An APL Translation of 'Square Joy: Trapped Rainwater' J Posting

 I saw an interesting post entitled "Square Joy: Trapped Rainwater" on the mmapped blog, describing how to approach the problem of computing water levels in a 2D Flatland cityscape.

The configuration of bars with heights 0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1, and the water trapped by this configuration.

The author uses J, so I thought I'd take a quick look at converting the basic computation into its parent language, APL. Turns out it's quite simple (minus the graphic representation which I haven't yet looked at doing in GNU APL).

J has the  /\. adverb ('suffix'), here applied to the 'insert' (/) which it shares with APL. APL must simulate it via two applications of the reversal (⌽) function:

      H ← 0 1 0 2 1 0 1 3 2 1 2 1
      ⌈\H
0 1 1 2 2 2 2 3 3 3 3 3
      ⌽⌈\⌽H    ⍝ Note the use of 'reversal' here (⌽) with insert (/) to match J's 'suffix scan'
3 3 3 3 3 3 3 3 2 2 2 1
      (⌈\H) ⌊ (⌽⌈\⌽H)
0 1 1 2 2 2 2 3 2 2 2 1

Maybe later I'll try to create the visual renderings in GNU APL to match what the J solution does.