This is a not-so-short article teeming with "Aha!" moments.

1. reduce all branching in the solution to a math expression
2. converted to a lookup algorithm
3. we need a perfect hash function
4. use multiplication + shr as bit mixer
5. store answers directly in a single u32 integer
6. cram the answers even tighter with overlaps

The post shows off lot of tricks, very interesting read.