Same output (based on input) on each run:
Å1āÉI<.Da)
Port of @Somebody's Python answer.
Try it online or verify the first ten sizes.
Random valid output on each run:
1ÝIãIãʒ€ü2ü2εøOO4Ö≠}˜P}ʒD_‚ε©˜ƶ®gäΔ2Fø0δ.ø}2Fø€ü3}®*εεÅsyøÅs«à}}}˜Ùg<}P}Ω
Try it online. (Slightly modified ʒ...}Ω to .r.Δ... to speed it up, but unfortunately it'll still time out for \$n\geq4\$.)
Explanation:
Å1 # Push a list of the (implicit) input amount of 1s ā # Push a list in the range [1,length] (without popping) É # Check for each whether it's odd: [1,0,1,0,1,0,...] I< # Push the input-1 .D # Duplicate the [1,0,1,0,1,0,...]-list that many times a # Change the top list to a list of 0s instead with an is_letter check ) # Wrap all lists on the stack into a list # (after which this matrix is output implicitly as result)
Step 1: Create a list of all possible input by input matrices with 0s and 1s:
1Ý # Push pair [0,1] Iã # Take the cartesian power of the input to get all input-sized lists using # 0s and 1s Iã # And again, to get all possible matrices
Step 2: Filter this list of matrices to keep all where each overlapping 2x2 block contains at least one 1 and at least one 0:
ʒ # Filter this list of matrices by: €ü2ü2εø # Get all overlapping 2x2 blocks: € # Map over each row: ü2 # Get its overlapping pairs ü2 # Get the overlapping lists of lists of pairs ε # Map over each: ø # Zip/transpose; swapping rows/columns OO # Sum each inner 2x2 block 4Ö≠ # Check for each sum whether it's NOT divisible by 4 # (aka it's 1, 2, or 3, and NOT 0 or 4) } # Close the map ˜ # Flatten this matrix of 2x2 block sum checks P # Check that all are truthy by taking the product } # Close the filter
Step 3: Filter it again to keep those where all matrices where both the 1s and 0s form a single island:
ʒ # Filter this list of matrices again: D # Duplicate this matrix _ # Invert each 0s to 1 and vice-versa in the copy ‚ # Pair the two inverted matrices together ε # Map over this pair: © # Store the current matrix in variable `®` (without popping) ˜ # Flatten it to a single list ƶ # Multiply each value by its 1-based index ®gä # Convert it back to a matrix of size `®` Δ # Loop until the result no longer changes to flood-fill: 2Fø0δ.ø} # Add a border of 0s around the matrix: 2F } # Loop 2 times: ø # Zip/transpose; swapping rows/columns δ # Map over each row: 0 .ø # Add a leading/trailing 0 2Fø€ü3} # Convert it into overlapping 3x3 blocks: 2F } # Loop 2 times again: ø # Zip/transpose; swapping rows/columns € # Map over each inner list: ü3 # Convert it to a list of overlapping triplets ®* # Multiply each 3x3 block by the value in matrix `®` # (so the 0s remain 0s) εεÅsyøÅs«à # Get the largest value from the horizontal/vertical cross of each # 3x3 block: εε # Nested map over each 3x3 block: Ås # Pop and push its middle row y # Push the 3x3 block again ø # Zip/transpose; swapping rows/columns Ås # Pop and push its middle rows as well (the middle column) « # Merge the middle row and column together to a single list à # Pop and push its maximum }} # Close the nested maps } # Close the changes-loop ˜ # Flatten the flood-filled matrix Ù # Uniquify this list g< # Pop and push its length-1 # (only 1 is truthy in 05AB1E, so this checks if two islands remain) } # Close the map P # Check that both are truthy, for the regular and inverted matrix } # Close the filter Ω # Pop and push a random matrix from this filtered list # (which is output implicitly as result)
