LeetCode 226: Invert Binary Tree — Python Solution

Solve LeetCode 226: Invert Binary Tree in Python with a recursive swap 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

Swap each node’s children and recursively invert the two resulting subtrees.

Algorithm

1. Swap each node’s children and recursively invert the two resulting subtrees.
2. Maintain this invariant: Every returned subtree is the mirror image of its original subtree.
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 invertTree(self, root):
        if root:
            root.left, root.right = self.invertTree(root.right), self.invertTree(root.left)
        return root

Why this is correct

The proof follows the maintained state: Every returned subtree is the mirror image of its original subtree. 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

An empty tree remains empty.

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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