Leetcode 997. Find the Town Judge  Summary and Q&A
TL;DR
A method to identify the town judge using indegree and outdegree concepts in graph theory.
Key Insights
 😫 The town judge is defined within a set of relationships, focusing on trust and lack thereof.
 🔂 A single array element representing trust contains a pair indicating who trusts whom.
 📈 The effective identification of the town judge utilizes graph theory principles applied through indegree and outdegree metrics.
 🧑 Handling edge cases like the scenario where n equals 1 is critical, as it simplifies the judgment to asserting that person as the judge.
 🧘 The algorithm efficiently traverses the relationships to determine trust, ensuring that each individual's position is assessed.
 🦔 The worstcase time complexity may reach O(n^2) based on the total number of edges or trust relationships in the graph.
 🌍 The solution emphasizes the robustness of graph concepts in solving realworld relationshipdriven problems.
Transcript
hello everyone welcome back to lead coding today we are solving find the town judge is a basic graph problem and let us go through the description of the problem in a town there are n people labeled from 1 to n there's a rumor that one of the people is secretly down judge so for the town church there are three conditions the first one is the town j... Read More
Questions & Answers
Q: What are the key conditions for someone to be the town judge?
To qualify as the town judge, a person must be trusted by exactly n1 other individuals and must not trust anyone themselves. This means all other individuals should point towards the judge, while the judge maintains no outgoing trust relationships.
Q: How are indegrees and outdegrees determined in this problem?
Indegrees are calculated by counting how many people trust a specific individual, while outdegrees are counted by how many individuals that specific person trusts. An indegree of n1 indicates that the person is trusted by everyone except themselves, and an outdegree of 0 means they trust no one.
Q: What must be returned if no valid town judge is found?
If there is no person who satisfies the criteria of being a town judge, the function should return 1. This indicates that either there are multiple judges or that the relationships do not support the existence of a single town judge.
Q: Why is the space complexity O(n) for this problem?
The space complexity is O(n) because two separate arrays (or vectors) are maintained to track the indegrees and outdegrees for each of the n individuals, leading to linear space usage relative to the number of people in the town.
Summary & Key Takeaways

The town judge problem involves identifying a single individual who is trusted by everyone but trusts no one within a list of trust relationships.

The solution utilizes the indegree and outdegree counts of each individual to determine if a person qualifies as the town judge, specifically requiring an indegree of n1 and an outdegree of 0.

The approach has a time complexity related to the number of trust relationships and space complexity of O(n) for storing counts, and it handles special cases where only one person exists.