
+    def isBalanced(self, root: Optional[TreeNode]) -> bool:
+        Result = namedtuple('Result', 'is_balanced height')
+        
+        def dfs(node):
+            """
+            Instead of doing top-down, we'll do bottom-up recursion
+            via DFS to solve subproblems and bubble back up to the root
+            """
+            
+            # This happens when we reach leaf node, in which case, we assume
+            # things are balanced and return 0 height
+            if node is None: return Result(True, 0)
+            
+            # DFS recursion
+            right = dfs(node.right)
+            left = dfs(node.left)
+            
+            # For current `node`, things are only going to be balanced if
+            # both left and right subtrees are balanced. Otherwise, we can
+            # return False right away.
+            has_balanced_subtrees = right.is_balanced and left.is_balanced
+            
+            # Besides having left and right subtrees themselves *individually*
+            # being balanced, we need to next check height difference <= 1.
+            if has_balanced_subtrees and abs(right.height - left.height) <= 1:
+                # Height of tree formed by current `node` would be the max
+                # height of its left/right subtree + 1 (itself)
+                return Result(True, 1 + max(left.height, right.height))
+            
+            # If it reaches here, that means either height diff > 1 or left/right
+            # subtrees are already imbalanced.
+            return Result(False, 0)
+        
+        
+        return dfs(root).is_balanced