Find the Town Judge (Graph representation)

To solve this efficiently, I would first clarify that we need to find a node with an in-degree of N-1 and an out-degree of 0. Building a full graph using an adjacency matrix would take O(N^2) space, which is unnecessary here. Instead, I propose using a single integer array of size N+1 to track net trust scores. As we iterate through the trust array, for every pair [a, b], we increment the score for b because they are trusted, and decrement the score for a because they cannot be the judge if they trust anyone. After processing all trust relationships in a single pass, we check if any person has a score exactly equal to N-1. If such a person exists, they are the judge; otherwise, no judge exists. For example, if N=3 and trust=[[1,3],[2,3]], person 3 gets +1 from 1 and +1 from 2, resulting in a score of 2, which equals N-1. This approach ensures O(N) time complexity and O(N) space complexity, meeting the strict performance requirements often seen in network routing scenarios at Cisco.