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Diffstat (limited to 'math/py-z3-solver/files/example-sudoku.py')
-rw-r--r-- | math/py-z3-solver/files/example-sudoku.py | 53 |
1 files changed, 53 insertions, 0 deletions
diff --git a/math/py-z3-solver/files/example-sudoku.py b/math/py-z3-solver/files/example-sudoku.py new file mode 100644 index 000000000000..e0a19b17bf6f --- /dev/null +++ b/math/py-z3-solver/files/example-sudoku.py @@ -0,0 +1,53 @@ +# example from https://ericpony.github.io/z3py-tutorial/guide-examples.htm + +from z3 import Int, And, Distinct, If, Solver, sat, print_matrix + + +# 9x9 matrix of integer variables +X = [ [ Int("x_%s_%s" % (i+1, j+1)) for j in range(9) ] + for i in range(9) ] + +# each cell contains a value in {1, ..., 9} +cells_c = [ And(1 <= X[i][j], X[i][j] <= 9) + for i in range(9) for j in range(9) ] + +# each row contains a digit at most once +rows_c = [ Distinct(X[i]) for i in range(9) ] + +# each column contains a digit at most once +cols_c = [ Distinct([ X[i][j] for i in range(9) ]) + for j in range(9) ] + +# each 3x3 square contains a digit at most once +sq_c = [ Distinct([ X[3*i0 + i][3*j0 + j] + for i in range(3) for j in range(3) ]) + for i0 in range(3) for j0 in range(3) ] + +sudoku_c = cells_c + rows_c + cols_c + sq_c + +# sudoku instance, we use '0' for empty cells +instance = ((0,0,0,0,9,4,0,3,0), + (0,0,0,5,1,0,0,0,7), + (0,8,9,0,0,0,0,4,0), + (0,0,0,0,0,0,2,0,8), + (0,6,0,2,0,1,0,5,0), + (1,0,2,0,0,0,0,0,0), + (0,7,0,0,0,0,5,2,0), + (9,0,0,0,6,5,0,0,0), + (0,4,0,9,7,0,0,0,0)) + +instance_c = [ If(instance[i][j] == 0, + True, + X[i][j] == instance[i][j]) + for i in range(9) for j in range(9) ] + +s = Solver() +s.add(sudoku_c + instance_c) +if s.check() == sat: + m = s.model() + r = [ [ m.evaluate(X[i][j]) for j in range(9) ] + for i in range(9) ] + print_matrix(r) +else: + print ("failed to solve") + |