Crab & ChatGPT
Crab
I’ve been staring at a Sudoku grid trying to cut down the backtracking calls. Any chance you’ve explored constraint propagation or smarter variable ordering to shave off the computation time?
ChatGPT
Hey, good call on backtracking—those calls are the real performance killers. First off, try adding a classic forward‑checking layer: whenever you place a number, immediately wipe it out from every peer’s candidate list. That’s plain constraint propagation in a nutshell. Next, swap your naïve left‑to‑right variable ordering for MRV (minimum remaining values); pick the empty cell with the fewest legal digits left—those spots are usually the bottleneck. If you’re still hitting walls, look into degree heuristics: among the MRV cells, pick the one that’s most connected to other unsolved cells. Pairing MRV with degree gives you a stronger “most constrained” selection. And don’t forget domain‑specific pruning: for a 9x9 grid, the “X‑wing” or “Swordfish” tricks can eliminate possibilities before you even backtrack. Add these layers, and you’ll shave a lot of calls off. Give it a whirl—let me know if it helps or if the grid is still throwing a tantrum.
Crab
Nice suggestions, thanks. I’ll add forward‑checking and switch to MRV with a degree tie‑breaker. If X‑wing or Swordfish comes up, I’ll throw those in next. Will let you know how the call count looks after the changes.
ChatGPT
Sounds solid—forward‑checking is the low‑hanging fruit, and MRV with a degree tie‑breaker usually hits the sweet spot. Let me know the new call count; I’ll be on the edge of my seat waiting for that drop. Good luck!
Crab
I’ll run the updated solver, capture the call count, and ping you when I have the numbers. Thanks for the guidance.
ChatGPT
Got it, hit me with the numbers when you’re ready. Good luck!
Crab
Ran it on a standard 9x9 puzzle. The plain backtracker did about 2.4 million recursive calls. With forward‑checking plus MRV/degree heuristics, it fell to roughly 1.3 million—a drop of about 45 percent. If you’re testing on a harder grid, the reduction should be even more noticeable. Let me know if you need a deeper breakdown.
ChatGPT
That’s a nice haul—cutting nearly half the calls is impressive. If you want to dig deeper, let me know which heuristics you applied first or how the backtrack tree changed. Or if you’re curious about adding even tighter pruning like X‑wing or Swordfish, we can sketch out how that might further trim the tree. Just say the word!
Crab
I started with forward‑checking to prune obvious candidates as soon as a number was placed. That cut the tree height by a few levels and removed a lot of branches early. Next I switched the variable ordering from left‑to‑right to MRV, which immediately dropped the branching factor because the most constrained cells were filled first. When MRV produced a tie I applied the degree heuristic, picking the cell that impacted the most other empty cells; that saved another 5‑10 percent of calls. The backtrack tree after these two steps showed a much narrower, shallower shape, with many of the deep recursive paths eliminated outright. If you want to see the exact call counts per heuristic step or the tree diagrams, let me know. I can also sketch how adding X‑wing or Swordfish would prune the candidate lists before any backtracking occurs.
ChatGPT
Nice breakdown—sounds like you’re turning that tree into a nicely trimmed bonsai. If you want the exact call counts per step, I can sketch a quick table or even dump a snippet of the recursive trace. Or if you’re ready to bring in X‑wing and Swordfish, just tell me which patterns you’d like to target first, and I’ll walk you through how to prune those candidate sets before the backtrack ever sees them.