If this was a thousand piece puzzle, I would still venture recursive backtracker with good heuristics will beat CP-SAT, even in the sudoku case some good heuristics with backtracking beats CP-SAT. Not sure why Claude immediately jumped to using CP-SAT.
I've spent significant chunks of my career help people throw away backtracking searchers people polished over years with a CP-SAT model I threw together in 30 minutes, often much to their upset.
You can for Sudoku often beat a CP-SAT solver, but that's because the problems are trivial and take milliseconds. If you look at more difficult Sudoku variants, or 16x16 grids, backtracking solvers start to fall behind.
I'm not familiar with CP-SAT, but TTBOMK all SAT solvers use a type of backtracking search underneath called DPLL. Modern ones are highly tuned in terms of which variable they choose to branch on next, and in what order to try its possible values; this can have an enormous impact on runtime. They probably use several tricks on top of that; the big one that I'm aware is conflict-driven clause learning, where the solver adds new constraints that it discovers as it goes along (e.g., it might be able to determine that x and y always have the same value in every solution), which can shrink the search space a lot.
nh23423fefe•57m ago
Eventually shitting on LLM code will be seen by all as lazy cope. I too am aware of the existence of SAT but I really would struggle to immediately see through some problem i was having and interpret SAT unless I did it a bunch. Having agent suggest the "right thing" is clearly better. And hopefully would help my intuition in the future.