Water collected between towers: Difference between revisions
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Write a function, in your language, from a given array of heights, to the number of water units that would be collected in this way, by a corresponding bar chart. |
Write a function, in your language, from a given array of heights, to the number of water units that would be collected in this way, by a corresponding bar chart. |
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Display test results for water collected by bar charts for the following 6 series of values: |
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[ [1, 5, 3, 7, 2], |
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[5, 3, 7, 2, 6, 4, 5, 9, 1, 2], |
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[5, 5, 5, 5], |
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[5, 6, 7, 8], |
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[8, 7, 7, 6], |
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[6, 7, 10, 7, 6]] |
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=={{header|Haskell}}== |
=={{header|Haskell}}== |
Revision as of 18:34, 6 December 2016
- Task
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, filling any convex enclosures in the chart with water.
9 ██ 9 ██ 8 ██ 8 ██ 7 ██ ██ 7 ██░░░░░░░░██ 6 ██ ██ ██ 6 ██░░██░░░░██ 5 ██ ██ ██ ████ 5 ██░░██░░██░░████ 4 ██ ██ ████████ 4 ██░░██░░████████ 3 ██████ ████████ 3 ██████░░████████ 2 ████████████████ ██ 2 ████████████████░░██ 1 ████████████████████ 1 ████████████████████
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 would be collected in this way, by a corresponding bar chart.
Display test results for water collected by bar charts for the following 6 series of values:
[ [1, 5, 3, 7, 2],
[5, 3, 7, 2, 6, 4, 5, 9, 1, 2], [5, 5, 5, 5], [5, 6, 7, 8], [8, 7, 7, 6], [6, 7, 10, 7, 6]]
(See, for example, Water collected between towers on Stack Overflow, from which the example above is taken).
Haskell
Following cdk's Haskell solution at Stack Overflow:
<lang haskell>waterCollected :: [Int] -> Int waterCollected xs =
-- water collects only in flanked concavities -- (i.e. where there is a gap between the high tide mark -- and the sea bed beneath) sum (filter (> 0) (zipWith (-) levels xs)) where -- high tide is the level of the lower of the -- two flanking walls levels = zipWith min (init $ scanr max 0 xs) (tail $ scanl max 0 xs)
main :: IO () main = mapM_ (putStrLn . show . waterCollected) [
[1, 5, 3, 7, 2], [5, 3, 7, 2, 6, 4, 5, 9, 1, 2], [5, 5, 5, 5], [5, 6, 7, 8], [8, 7, 7, 6], [6, 7, 10, 7, 6]]</lang>
- Output:
2 14 0 0 0 0
JavaScript
ES6
<lang JavaScript>(() => {
'use strict';
const waterCollected = xs => { const maxToRight = scanr(max, 0, xs), maxToLeft = scanl(max, 0, xs), levels = zipWith(min, init(maxToLeft), tail(maxToRight));
return zipWith((a, b) => a - b, levels, xs) .filter(x => x > 0) .reduce((a, b) => a + b, 0); }
// GENERIC FUNCTIONS ----------------------------------------
// zipWith :: (a -> b -> c) -> [a] -> [b] -> [c] const zipWith = (f, xs, ys) => { const ny = ys.length; return (xs.length <= ny ? xs : xs.slice(0, ny)) .map((x, i) => f(x, ys[i])); }
// scanl :: (b -> a -> b) -> b -> [a] -> [b] const scanl = (f, startValue, xs) => { const lst = [startValue]; return ( xs.reduce((a, x) => { const v = f(a, x); return (lst.push(v), v); }, startValue), lst ); };
// scanr :: (b -> a -> b) -> b -> [a] -> [b] const scanr = (f, startValue, xs) => { const lst = [startValue]; return ( xs.reduceRight((a, x) => { const v = f(a, x); return (lst.push(v), v); }, startValue), lst.reverse() ); };
// max :: Ord a => a -> a -> a const max = (a, b) => a > b ? a : b;
// min :: Ord a => a -> a -> a const min = (a, b) => b < a ? b : a;
// init :: [a] -> [a] const init = xs => xs.length ? xs.slice(0, -1) : undefined;
// tail :: [a] -> [a] const tail = xs => xs.length ? xs.slice(1) : undefined;
// TEST --------------------------------------------------- return [ [1, 5, 3, 7, 2], [5, 3, 7, 2, 6, 4, 5, 9, 1, 2], [5, 5, 5, 5], [5, 6, 7, 8], [8, 7, 7, 6], [6, 7, 10, 7, 6] ].map(waterCollected);
//--> [2, 14, 0, 0, 0, 0]
})();</lang>
- Output:
<lang>[2, 14, 0, 0, 0, 0]</lang>