I'm trying to do leet puzzle https://leetcode.com/problems/max-area-of-island/, requiring labelling connected (by sides, not corners) components.
How can I transform something like
0 0 1 0 0
0 0 0 0 0
0 1 1 0 1
0 1 0 0 1
0 1 0 0 1
into
0 0 1 0 0
0 0 0 0 0
0 2 2 0 3
0 2 0 0 3
0 2 0 0 3
I've played with the stencil ⌺
operator and also tried using scan operators but still not quite there. Can somebody help?
We can start off by enumerating the ones. We do the by applying the function ⍸
(where, but since all are 1s, it is equivalent to 1,2,3,…) @
at the subset masked by ⊢
the bits themselves, i.e. ⍸@⊢
:
⍸@⊢m
0 0 1 0 0
0 0 0 0 0
0 2 3 0 4
0 5 0 0 6
0 7 0 0 8
Now we need to flood-fill the lowest number in each component. We do this with repeated application until the fix-point ⍣≡
of processing Moore neighbourhoods ⌺3 3
. To get the von Neumann neighbours, we reshape the 9 elements in the Moore neighbourhood into a 4-row 2-column matrix with 4 2⍴
and use ⊢/
to select the right column. We remove any 0s with 0~⍨
them prepend ,
the original value ⍵[2;2]
(even if 0) and have ⌊/
select the smallest value:
{⌊/⍵[2;2],0~⍨⊢/4 2⍴⍵}⌺3 3⍣≡⍸@⊢m
0 0 1 0 0
0 0 0 0 0
0 2 2 0 4
0 2 0 0 4
0 2 0 0 4
We map the values to indices by finding their ⊢
indices ⍳⍨
in the unique elements of ∘∪
0 followed by ,
the ravelled matrix ,
:
(⊢⍳⍨∘∪0,,){⌊/⍵[2;2],0~⍨⊢/4 2⍴⍵}⌺3 3⍣≡⍸@⊢m
1 1 2 1 1
1 1 1 1 1
1 3 3 1 4
1 3 1 1 4
1 3 1 1 4
And decrement which adjusts back to begin with zero:
¯1+(⊢⍳⍨∘∪0,,){⌊/⍵[2;2],0~⍨⊢/4 2⍴⍵}⌺3 3⍣≡⍸@⊢m
0 0 1 0 0
0 0 0 0 0
0 2 2 0 3
0 2 0 0 3
0 2 0 0 3