The recruiter called it an ML coding round so I showed up mentally prepped to talk about model training pipelines or loss functions or something.
Model the system as a directed graph where each node moves toward its target at a constant speed. Analyze the long-term behavior by identifying cycles and chains, then determine convergence based on whether the graph has a single sink or multiple sinks. Use mathematical reasoning to show that points in cycles converge to the cycle's centroid, while chains converge to the sink.
Pro tip: Relate the problem to real-world applications like particle systems in animation or distributed consensus, showing you can connect theory to practice. Mention that the convergence time depends on the initial distances and speeds, and discuss edge cases like multiple cycles or disconnected components.
Represent the points and their targets as a directed graph, where each node has exactly one outgoing edge (its target). Identify cycles and chains (trees leading into cycles).
For a cycle of points, show that they move toward each other and eventually meet at the centroid of the cycle. Use symmetry or linear algebra to prove convergence.
For chains (nodes not in cycles), they eventually enter a cycle or a sink. If the graph has a single sink (a node with no outgoing edge), all points converge to that sink. If multiple sinks, points converge to their respective sinks.
Determine if all points converge to a single location: this happens only if the graph has a single sink (which could be a cycle or a fixed point). Otherwise, points converge to multiple locations (one per sink).
Discuss that convergence time depends on the initial distances and speeds. In continuous time, convergence is asymptotic; in discrete steps, it may be finite if points meet exactly.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.