# Haskell Quiz/Weird Numbers/Solution Dolio

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< Haskell Quiz | Weird Numbers(Difference between revisions)

(Naive solution) |
(Efficient solution) |
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weird n = sum s > n && all (n/=) (map sum ss) |
weird n = sum s > n && all (n/=) (map sum ss) |
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where (s:ss) = power $ divisors n |
where (s:ss) = power $ divisors n |
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+ | |||

+ | main = print . filter weird . enumFromThenTo 70 72 . read . head =<< getArgs |
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+ | </haskell> |
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+ | |||

+ | |||

+ | A much more efficient solution, implementing some of the techniques from the rubyquiz discussion: |
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+ | |||

+ | <haskell> |
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+ | module Main where |
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+ | import Control.Monad.Reader |
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+ | import Data.List |
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+ | import System |
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+ | |||

+ | power = filterM $ const [True,False] |
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+ | |||

+ | divisors n = nub $ 1 : l ++ map (div n) (reverse l) |
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+ | where l = filter ((==0) . (mod n)) . takeWhile ((<=n) . join (*)) $ [2..] |
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+ | |||

+ | weird n |
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+ | | a <= 0 = False |
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+ | | a `elem` d = False |
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+ | | sd == a = False |
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+ | | sd < a = True |
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+ | | otherwise = checkSubset a d |
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+ | where d = divisors n |
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+ | sd = sum d |
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+ | a = sd - n |
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+ | |||

+ | checkSubset a [] = True |
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+ | checkSubset a l@(x:xs) |
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+ | | a `seq` False = undefined -- strictness |
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+ | | a < 0 = True |
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+ | | a `elem` l = False |
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+ | | null xs = True |
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+ | | otherwise = checkSubset (a - x) xs && checkSubset a xs |
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main = print . filter weird . enumFromThenTo 70 72 . read . head =<< getArgs |
main = print . filter weird . enumFromThenTo 70 72 . read . head =<< getArgs |

## Revision as of 02:49, 27 October 2006

A first, rather naive solution:

module Main where import Control.Monad.Reader import Data.List import System power = filterM $ const [True,False] divisors n = sort $ 1 : join [ [x, n `div` x] | x <- l ] where l = filter ((==0) . (mod n)) . takeWhile ((<n) . join (*)) $ [2..] weird n = sum s > n && all (n/=) (map sum ss) where (s:ss) = power $ divisors n main = print . filter weird . enumFromThenTo 70 72 . read . head =<< getArgs

A much more efficient solution, implementing some of the techniques from the rubyquiz discussion:

module Main where import Control.Monad.Reader import Data.List import System power = filterM $ const [True,False] divisors n = nub $ 1 : l ++ map (div n) (reverse l) where l = filter ((==0) . (mod n)) . takeWhile ((<=n) . join (*)) $ [2..] weird n | a <= 0 = False | a `elem` d = False | sd == a = False | sd < a = True | otherwise = checkSubset a d where d = divisors n sd = sum d a = sd - n checkSubset a [] = True checkSubset a l@(x:xs) | a `seq` False = undefined -- strictness | a < 0 = True | a `elem` l = False | null xs = True | otherwise = checkSubset (a - x) xs && checkSubset a xs main = print . filter weird . enumFromThenTo 70 72 . read . head =<< getArgs