Programming Praxis – Subset Sums

In today’s Programming Praxis exercise, we have to solve the third part of the Greplin challenge, which is to find the amount of subsequences of a list of integers where the largest number is equal to the sum of the rest. Let’s get started, shall we?

A quick import:

import Data.List

In keeping with the spirit of the original challenge, we’re going to go with the naive but simple method, which is mostly just a matter of translating the problem description from English to Haskell syntax. The only extra element is tail, which is needed to get rid of an empty list element.

greplin3 :: [Integer] -> Int
greplin3 = length . filter (\s -> sum (init s) == last s) .
           tail . subsequences

Applying this function to the given list gives us the expected answer of 179.

main :: IO ()
main = print $ greplin3 [ 3, 4, 9,14,15,19,28,37,47,50,54

The program runs in about 1.1 seconds, so for the challenge it’s fast enough. For the primes below 210 a more efficient algorithm will be needed though.

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