Water collected between towers: Difference between revisions

Or, using Data.List for simplicity, and adding diagrams:

<lang haskell>import Data.List (replicate, transpose)

towerPools :: [Int] -> [(Int, Int)]

towerPools xs =

zip

xs

((zipWith (-) =<< -- Where coverages are differences between:

(zipWith min . -- the lower water level in each case of:

scanl1 max <*> -- highest wall to left, and

scanr1 max)) -- highest wall to right.

xs)

main :: IO ()

main =

mapM_

(putStrLn . (((++) . showTowers <*> (('\n' :) . showLegend)) . towerPools))

[ [1, 5, 3, 7, 2]

, [5, 3, 7, 2, 6, 4, 5, 9, 1, 2]

, [2, 6, 3, 5, 2, 8, 1, 4, 2, 2, 5, 3, 5, 7, 4, 1]

, [5, 5, 5, 5]

, [5, 6, 7, 8]

, [8, 7, 7, 6]

, [6, 7, 10, 7, 6]

]

showTowers :: [(Int, Int)] -> String

showTowers xs =

let upper = maximum (fst <$> xs)

in '\n' :

(unlines .

transpose .

fmap

(\(x, d) ->

concat $

replicate (upper - (x + d)) " " ++

replicate d "x" ++ replicate x "█"))

xs

showLegend :: [(Int, Int)] -> String

showLegend =

((++) . show . fmap fst) <*> ((" -> " ++) . show . foldr ((+) . snd) 0)</lang>

{{Out}}

<pre>

█

█

█x█

█x█

███

████

█████

[1,5,3,7,2] -> 2

█

█

█xxxx█

█x█xx█

█x█x█x██

█x█x████

███x████

████████x█

██████████

[5,3,7,2,6,4,5,9,1,2] -> 14

█

█xxxxxxx█

█xxx█xxxxxxx█

█x█x█xxxx█x██

█x█x█x█xx█x███

███x█x█xx█████

██████x████████

████████████████

[2,6,3,5,2,8,1,4,2,2,5,3,5,7,4,1] -> 35

████

████

████

████

████

[5,5,5,5] -> 0

█

██

███

████

████

████

████

████

[5,6,7,8] -> 0

█

███

████

████

████

████

████

████

[8,7,7,6] -> 0

█

█

█

███

█████

█████

█████

█████

█████

█████

[6,7,10,7,6] -> 0</pre>