From fb28cb4ed2d618c2bcf3a4a0cd2b5a550b245113 Mon Sep 17 00:00:00 2001
From: jleightcap <jack@leightcap.com>
Date: Mon, 21 Jun 2021 06:04:15 -0400
Subject: [PATCH] README

---
 README.md   | 125 ++++++++++++++++++++++++++++++++++++++++++++++++++++
 nono.prolog |   5 +--
 2 files changed, 126 insertions(+), 4 deletions(-)
 create mode 100644 README.md

diff --git a/README.md b/README.md
new file mode 100644
index 0000000..a657544
--- /dev/null
+++ b/README.md
@@ -0,0 +1,125 @@
+# 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,
+
+```bash
+$ 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.
+
+```prolog
+?- 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;
+
+```prolog
+?- 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|
++---+
+```
+
+```prolog
+?- 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|
+     +---+
+```
diff --git a/nono.prolog b/nono.prolog
index 3801a4e..8c9de07 100644
--- a/nono.prolog
+++ b/nono.prolog
@@ -15,8 +15,6 @@
  * along with this program.  If not, see <https://www.gnu.org/licenses/>.
  */
 
-% try this out: https://swish.swi-prolog.org/
-
 :- use_module(library(clpfd)). % just used for transpose/2
 
 % solve a given picross puzzle.
@@ -81,8 +79,7 @@ decode(N, E, X) :-
 % ?- add_encode(1, 1, [1, 2, 3], X).
 % X = [3, 3].
 add_encode(1, 1, [], X) :- X = [2].
-add_encode(0, 0, S, X) :- X = S.
-add_encode(0, 1, S, X) :- X = S.
+add_encode(0, _, S, X) :- X = S.
 add_encode(1, 0, S, X) :- X = [1|S].
 add_encode(1, 1, S, X) :-
     X = [A|R],
-- 
2.45.2