- Documentation
- Reference manual
- The SWI-Prolog library
- library(clpfd): CLP(FD): Constraint Logic Programming over Finite Domains
- Introduction
- Arithmetic constraints
- Declarative integer arithmetic
- Example: Factorial relation
- Combinatorial constraints
- Domains
- Example: Sudoku
- Residual goals
- Core relations and search
- Example: Eight queens puzzle
- Optimisation
- Reification
- Enabling monotonic CLP(FD)
- Custom constraints
- Applications
- Acknowledgments
- CLP(FD) predicate index
- Closing and opening words about CLP(FD)
- library(clpfd): CLP(FD): Constraint Logic Programming over Finite Domains
- The SWI-Prolog library
- Packages
- Reference manual
A.8.7 Example: Sudoku
As another example, consider Sudoku: It is a popular puzzle over integers that can be easily solved with CLP(FD) constraints.
sudoku(Rows) :- length(Rows, 9), maplist(same_length(Rows), Rows), append(Rows, Vs), Vs ins 1..9, maplist(all_distinct, Rows), transpose(Rows, Columns), maplist(all_distinct, Columns), Rows = [As,Bs,Cs,Ds,Es,Fs,Gs,Hs,Is], blocks(As, Bs, Cs), blocks(Ds, Es, Fs), blocks(Gs, Hs, Is). blocks([], [], []). blocks([N1,N2,N3|Ns1], [N4,N5,N6|Ns2], [N7,N8,N9|Ns3]) :- all_distinct([N1,N2,N3,N4,N5,N6,N7,N8,N9]), blocks(Ns1, Ns2, Ns3). problem(1, [[_,_,_,_,_,_,_,_,_], [_,_,_,_,_,3,_,8,5], [_,_,1,_,2,_,_,_,_], [_,_,_,5,_,7,_,_,_], [_,_,4,_,_,_,1,_,_], [_,9,_,_,_,_,_,_,_], [5,_,_,_,_,_,_,7,3], [_,_,2,_,1,_,_,_,_], [_,_,_,_,4,_,_,_,9]]).
Sample query:
?- problem(1, Rows), sudoku(Rows), maplist(writeln, Rows). [9,8,7,6,5,4,3,2,1] [2,4,6,1,7,3,9,8,5] [3,5,1,9,2,8,7,4,6] [1,2,8,5,3,7,6,9,4] [6,3,4,8,9,2,1,5,7] [7,9,5,4,6,1,8,3,2] [5,1,9,2,8,6,4,7,3] [4,7,2,3,1,9,5,6,8] [8,6,3,7,4,5,2,1,9] Rows = [[9, 8, 7, 6, 5, 4, 3, 2|...], ... , [...|...]].
In this concrete case, the constraint solver is strong enough to find the unique solution without any search.