# September LeetCoding Challenge, Day 8: Sum of Root To Leaf Binary Numbers

September 9, 2020

This is part of a series of posts about the September LeetCoding Challenge. Check the first post for more information.

The problem for September 8 is Sum of Root to Leaf Binary Numbers. You’re given a binary tree in which each node has value 0 or 1. In this case, each path from the root to a leaf represents a binary number starting with the most significant bit. For example, a path from root to leaf $$0 \rightarrow 1 \rightarrow 1 \rightarrow 0 \rightarrow 1$$ represents the number $$01101$$ in binary, or $$13$$ in decimal. We’re interested in the sum of numbers produced from the paths from the root to every leaf in the tree.

We’re told that the number of nodes in the tree doesn’t exceed 1000 and that the sum will not exceed $$2^{31} - 1$$. Therefore, we can do a DFS on the tree while keeping track of the number at each path, accumulating the current number whenever we reach a leaf. Since the path follows the significance of the bits in the resulting number, we can keep track of the current number while traversing the tree by multiplying the current number by 2 whenever we go either left or right, and sum the value at the node we’re visiting. The following is an implementation of this idea: