#294 is completed with a DFS approach

Author: Hamid Gasmi

09-problems/lc_865_subtree_with_all_deepest.py

@@ -0,0 +1,67 @@
+class TreeNode:
+    def __init__(self, val=0, left=None, right=None):
+        self.val = val
+        self.left = left
+        self.right = right
+
+"""
+    1. Problem Summary / Clarifications / TDD:
+        Case 1: Return 2
+            1
+           / \
+          2   3
+         / \   \        
+        4   5   6
+       / \   \
+      7  8    9
+
+        Case 2: Return 10
+            1
+           / \
+          2   3
+         / \   \        
+        4   5   6
+       / \   \
+      7  8    9
+        /
+       10
+
+    2. Inuition
+        - DFS traversal: for each branch, return its height and its subtree with all deepest nodes
+        - If left height == right hight, return root
+        - If left height > right height, return left substree
+        - If left height < right height, return right substree
+    
+    3. Implementation:
+    4. Tests:
+            - All cases above
+            - Edge cases: empty tree, a tree with one node
+            - Special cases: Tree as a linked list, balanced tree
+                1               1
+                 \             /
+                  2           2
+                   \         /
+                    3       3
+
+    4. Complexity Analysis:
+        Time Complexity: O(N): we need to visit all nodes
+        Space Complexity: 
+            - Worst case: O(N): when the tree looks like a linked-list.
+            - Best case: O(height): when the tree is balanced.
+
+"""
+
+class SolutionDFS:
+    
+    def subtree_with_all_deepest(self, root: TreeNode) -> TreeNode:
+        
+        return self.dfs(root)[1]        
+        
+    def dfs(self, root: TreeNode) -> (int, TreeNode):
+        if root is None:
+            return 0, None
+        
+        l_height, l_subtree = self.dfs(root.left)
+        r_height, r_subtree = self.dfs(root.right)
+            
+        return max(l_height, r_height) + 1, l_subtree if l_height > r_height else r_subtree if l_height < r_height else root