## DEV Community

Abhishek Chaudhary

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# Smallest Subtree with all the Deepest Nodes

Given the `root` of a binary tree, the depth of each node is the shortest distance to the root.

Return the smallest subtree such that it contains all the deepest nodes in the original tree.

A node is called the deepest if it has the largest depth possible among any node in the entire tree.

The subtree of a node is a tree consisting of that node, plus the set of all descendants of that node.

Example 1:

Input: root = [3,5,1,6,2,0,8,null,null,7,4]
Output: [2,7,4]
Explanation: We return the node with value 2, colored in yellow in the diagram.
The nodes coloured in blue are the deepest nodes of the tree.
Notice that nodes 5, 3 and 2 contain the deepest nodes in the tree but node 2 is the smallest subtree among them, so we return it.

Example 2:

Input: root = [1]
Output: [1]
Explanation: The root is the deepest node in the tree.

Example 3:

Input: root = [0,1,3,null,2]
Output: [2]
Explanation: The deepest node in the tree is 2, the valid subtrees are the subtrees of nodes 2, 1 and 0 but the subtree of node 2 is the smallest.

Constraints:

• The number of nodes in the tree will be in the range `[1, 500]`.
• `0 <= Node.val <= 500`
• The values of the nodes in the tree are unique.

Note: This question is the same as 1123: https://leetcode.com/problems/lowest-common-ancestor-of-deepest-leaves/

SOLUTION:

``````# 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 maxDepth(self, root):
if root:
a = 1 + self.maxDepth(root.left)
b = 1 + self.maxDepth(root.right)
return max(a, b)
return -1

def subtreeWithAllDeepest(self, root: TreeNode) -> TreeNode:
if root:
left = self.maxDepth(root.left)
right = self.maxDepth(root.right)
if left > right:
return self.subtreeWithAllDeepest(root.left)
elif right > left:
return self.subtreeWithAllDeepest(root.right)
else:
return root
``````