Precision and Recall at K

Nobody scrolls past the first handful of recommendations, so recommender systems are judged on the top k and nothing else.

• Precision@k — of the k items you showed, what fraction were relevant?
• Recall@k — of all the relevant items that exist, what fraction did you show?

Task: write precision_recall_at_k(recommended, relevant, k) returning [precision, recall], both rounded to 4 decimal places.

• recommended is ordered best-first; only its first k entries count.
• If the list is shorter than k, use what's there — precision divides by how many you actually showed.
• Return 0.0 for either metric when its denominator would be zero.
• relevant is a set of items, unordered.

The two pull against each other. Recommending everything makes recall perfect and precision worthless; recommending one sure thing does the reverse. Fixing k is what forces the system to commit.