There is no need to test all cases. The ideal case is a swiss cheese in which no guest share a wall. Just start filling rooms from there if needed (the only problems is that room filling must follow an order, which makes the code quite large (but repetitive and boring), and there are two base cases for the swiss cheese structure). Maybe it's possible to create a function and decrease code size, but unless you see it at the moment that you are coding it, it would mean loosing too much time during competition when a Ctrl+C, Ctrl+V would be faster (and better than testing all cases).
Currently, my solutions and this one are the only that don't use brute force, but this one is the smallest. Congrats. :) (I was able to create a smaller solution after looking at your code.)
Getting the indices from a vector
Duplicate a character
Dots in a Sphere
Extract Built In Functions and Toolbox Functions from String or Function Handle
PACMAT - G03 Ghosts use minimum path to PACMAT; 3 Lives
Knots Contest: Score (TestSuite)
GJam 2014 Rd 1c: Reordering Train Cars (Large)
Rubik's Cube: Solve Randomized Cube - Score : Moves
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