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→Finding maxima
| Line 161: | Line 161: | ||
8 11 11 8 | 8 11 11 8 | ||
</source> | </source> | ||
But obviously, we can't let the circles touch, so we add 1. | But obviously, we can't let the circles touch, so we add 1. This gives us all the centre-to-centre distances from the neighbours on the left (or above): | ||
<source lang=apl> | |||
1+⌈⌿2+/sizes | |||
9 12 12 9 | |||
</source> | |||
We also need an "offset" of the left/top-most circles which don't have any neighbours, so we prepend a 0: | |||
<source lang=apl> | |||
0,1+⌈⌿2+/sizes | |||
0 9 21 33 42 | |||
</source> | |||
Finally, we compute the total offset for each column/row by finding the running total of the offsets: | |||
<source lang=apl> | <source lang=apl> | ||
⊢offsets←0,+\1+⌈⌿2+/sizes | ⊢offsets←0,+\1+⌈⌿2+/sizes | ||
0 9 21 33 42 | 0 9 21 33 42 | ||
</source> | </source> | ||
<source lang=apl inline>⊢</source> is the [[identity]] function, which is just used here get the pass-though value from the assignment, as it would otherwise be hidden. (We call assignment ''shy''.) | <source lang=apl inline>⊢</source> is the [[identity]] function, which is just used here get the pass-though value from the assignment, as it would otherwise be hidden. (We call assignment ''shy''.) <source lang=apl inline>\</source> is just like <source lang=apl inline>/</source> but gives us the intermediate values. | ||
=== Generating indices in 2D === | === Generating indices in 2D === | ||
<source lang=apl inline>⍴r</source> is the [[shape]] of our array of radii. Now, you remember <source lang=apl inline>⍳</source>, [[#Generating_indices|right]]? As it turns out, it can actually generate of an array of any number of dimensions; two in our case: | <source lang=apl inline>⍴r</source> is the [[shape]] of our array of radii. Now, you remember <source lang=apl inline>⍳</source>, [[#Generating_indices|right]]? As it turns out, it can actually generate of an array of any number of dimensions; two in our case: | ||