Understanding the stateless root to leaf path pattern

A root-to-leaf path in a binary tree is a path made up of nodes starting from the root node and ending at a leaf node, and there are as many root-to-leaf paths in a binary tree as there are leaves. Many binary tree problems require us to find, for all root-to-leaf paths, the aggregated value of a function f over some or all nodes in a root-to-leaf path. Some problems go even further to find the aggregated value of some other function g over all aggregated values of all the root-to-leaf paths and return a single result.

There are two ways to solve this problem: one requires some shared state to be maintained, while the other is completely stateless. The choice between these options depends on the function fandgand the complexity of the problem. Depending on the functions fandg, the problem can be solved using the stateless root-to-leaf path technique.