Leetcode 997. Find the Town Judge | Summary and Q&A
TL;DR
A method to identify the town judge using in-degree and out-degree 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 in-degree and out-degree 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 worst-case 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 real-world relationship-driven 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 n-1 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 in-degrees and out-degrees determined in this problem?
In-degrees are calculated by counting how many people trust a specific individual, while out-degrees are counted by how many individuals that specific person trusts. An in-degree of n-1 indicates that the person is trusted by everyone except themselves, and an out-degree 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 in-degrees and out-degrees for each of the n individuals, leading to linear space usage relative to the number of people in the town.
Summary & Key Takeaways
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The town judge problem involves identifying a single individual who is trusted by everyone but trusts no one within a list of trust relationships.
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The solution utilizes the in-degree and out-degree counts of each individual to determine if a person qualifies as the town judge, specifically requiring an in-degree of n-1 and an out-degree of 0.
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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.