feat: added trapping rain water.

src/bqn/rollim.bqn

@@ -58,3 +58,5 @@ HS ← +´∨≥1+⊒˜
 (HL≡HS)◶@‿HL 14‿14‿11‿9‿5‿5‿1‿1‿1‿1‿0
 
 HL‿HS {𝕎•_timed𝕩}¨< 1e8 •rand.Range 1e3
+
+(+´⊢-˜⌈`⌾⌽⌊⌈`) [0,1,0,2,1,0,1,3,2,1,2,1]

src/rollim.org

@@ -272,6 +272,22 @@ If someone ever published that much, sorting will eventually be slower:
 A testament to the idea that the simplest solution in BQN is often the most efficient:
 I initially clip my citations array with ={≠¨⊔≠∘𝕩¨⌾(≥⟜≠∘𝕩⊸/)𝕩}=, which is just =/⁼≠⊸⌊=.
 
+** Trapping rain water
+
+This problem is a classic in the realm of algorithms, and it can be solved in linear time. Interestingly,
+it admits a very elegant array solution as well:
+
+#+begin_src bqn :tangle ./bqn/rollim.bqn :exports both
+  (+´⊢-˜⌈`⌾⌽⌊⌈`) [0,1,0,2,1,0,1,3,2,1,2,1]
+#+end_src
+
+#+RESULTS:
+: 6
+
+That is, we do a max scan from the left and from the right, and then take the minimum of the two,
+then we subtract the height of the building at that point. The sum of all these values is the answer.
+A closely related problem is [[https://leetcode.com/problems/container-with-most-water/][container with most water]], which can be solved:
+
 [fn:1] Almost Perfect Artifacts Improve only in Small Ways: APL is more French than English,
 Alan J. Perlis (1978). From [[https://www.jsoftware.com/papers/perlis78.htm][jsoftware]]'s papers collection.
 [fn:2] Initially, I intended to rigorously attribute all contributions, but this