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Haskell Quiz/Weird Numbers/Solution Dolio

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< Haskell Quiz | Weird Numbers(Difference between revisions)
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(Naive solution)
 
(Efficient solution)
Line 14: Line 14:
 
weird n = sum s > n && all (n/=) (map sum ss)
 
weird n = sum s > n && all (n/=) (map sum ss)
 
  where (s:ss) = power $ divisors n
 
  where (s:ss) = power $ divisors n
 +
 +
main = print . filter weird . enumFromThenTo 70 72 . read . head =<< getArgs
 +
</haskell>
 +
 +
 +
A much more efficient solution, implementing some of the techniques from the rubyquiz discussion:
 +
 +
<haskell>
 +
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
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checkSubset a l@(x:xs)
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    | 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
 
main = print . filter weird . enumFromThenTo 70 72 . read . head =<< getArgs
 
</haskell>
 
</haskell>

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