Problem 56478. IQpuzzler Preparation #3: Detect isolated groups of zeros in a matrix
Return true if any small, rectangular shaped, isolated groups of zeros (size 1x1, 1x2, 2x1, 1x3, 3x1 or 2x2) are present in a matrix, with all vertically and horizontally adjacent elements being non-zero.
The matrix will always be 3-by-3 or larger.
Examples:
11 2 3 2 9 10 10 11 6 7 4
12 4 13 6 1 10 1 10 5 6 9
2 8 13 12 0 0 0 5 10 9 9
12 13 7 11 13 9 1 13 11 10 3
9 13 11 13 9 3 2 1 3 10 2
==> true
11 2 3 2 9 10 10 11 6 7 4
12 4 13 6 1 10 1 10 5 6 9
2 8 13 12 0 0 0 1 10 9 9
12 13 7 11 13 0 1 13 11 10 3
9 13 11 13 9 3 2 1 3 10 2
==> false
7 10 13 11 5 5 4 1 2 3 8
13 0 8 4 3 11 10 1 8 11 4
5 0 2 11 4 8 10 7 7 5 9
8 0 2 4 9 8 5 11 1 7 9
3 12 4 13 7 12 8 13 5 3 10
==> true
Background:
This function or variations of it may be useful in some board games like Go, or in the upcoming IQpuzzler challenge.
Hint:
The built-in function conv2 may be helpful for your implementation.
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