Determine Players with Unique Ranks from Match Results (Reachability Counts in a Directed Graph)

Problem: Determine Players with Uniquely Decidable Ranks from Match Results There are n players with a true, unique ranking from 1..n (no ties). The rule is: If player x is ranked higher than player y, then x will always beat y. You are given m known match outcomes, each as a beat b, meaning a is definitely stronger than b (i.e., a must be ranked higher). Your task is to find all players whose exact rank can be uniquely determined from the given outcomes, and output those ranks. A player p has a uniquely decidable rank if: the number of players that are definitely stronger than p (nodes that can reach p), plus the number of players that are definitely weaker than p (nodes reachable from p) equals n - 1. Input Format First line: two integers n m Next m lines: two integers a b meaning a beat b Output Format Output multiple lines player rank for each player whose rank is uniquely determined. Example Input 5 4 1 2 2 3 1 3 4 5 Output 1 1 2 2 3 3 Explanation: the relative order among 1,2,3 is fully implied; players 4 and 5 cannot be placed uniquely in the global ranking. Example Input 5 4 1 2 2 3 1 3 4 5 Output 1 1 2 2 3 3