Mark Needham

Thoughts on Software Development

Haskell: Creating a sliding window over a collection

with 7 comments

A couple of years ago when I was playing around with F# I came across the Seq.windowed function which allows you to create a sliding window of a specific size over a collection.

Taking an example from the F# documentation page:

let seqNumbers = [ 1.0; 1.5; 2.0; 1.5; 1.0; 1.5 ] :> seq<float>
let seqWindows = Seq.windowed 3 seqNumbers

We end up with this:

Initial sequence: 
1.0 1.5 2.0 1.5 1.0 1.5 
 
Windows of length 3: 
[|1.0; 1.5; 2.0|] [|1.5; 2.0; 1.5|] [|2.0; 1.5; 1.0|] [|1.5; 1.0; 1.5|]

Problem 8 of Project Euler is defined like so:

Find the greatest product of five consecutive digits in the 1000-digit number.

73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450

In order to do that I need to convert that number into arrays of size 5 which first involves converting the number into an array of the individual digits:

charToArray :: [Char] -> [Int]
charToArray [] = []
charToArray (x:xs) = (read [x]::Int) : (charToArray xs)							
number = "7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450"

As far as I know there isn’t a windowed function in Haskell so I wrote the following one to get the arrays of 5 consecutive elements:

windowed :: Int -> [a] -> [[a]]
windowed size ls = 
	(case ls of 
		[] -> []
		x:xs -> 
			if length ls >= size then 
				(take size ls) : windowed size xs
			else windowed size xs)

We can then use it like this:

*Main> maximum (map (\ls -> foldl (*) 1 ls) (windowed 5 (charToArray number)))
40824
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Written by Mark Needham

February 28th, 2012 at 12:21 am

Posted in Haskell

Tagged with

  • You could try using guards or multiple function definitions instead of case.

  • @twitter-20753504:disqus I think I tried that but then got confused about how I could reference the list as a whole (ls) and then refer to the head and the rest (x:xs)…maybe I’m missing something?

  • You can use ls@(x:xs) to capture the list, the head and the tail at the same time.

    See: as-patterns.

  • Ah sweet – I should have known that, I’m sure you can do the same thing in scala.

    New version looks like this:

    windowed :: Int -> [a] -> [[a]]
    windowed size [] = []
    windowed size ls@(x:xs) = if length ls >= size then (take size ls) : windowed size xs else windowed size xs

  • chris norris

    how about windowed size ls@(x:xs) = take n l : if n < length l then windows n xs else [].

  • chris norris

    sorry I changed front bit to match your names for paramaters. Mine starts as windows n l@(x:xs)

  • tonymorris

    The Extend (related: Comonad) instance for [] will help you with your windowed function.