Outputs 1 if the matrix contains mountain ranges, 0 otherwise.
How it works
I may be able to shorten the code a bit, so this section will probably undergo heavy editing.
The helper link
,Z.ịḊṖ$€Ɗ€ – Helper link. Let S be the input matrix.
,Z – Pair S with its transpose.
Ɗ€ – For each matrix (S and Sᵀ), Apply the previous 3 links as a monad.
.ị – Element at index 0.5; In Jelly, the ị atom returns the elements at
indices floor(x) and ceil(x) for non-integer x, and therefore this
returns the 0th and 1st elements. As Jelly is 1-indexed, this is the
same as retrieving the first and last elements in a list.
ḊṖ$€ – And for each list, remove the first and last elements.
For example, given a matrix in the form:
A(1,1) A(1,2) A(1,3) ... A(1,n)
A(2,1) A(2,2) A(2,3) ... A(2,n)
A(3,1) A(3,2) A(3,3) ... A(3,n)
...
A(m,1) A(m,2) A(m,3) ... A(m,n)
This returns the arrays (the order doesn't matter):
A(1,2), A(1,3), ..., A(1,n-1)
A(m,2), A(m,3), ..., A(m,n-1)
A(2,1), A(3,1), ..., A(m-1,1)
A(2,n), A(3,n), ..., A(m-1,n)
Long story short, this generates the outermost rows and columns, with the corners removed.
The main link
Ẇ€Z$⁺Ẏµ,ZẈ>2ẠµƇµḊṖZƊ⁺FṀ<ÇȦ)Ṁ – Main link. Let M be the input matrix.
Ẇ€ – For each row of M, get all its sublists.
Z$ – Transpose and group into a single link with the above.
⁺ – Do twice. So far, we have all contiguous sub-matrices.
Ẏ – Flatten by 1 level.
µ µƇ – Filter-keep those that are at least 3 by 3:
,Z – Pair each sub-matrix S with Sᵀ.
Ẉ – Get the length of each (no. rows, no. columns).
>2 – Element-wise, check if it's greater than 2.
Ạ – All.
µ ) – Map over each sub-matrix S that's at least 3 by 3
ḊṖ – Remove the first and last elements.
ZƊ – Zip and group the last 3 atoms as a single monad.
⁺ – Do twice (generates the inner cells).
FṀ – Flatten, and get the maximum.
<Ç – Element-wise, check if the results of the helper
link are greater than those in this list.
Ȧ – Any and all. 0 if it is empty, or contains a falsey
value when flattened, else 1.
Ṁ – Maximum.
