LeetCode 129: Sum Root to Leaf Numbers — Python Solution

Solve LeetCode 129: Sum Root to Leaf Numbers in Python with a prefix-number DFS 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

Extend the current number by multiplying by ten and adding the node digit; return it at leaves and sum child results.

Algorithm

1. Extend the current number by multiplying by ten and adding the node digit; return it at leaves and sum child results.
2. Maintain this invariant: The accumulator is exactly the decimal number represented by the current root-to-node path.
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 sumNumbers(self, root):
        def visit(node, prefix):
            if not node:
                return 0
            value = prefix * 10 + node.val
            if not node.left and not node.right:
                return value
            return visit(node.left, value) + visit(node.right, value)
        return visit(root, 0)

Why this is correct

The proof follows the maintained state: The accumulator is exactly the decimal number represented by the current root-to-node path. 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

A zero digit still shifts the prefix; an empty tree contributes zero.

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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