✅Day 53 | LeetCode 997. Find the Town Judge

🌟 Welcome to the Leetcode Daily Challenge Solution! 🚀

Embark on an intriguing exploration through the realm of directed graphs and trust relationships as we tackle the task of finding the judge in a town. Brace yourself for an adventure through algorithmic ingenuity and graph analysis mastery.

🎯 Problem Overview:

Our mission is to determine the judge in a town consisting of 'N' people, where the judge is the only person trusted by everyone else but trusts nobody. We aim to devise an algorithm that efficiently computes and returns the identity of the judge.

🚀 Algorithm Breakdown:

Create two vectors 'in' and 'out' of size 'N+1' to represent the number of incoming and outgoing trusts for each person in the town.
Iterate through the 'trust' vector and update the 'in' and 'out' vectors based on the trust relationships.
After processing all trust relationships, iterate through the 'in' and 'out' vectors to find the person who is trusted by everyone ('in[i] == N-1') and trusts nobody ('out[i] == 0').
Return the identity of the judge if found; otherwise, return -1.
📊 Complexity Analysis:

Time Complexity: O(T + N), where T is the number of trust relationships and N is the number of people in the town. The first loop iterates through the trust relationships, and the second loop iterates through the 'in' and 'out' vectors.
Space Complexity: O(N) - Additional space required for the 'in' and 'out' vectors.

Delve into the intricacies of graph analysis and algorithmic logic as we unravel the solution together! Feel empowered to explore, modify, and deepen your understanding of efficient strategies for finding the judge in a town based on trust relationships. 🔗✨

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