One of the things I have realised, from codeforces and a bit of help from jipit, structures are not data strucutres, they are more like properties/behaviours.
Here goes the list:
Does something only increase/decrease?
→ monotonicity
Does something become permanently irrelevant?
→ dominance
Do slopes/marginal gains increase/decrease?
→ convexity/concavity
Does something repeat?
→ DP / memoization
Does a quantity accumulate?
→ prefix sums
Does only odd/even matter?
→ parity
Does ordering matter?
→ sorting / binary search / sweep line
Can candidates be eliminated permanently?
→ greedy / monotonic structure
Does the same state appear again?
→ dynamic programming
Does the problem have a graph/tree structure?
→ graph algorithms