# 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