Add (opinionated) warnings for keywords

[gkreitz]

Keywords are currently very underspecified in the problem standard. To help problem setters, and the community, it would make sense to me if problemtools was a bit opinionated in keyword usage (obviously, never giving an error, but nudging via warnings).

Firstly, we should probably add the same rule we're moving to in Kattis: keywords should only consist of lowercase letters, numbers, and hyphens. This will catch a number of errors and inconsistencies that we've seen in problem packages, with keywords such as "ad", "hoc", or "combinatorics," (with a trailing comma in the keyword).

Secondly, I'm toying with the idea of creating a list of "recommended" keywords, and nudging toward their usage. There are concepts that can be written in multiple ways ("bfs" vs "breadth-first-search", "maths" vs. "math"), and I think it would be useful to nudge all problems in one direction. One potential implementation would be to attempt to maintain a list of "well-known" keywords, and nudge towards those. Obviously, that list will never be complete - my hope would be that people would contribute things they feel are missing.

[Matistjati]

This is a good direction. IMHO, the biggest problem with keywords right now is that we aren't opinionated enough.
I like the idea of a set of well-known keywords. It might also be a good idea to impose some sort of tree structure. Example:

graph
  2-sat
  flow
    matching
  dfs
  shortest path
  dsu
  trees

queries
  range queries

math
  combinatorics
  number theory
    

We will probably have to take a decision on what a tog should even be. For an interesting example, I think that Ford-Fulkersson, Edmonds-Karp and Push-relabel don't deserve a tag- in 98% of problems, they are interchangable- thus these tags should instead just be "flow". On the other hand, I would argue that berlekamp-massey deserves its own tag- even if you can recover linear recurrences via matrix math or half-gcd, this is what the community knows it by.

Potential sources of inspiration

KACTL's could probably serve as a good source of inspiration: https://github.com/kth-competitive-programming/kactl/tree/main/content

Codeforces' also has their own set of pretty arbitrary tags:

Details

2-sat
binary search
bitmasks
brute force
chinese remainder theorem
combinatorics
communication
constructive algorithms
data structures
dfs and similar
divide and conquer
dp
dsu
expression parsing
fft
flows
games
geometry
graph matchings
graphs
greedy
hashing
implementation
interactive
math
matrices
meet-in-the-middle
number theory
probabilities
schedules
shortest paths
sortings
string suffix structures
strings
ternary search
trees
two pointers