The three-prizes problem: decide the rules first

The prize example asks for three high-scoring students, with two extra rules: each should be a subject topper in at least one subject, and the final group should include both genders represented by M and F in the supplied dataset. We must make these rules precise before writing the algorithm.

Break a big problem into smaller questions #

First decide what “top three in a subject” means when scores tie. Compute the subject cutoffs. Filter the eligible students. Rank their totals while keeping their IDs. Finally check the group rule. For these cards the three winners above qualify and include M and F.

A successful example does not settle every case #

What if four students tie at the last prize? What if there is no eligible student from one required category? What if a high-total student misses every subject cutoff? State a tie policy and what to do if the rules cannot all be satisfied. Do not quietly change the criteria after seeing a difficult case.

The lecture’s initial “top three overall, then verify” exploration and its later “filter subject toppers, then rank totals” algorithm agree on our dataset. They can differ on other datasets. Say which rule you intend rather than treating them as universally interchangeable.