Solving Nonograms (Picross)

Question

it\'s Friday afternoon, let\'s have a fun puzzle/algorithm problem to solve.

One of my favorite Nintendo DS games is Picross DS. The game is quite simple, it involves so

Answer 1

The real problem is whether anyone can come up with an algorithm that solves the said puzzle faster than a human? This is easy for relatively easy puzzles such as the reference one but if the puzzle grows most of the algorithms here will quickly slow down. Here is the puzzle I tried to solve. The problem is that the 4th row for example has 2220075 possible combinations I believe. If Charlie's algorithm temporarily accepts a wrong row for row 3, it will go through all these combinations for row 4. And this is not to mention the case where the algorithm contradicts itself on row 35 over a mistake it made on row 2.

My algorithm was similar to John's. It failed to run in x86 mode on my 64bit desktop. When I switched it to 64bit mode and let it run overnight, my computer was completely unusable in the morning. The process was reserving 8 Gigs of memory (8 Gigs physical on the desktop) and the computer wouldn't respond due to the frantic swapping. And it hadn't even solved all the possible rows. Not to mention it hadn't even touched the possible column combinations.

List> rows =
                new List>()
                {
                    new List { 8,29,4 },
                    new List { 6,4,25,4,3 },
                    new List { 5,3,2,3,9,4,2,1,3 },
                    new List { 4,2,2,2,2,1,2,2 },
                    new List { 4,1,1,9,10,2,2,1 },
                    new List { 3,2,6,5,5,1,1 },
                    new List { 3,1,5,5,1,1 },
                    new List { 3,1,4,4,1,1 },
                    new List { 3,1,4,4,1,1 },
                    new List { 3,1,3,3,1,1 },
                    new List { 3,1,3,6,2 },
                    new List { 3,1,2,3,2,4,2 },
                    new List { 4,3,1,8,7,1,2,3 },
                    new List { 4,2,1,12,11,1,2,4 },
                    new List { 5,1,2,7,2,2,6,1,1,4 },
                    new List { 4,1,1,1,6,2,2,6,1,2,1,3 },
                    new List { 4,1,1,2,4,3,4,3,1,1,1,1,3 },
                    new List { 4,1,1,2,1,4,1,2,3,2,1,2,2 },
                    new List { 3,1,1,1,2,5,6,1,1,1,3,2 },
                    new List { 3,2,1,1,2,1,5,4,4,2,1,2,1,2 },
                    new List { 3,2,2,1,1,4,2,2,3,1,1,2,1,1,2 },
                    new List { 3,1,3,2,1,1,4,1,5,3,2,1,3,1,2 },
                    new List { 3,1,2,1,2,1,3,7,4,1,4,2,2 },
                    new List { 2,1,4,1,1,1,2,6,2,2,2,3,2,1 },
                    new List { 2,2,4,1,2,1,2,5,2,1,1,3,2,1 },
                    new List { 2,2,1,4,1,1,3,3,2,1,4,4,1 },
                    new List { 2,3,3,2,1,3,3,7,4,1 },
                    new List { 2,3,2,4,5,8,1,2,1 },
                    new List { 1,1,3,11,6,7,1,3,1 },
                    new List { 1,1,2,2,13,10,2,3,2 },
                    new List { 1,2,3,1,6,1,1,7,1,5,2 },
                    new List { 1,1,3,2,6,1,1,1,1,4,1,4,2 },
                    new List { 1,1,6,7,2,4,2,5,6,1 },
                    new List { 1,1,2,3,1,4,2,2,11,2,1 },
                    new List { 1,1,1,1,2,1,5,10,1,1,1 },
                    new List { 1,1,1,1,4,7,4,10,1,1,1 },
                    new List { 1,2,1,1,28,1,1,3 },
                    new List { 1,2,1,2,27,2,1,3 },
                    new List { 1,1,1,1,26,1,1,1,1 },
                    new List { 2,3,1,28,2,1,2,1 }
                };
            List> cols =
                new List>()
                {
                    new List { 40 },
                    new List { 28,1 },
                    new List { 23,8 },
                    new List { 5,6,7,4 },
                    new List { 3,6,1,9,3,1 },
                    new List { 2,3,2,5,4,2,2 },
                    new List { 1,2,4,1,2,5,2 },
                    new List { 1,1,4,9,2,3,2 },
                    new List { 2,4,2,6,1,4,3 },
                    new List { 1,4,1,3,4,1,6 },
                    new List { 1,4,3,2,3,5,5 },
                    new List { 2,4,1,2,3,4,1,3 },
                    new List { 1,2,3,4,2,2,4,4,1 },
                    new List { 1,1,2,3,2,1,4,2,4 },
                    new List { 2,3,5,3,3,5,4 },
                    new List { 3,1,6,1,2,5,5 },
                    new List { 3,2,6,2,15 },
                    new List { 3,1,8,2,13 },
                    new List { 2,2,4,5,15 },
                    new List { 2,2,2,2,22 },
                    new List { 2,1,1,1,12,6 },
                    new List { 2,1,10,4,5 },
                    new List { 3,1,3,1,2,4 },
                    new List { 3,1,1,4,3,1,4 },
                    new List { 3,2,2,3,2,2,5 },
                    new List { 3,1,1,5,1,1,5 },
                    new List { 3,1,1,5,1,1,5 },
                    new List { 3,1,1,5,1,1,5 },
                    new List { 3,2,5,2,1,1,4 },
                    new List { 3,1,1,3,2,2,4 },
                    new List { 3,1,6,4,5 },
                    new List { 2,2,12,2,6 },
                    new List { 2,2,1,1,22 },
                    new List { 2,1,2,2,5,15 },
                    new List { 3,1,4,3,2,14 },
                    new List { 3,1,7,2,1,13 },
                    new List { 3,2,6,1,1,6,8 },
                    new List { 3,2,5,2,2,4,7 },
                    new List { 2,1,2,4,1,1,1,4,1,4,2 },
                    new List { 1,1,4,4,3,1,4,5,1 },
                    new List { 1,1,5,1,1,2,1,2,2,3,2 },
                    new List { 1,5,2,2,1,5,5,3 },
                    new List { 1,6,2,1,4,2,6,1 },
                    new List { 1,6,2,6,5,2 },
                    new List { 1,5,3,1,9,2 },
                    new List { 2,2,4,2,6,3 },
                    new List { 1,2,2,2,9,2,1 },
                    new List { 3,5,5,8,4 },
                    new List { 4,13,9 },
                    new List { 27,2 }
                };

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