allgebrist / sudoku-solver

SAT-based Sudoku Solver

SAT-based Sudoku Solver

A rewrite of a side project: https://github.com/rkkautsar/sudoku-solver-nim

Description

A general n × n Sudoku solver that works by encoding the constraints to SAT and use SAT solver to solve it.

Featuring:

• accepts n × n sudoku input (either multiline or one line for 9x9 sudoku)
• can print out the CNF encoding only
• has built-in SAT solver (gini) or can use custom SAT solver
• bimander encoding for at-most-one
• parallel CNF encoding
• fast, but not as fast as specialized solvers (0.6ms for ai-escargot, naïve backtracking is around 30ms)
• pretty fast for larger sudokus, for example a 144x144 sudoku can be solved in 4s
• pretty simple code

Benchmarks

About 5.8s (8474 puzzle/s or 118 ns/puzzle) to solve the benchmark of 49k 17-clue 9x9 sudoku from here: https://codegolf.stackexchange.com/questions/190727/the-fastest-sudoku-solver

Fastest on this benchmark is tdoku which took 0.2s to complete 🚀. Other SAT-based solver with minisat took 11.7s.

Other benchmarks available in make bench:

↳ make bench
if ! command -v cadical &> /dev/null; then echo "[!] Please install cadical first: $(tput bold)brew install cadical$(tput sgr0)"; exit 1; fi
go test -run=XXX -benchmem -bench=. ./sudokusolver
goos: darwin
goarch: arm64
pkg: github.com/rkkautsar/sudoku-solver/sudokusolver
BenchmarkSolveAiEscargot-10               	    1911	    647132 ns/op	  369585 B/op	    2929 allocs/op
BenchmarkSolveHard9x9-10                  	    2706	    431285 ns/op	  396274 B/op	    3352 allocs/op
BenchmarkSolve17clue9x9-10                	   28108	     47913 ns/op	  107654 B/op	     634 allocs/op
BenchmarkSolve25x25-10                    	     262	   4780719 ns/op	 5455202 B/op	   43100 allocs/op
BenchmarkSolve64x64-10                    	       4	 332938156 ns/op	33512906 B/op	  206324 allocs/op
BenchmarkSolve81x81-10                    	       5	 213718425 ns/op	101065350 B/op	  771714 allocs/op
BenchmarkSolve100x100-10                  	      18	  63925764 ns/op	71169493 B/op	  340853 allocs/op
BenchmarkSolve144x144-10                  	       5	 249753067 ns/op	111240065 B/op	  158053 allocs/op
BenchmarkSolve225x225-10                  	       3	 415970389 ns/op	444639680 B/op	  393479 allocs/op
BenchmarkSolveWithCadicalAiEscargot-10    	     322	   3993171 ns/op	  344782 B/op	    5535 allocs/op
BenchmarkSolveWithCadicalHard9x9-10       	     381	   3329669 ns/op	  444484 B/op	    6674 allocs/op
BenchmarkSolveWithCadicalHard17clue-10    	     598	   2121930 ns/op	  127355 B/op	     720 allocs/op
BenchmarkSolveWithCadical25x25-10         	     100	  12874129 ns/op	 5965580 B/op	  101945 allocs/op
BenchmarkSolveWithCadical64x64-10         	       2	 682339458 ns/op	29716664 B/op	  474691 allocs/op
BenchmarkSolveWithCadical81x81-10         	       4	 321655042 ns/op	110022726 B/op	 1865605 allocs/op
BenchmarkSolveWithCadical100x100-10       	       8	 126807734 ns/op	74976945 B/op	  779323 allocs/op
BenchmarkSolveWithCadical144x144-10       	       4	 256900156 ns/op	111567778 B/op	  181708 allocs/op
BenchmarkSolveWithCadical225x225-10       	       2	 504154167 ns/op	445448628 B/op	  452004 allocs/op
BenchmarkSolveManyHardest110626-10        	       4	 327428104 ns/op	149366518 B/op	 1302273 allocs/op
BenchmarkSolveMany17Clue2k-10             	       5	 236078600 ns/op	365466395 B/op	 2980678 allocs/op
BenchmarkSolveMany17Clue-10               	       1	5851515333 ns/op	8961331456 B/op	73508710 allocs/op
PASS
ok  	github.com/rkkautsar/sudoku-solver/sudokusolver	45.391s

Getting Started

Dependencies

• Go

Installing

From gobinaries

curl -sf https://gobinaries.com/rkkautsar/sudoku-solver/cmd/sudokusolver | sh

From source

go get github.com/rkkautsar/sudoku-solver/cmd/sudokusolver

Executing program

sudokusolver -help
sudokusolver -cnf < data/sudoku-9-1.txt
sudokusolver -solve < data/sudoku-9-1.txt
sudokusolver -solve -many < data/sudoku.many.17clue.txt

# brew install cadical
sudokusolver -solver "cadical -q" < data/sudoku-9-1.txt

License

This project is licensed under the MIT License - see the LICENSE.md file for details

Acknowledgments

Inspiration, code snippets, etc.

• gini
• tdoku
• Kwon, Gihwon, and Himanshu Jain. "Optimized CNF encoding for sudoku puzzles." Proc. 13th International Conference on Logic for Programming Artificial Intelligence and Reasoning (LPAR2006). 2006. (PDF)
• Klieber, Will, and Gihwon Kwon. "Efficient CNF encoding for selecting 1 from n objects." Proc. International Workshop on Constraints in Formal Verification. 2007. (PDF)
• Nguyen, Van-Hau, and Son T. Mai. "A new method to encode the at-most-one constraint into SAT." Proceedings of the Sixth International Symposium on Information and Communication Technology. 2015. (PDF)