Algorithm for solving Flow Free Game

Question

I recently started playing Flow Free Game.

Connect matching colors with pipe to creat

Answer 1

I found a blog post on Needlessly Complex that completely explains how to use SAT to solve this problem.

The code is open-source as well, so you can look at it (and understand it) in action.

I'll provide a quote from it here that describes the rules you need to implement in SAT:

• Every cell is assigned a single color.

• The color of every endpoint cell is known and specified.

• Every endpoint cell has exactly one neighbor which matches its color.
• The flow through every non-endpoint cell matches exactly one of the six direction types.
• The neighbors of a cell specified by its direction type must match its color.
• The neighbors of a cell not specified by its direction type must not match its color.

Thank you @Matt Zucker for creating this!