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Problem statement:

You are given $N$ points on a 2-D grid, and an integer number $K$. Cluster the points whose distance is less than $K$ and output each cluster and its corresponding point. Note that the points are transitive. e.g., say you are given $N=3$ points $(0,1)$, $(0,2)$, and $(0,3)$ and $K = 1$. This will give 3 clusters where each point is its own cluster.

I don't understand this question, and the example. What does "transitive" mean here? I think the definition in this context is what's not contributing to my understanding.

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