How can you solve Nonograms most quickly and efficiently?

Some of the recent algorithms come to the rescue for faster and more competent performance.

But before continuing, let us first understand a bit of the basic stuff:

**What Is A Nonogram?**

Nonogram, AKA cross numbers, Hanjie, Picross, and Griddlers, is a popular Japanese picture logic puzzle. It is a grid-based game with relatively simple rules. On top and left sides of the rows and columns are some numerical clues associated with each line. These numbers indicate the cells that are to be painted or crossed off. Multiple values mean that these are to be separated by at least one blank cell in between. It’s like decoding a grid to unleash the hidden mosaic.

Nonogram puzzles are either designed monochromatic or in multiple colors. Ones produced for human use contain only one unique solution and can be both easy and complicated. However, smaller or larger, multiple (valid) solution grids also exist, and those are super challenging. Below is an easy example of multiple solutions Nonogram problem where both answers are valid.

This is typically known as the NP-Complete problem, referring to problems in NP and NP-hard language.

**Nonogram Solving Algorithm**

So the most obvious approach to solving Nonograms is by considering each row and column separately with a line solver that uses **n x k sol** matrix. The

*solvedLine*stores the data about potential colors for any given cell. This way, the computer also doesn’t have to derive the info from the calculated

*sol*matrix. This can also be applied to lines containing known data about individual blocks.

Another technique uses a ** priority queue** data structure combined with the above line solver, where each element may have a priority associated with it. This way, high priority cells, especially longer ones, are addressed in the beginning. But this may soon become empty, and to further solve the puzzle, the

**will most likely reduce the search space by cutting the branches of the search tree, or else the performance may be dramatically degraded. This algorithm starts from the bottom, examining all the nodes moving up to the next level.**

*breadth-first search*Reaching a contradiction will stop the search and fill the opposite color. As the information is gained, the algorithm may revert to using the above line solver with the priority queue. If there’s no contradiction, assumptions are stored in the tree-based information structure, and the computer may backtrack upon hitting a contraction.

**Conclusion**

Such innovative algorithms are developed to compensate for the existing ones that fall short in producing answers for puzzles with multiple solutions. The above approaches can repeatedly scan through the possibilities rather than limiting to a specific cell and not capturing newer knowledge. Moreover, even experiments keep continuously happening to outperform previous generation solvers.

So we hope this information helps you!

Let us know if you have any more queries or suggestions – we’d love to hear from you!