Algorithm for solving Flow Free Game

Question

I recently started playing Flow Free Game.

Connect matching colors with pipe to creat

Answer 1

A few rules that lead to a sort of algorithm to solve levels in flow, based on the IOS vertions by Big Duck Games, this company seems to produce the canonical versions. The rest of this answer assumes no walls, bridges or warps.

Even if your uncannily good, the huge 15x18 square boards are a good example of how just going at it in ways that seem likely get you stuck just before the end over and over again and practically having to start again from scratch. This is probably to do with the already mentioned exponential time complexity in the general case. But this doesn’t mean that a simple stratergy isn’t overwhelmingly effective for most boards.

1. Blocks are never left empty, therefore orphaned blocks mean you’ve done something wrong.

2. Cardinally neighbouring cells of the same colour must be connected. This rules out 2x2 blocks of the same colour and on the hexagonal grid triangles of 3 neighbouring cells.

3. You can often make perminent progress by establishing that a color goes or is excluded from a certain square.

4. Due to points 1 and 2, on the hexagonal grid on boards that are hexagonal in shape a pipe going along an edge is usually stuck going along it all the way round to the exit, effectively moving the outer edge in and making the board smaller so the process can be repeated. It is predictable what sorts of neighbouring conditions guarantee and what sorts can break this cycle for both sorts of grid.

Most if not all 3rd party variants I’ve found lack 1 to 4, but given these restraints generating valid boards may be a difficult task.

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Answer:

Point 3 suggests a value be stored for each cell that is able to be either a colour, or a set of false/indeterminate values there being one for each colour.

A solver could repeatedly use points 1 and 2 along with the data stored for point 3 on small neighbourhoods of paths around the ends of pipes to increasingly set colours or set the indeterminate values to false.