This paper describes a parametrized distributed algorithm applicable to any directed graph topology. The function parameter of our algorithm is instantiated to produce distributed algorithms for both fundamental and high level applications, such as shortest path calculus and depth-first-search tree construction. Due to fault resilience properties of our algorithm, the resulting protocols are self-stabilizing at no additional cost. Self-stabilizing protocols can resist transient failures and guarantee system recovery in a finite time. Since the condition on the function parameter (being a strictly idempotent $r$-operator) permits a broad range of applications to be implemented, the solution presented in our paper can be useful for a large class of distributed systems.