Hi,
In the following solution to problem 24, why is nub ignored?
I.e. if you do lexOrder of "0012," you get twice as many permutations as with
"012," even though I have used nub.
puzzled,
Bar
-- file Euler.hs
module Euler where
import Data.List
{-
problem 24
A permutation is an ordered arrangement of objects. For example, 3124
is one possible permutation of the digits 1, 2, 3 and 4. If all of the
permutations are listed numerically or alphabetically, we call it
lexicographic order. The lexicographic permutations of 0, 1 and 2 are:
012 021 102 120 201 210
What is the millionth lexicographic permutation of the digits 0, 1, 2,
3, 4, 5, 6, 7, 8 and 9?
-}
lexI :: Char -> String -> Int
lexI c s = maybe 1 (id) $ elemIndex c s
lexOrder :: [Char] -> [[Char]]
lexOrder s
| length s == 1 = [s]
| length s == 2 = z : [reverse z]
| otherwise = concat $ map (\n -> h n) [0..((length s) - 1)]
where z = sort $ nub s -- why is the nub ignored here?
h :: Int -> [String]
h n = map (z!!n :) $ lexOrder $ filter (\c -> lexI c
z /= n) z
p24 = (lexOrder "1234567890")!!999999
main :: IO()
main =
do
putStrLn $ show $ p24
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