# [Haskell-cafe] warning - Euler problem spoiler enclosed

Barbara Shirtcliff barcs at gmx.com
Wed May 4 15:13:07 CEST 2011

```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
```