# Haskell Quiz/Numeric Maze/Solution Dolio

From HaskellWiki

This is a simple breadth-first search with some pruning. It avoids visiting numbers that have already been seen in a shorter sequence, and trims in too-large values (I noticed that no shortest sequences seemed to use numbers greater than 2*max(init, target) + 2, so such values could be discarded).

```
{-# OPTIONS_GHC -fglasgow-exts #-}
module Main where
import Control.Monad
import Data.IntSet (fromList, insert, empty, notMember, union)
import Data.List (findIndex)
import Data.Ratio
import System
search init target = reverse . map numerator $ search' [[init % 1]] (fromList [init])
where
t = target % 1
search' ls s
| Just i <- findIndex ((==t) . head) ls = ls !! i
| otherwise = search' ls' s'
where
s' = s `union` fromList (map (numerator . head) ls')
ls' = do l@(h:_) <- ls
n <- [h + 2, h * 2, h / 2]
guard (denominator n == 1)
guard (numerator n `notMember` s)
guard (if target > init then n < 2*t + 1 else n < 2*(init%1) + 3)
return (n:l)
main = do [i, t] <- fmap (map read) getArgs
print $ search i t
```