Understanding the stateful root to leaf path pattern

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 with some problems going even further to find the aggregated value of some other function g over all root-to-leaf path aggregates and return a single result. We learned the stateless solution to this problem that doesn't require creating shared variables that all nodes can access during the recursive execution. While the stateless solution can solve many such problems, some problems are easier to solve using the stateful solution.