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

Rather than trying to place the "first" row, it will cut down on your search substantially if you try to get information from the "most constrained" row or column, which may have several forced values. A quick indication is to add up all the values in a row/column and add #_of_values - 1, then look for the row/column with the biggest such value (or smallest difference between this value and the # of rows or columns, if the rows and columns differ). Thus if you have a 25x25 puzzle, and one of the rows is "5 1 1 6 1 1 3", that row has a value of 24, which means it is very constrained - the relative position of all but one of the blank squares in that row is known, and the last blank square can be in any of 8 different relative positions. So for each group of filled squares, there are only two possibilities: extra blank square is to the left of this group, or extra blank square is to the right of this group. So, for example, five of the filled squares in that group of 6 are already known.

Once you have some forced values from one direction, that further constrains any of the groups from the other direction that intersect with the known information. So the best approach is likely to be working back and forth between columns and rows as more information becomes known, which is pretty much the way you need to solve it by hand.