LeetCode 100: Same Tree — Python Solution

Solve LeetCode 100: Same Tree in Python with a paired recursion 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

Two nodes match when both are absent, or both exist with equal values and matching left and right subtrees.

Algorithm

1. Two nodes match when both are absent, or both exist with equal values and matching left and right subtrees.
2. Maintain this invariant: Every recursive pair represents corresponding positions in the two trees.
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 isSameTree(self, p, q):
        if not p or not q:
            return p is q
        return p.val == q.val and self.isSameTree(p.left, q.left) and self.isSameTree(p.right, q.right)

Why this is correct

The proof follows the maintained state: Every recursive pair represents corresponding positions in the two trees. 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 missing node immediately distinguishes the structures.

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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