Models Worth Keeping

A team trained several models and measured each one in the same way: for example accuracy (higher is better), size in MB (lower is better) and prediction time in ms (lower is better). The directions are given as a string better with one character per measure: ">" means higher is better, "<" means lower is better.

Model A beats model B when A is at least as good as B in every measure and strictly better in at least one. A model is worth keeping when no other model beats it.

Write worth_keeping(models, better) where models is a list of (name, scores) pairs and scores is a tuple with one number per measure. Return the names of the models worth keeping, in their input order.

Examples

Input:  models = [("big",   (0.95, 400, 30)),
                  ("small", (0.91,  20,  4)),
                  ("mid",   (0.91,  60,  9)),
                  ("tiny",  (0.80,   5,  2))]
        better = "><<"
Output: ["big", "small", "tiny"]
Explanation: small beats mid: equal accuracy, and smaller and faster.
             Nothing beats big (most accurate) or tiny (smallest and fastest).

Input:  models = [("a", (1, 1)), ("b", (1, 1))], better = "<<"
Output: ["a", "b"]
Explanation: Identical scores: neither is strictly better anywhere, so neither beats the other.

The setup defines random_models(n, d, seed), a list of n models with d random measures, so you can try your function with Run.

Constraints

• 0 <= len(models) <= 300, 1 <= len(better) <= 6
• every scores tuple has len(better) numbers; names are distinct.

Goals

• Express "no worse everywhere and better somewhere" with `all` and `any` over zipped values
• Bring measures with opposite directions to a common direction before comparing
• Filter a list by a condition that looks at every other item