Problem Statement

In a two-dimensional world, we begin with any bar-chart (or row of close-packed 'towers', each of unit width), and then it rains, completely filling all convex enclosures in the chart with water.

In the example above, a bar chart representing the values [5, 3, 7, 2, 6, 4, 5, 9, 1, 2] has filled, collecting 14 units of water. Write a function, in your language, from a given array of heights, to the number of water units that can be held in this way, by a corresponding bar chart. Calculate the number of water units that could be collected by bar charts representing each of the following seven series:

See, also:

Let's start with the solution:

(de water (Lst)
   (sum
      '((A)
         (cnt
            nT
            (clip (mapcar '((B) (>= B A)) Lst)) ) )
      (range 1 (apply max Lst)) ) )
(println
   (mapcar
      water
      (quote
         (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) ) ) )