Given a subreddit, determining all days in which it can be declared Subreddit of the Day is a trivial task.
Now, consider the following:
- S = the set of all N subreddits
- D = the set of all K days
- an edge between i ∈ S and j ∈ D denotes the fact that subreddit i can be declared Subreddit of the Day on day j.
Using this model, the problem becomes equivalent to finding a maximum matching in a bipartite graph.
Further reading: infoarena.