LeetCode 236: Lowest Common Ancestor of a Binary Tree — Python Solution

Solve LeetCode 236: Lowest Common Ancestor of a Binary Tree in Python with a postorder target propagation approach. The key is to make the state invariant explicit, so the implementation and complexity follow naturally.

This guide paraphrases the task and does not reproduce LeetCode’s prompt. Use the official page for the complete statement, examples, constraints, and submission runner.

What the problem is testing

Return a node when it is a target or when targets are found in both child subtrees; otherwise propagate the one non-null result.

Algorithm

1. Return a node when it is a target or when targets are found in both child subtrees; otherwise propagate the one non-null result.
2. Maintain this invariant: A non-null return means that subtree contains at least one target, and the first node receiving two results is their lowest common ancestor.
3. Continue until every input item or reachable state has been resolved, then return the accumulated result.

Python solution

LeetCode provides the list, tree, or graph node definition used by the method.

from collections import Counter, defaultdict, deque, OrderedDict
import random

class Solution:
    def lowestCommonAncestor(self, root, p, q):
        if not root or root is p or root is q:
            return root
        left = self.lowestCommonAncestor(root.left, p, q)
        right = self.lowestCommonAncestor(root.right, p, q)
        if left and right:
            return root
        return left or right

Why this is correct

The proof follows the maintained state: A non-null return means that subtree contains at least one target, and the first node receiving two results is their lowest common ancestor. Each iteration preserves that claim while permanently resolving at least one position, node, interval, or search state. When the loop or recursion ends, every candidate required by the problem has therefore been included or ruled out, so the returned value is correct.

Complexity

O(n) time and O(h) recursion space. The stated auxiliary space excludes the returned output unless the output is the data structure being built.

Edge cases

One target may be an ancestor of the other.

Tested reference code

This implementation is included in the site’s downloadable 100-solution Python library. The complete suite compiles every solution and runs a behavioral assertion for every problem before publication.

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