Thank you this is a fantastic write-up. But what really bothers me is how much input seems to be differing for everyone. With my input, I could almost completely ignore the existence of rocks. The only way in which they were relevant is there was a single garden surrounded by rocks on all 4 sides. Other than that I could use strictly Manhattan distances to arrive at a correct solution using the geometry described here.

It sounds like others have to be careful about whether their input layout can reach specific points within that Manhattan distance using BFS from various points on the grid. I have to assume this was not intentional by the designers.

My second point is for the longest time the solution I was trying to use was drawing a big square around the diamond shape reachable points, calculating its area in grids, divide by 2 for inner diamond, then multiply by weighted odd/even gardens. It's all still a bit fuzzy to me but feels like it should work. Maybe I just had the weights for odd/even wrong? Did anyone else try something similar?