LeetCode 112: Path Sum — Python Solution

Solve LeetCode 112: Path Sum in Python with a remaining-sum 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

Subtract each node value and accept only when a leaf makes the remaining target exactly zero.

Algorithm

1. Subtract each node value and accept only when a leaf makes the remaining target exactly zero.
2. Maintain this invariant: The remaining value equals the target minus the sum along 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 hasPathSum(self, root, targetSum):
        if not root:
            return False
        remaining = targetSum - root.val
        if not root.left and not root.right:
            return remaining == 0
        return self.hasPathSum(root.left, remaining) or self.hasPathSum(root.right, remaining)

Why this is correct

The proof follows the maintained state: The remaining value equals the target minus the sum along 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 matching internal node is not enough; the path must end at a leaf.

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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