LeetCode 101: Symmetric Tree — Python Solution

Solve LeetCode 101: Symmetric Tree in Python with a mirror 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

Compare the outer and inner children of paired nodes: left with right and right with left.

Algorithm

1. Compare the outer and inner children of paired nodes: left with right and right with left.
2. Maintain this invariant: Each recursive pair must occupy mirrored positions around the root.
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 isSymmetric(self, root):
        def mirror(left, right):
            if not left or not right:
                return left is right
            return left.val == right.val and mirror(left.left, right.right) and mirror(left.right, right.left)
        return mirror(root.left, root.right) if root else True

Why this is correct

The proof follows the maintained state: Each recursive pair must occupy mirrored positions around the root. 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

Two missing mirrored nodes match; exactly one missing node fails.

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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