#nonolog

solve nonogram/picross puzzles, that are:

• square: same number of rows are columns (duh)
• monochromatic: only single colored, boolean states
• and nothing fancier

#usage, examples

start up a prolog repl and load definitions,

$ swipl
?- [nono].
true.

to solve the example puzzle

     11 3
     22112
    +-----+
  2 |     |
2 2 |     |
  1 |     |
  3 |     |
2 1 |     |
    +-----+

picross/4 takes an array of row restrictions, array of column restrictions, the size, and corresponding matrix.

?- picross([[2], [2, 2], [1], [3], [2, 1]], [[1, 2], [1, 2], [1], [3, 1], [2]], 5, X).
00011
11011
00010
11100
11010
X = [[0, 0, 0, 1, 1], [1, 1, 0, 1, 1], [0, 0, 0, 1, 0], [1, 1, 1, 0, 0], [1, 1, 0, 1|...]] .

this is the expected solution,

     11 3
     22112
    +-----+
  2 |   XX|
2 2 |XX XX|
  1 |   X |
  3 |XXX  |
2 1 |XX X |
    +-----+

with under-constrained inputs, this detects all possible solutions, so for a less constrained input:

   221
  +---+
1 |   |
2 |   |
2 |   |
  +---+

two solutions are found;

?- picross([[1], [2], [2]], [[2], [2], [1]], 3, X).
100
110
011
X = [[1, 0, 0], [1, 1, 0], [0, 1, 1]] ;
001
110
110
X = [[0, 0, 1], [1, 1, 0], [1, 1, 0]] ;

corresponding to both valid outputs,

   221       221
  +---+     +---+
1 |X  |   1 |  X|
2 |XX |   2 |XX |
2 | XX|   2 |XX |
  +---+     +---+

and because this is constraint-based prolog, this works in the opposite direction. if we wanted to generate the constraints to generate the puzzle

+---+
|XXX|
| X |
|X X|
+---+

?- picross(X, Y, 3, [[1, 1, 1], [0, 1, 0], [1, 0, 1]]).
111
010
101
X = [[3], [1], [1, 1]],
Y = [[1, 1], [2], [1, 1]] ;

which are the constraints;

      1 1
      121
     +---+
   3 |XXX|
   1 | X |
 1 1 |X X|
     +---+