{-
https://projecteuler.net/problem=15

Starting in the top left corner of a 2x2 grid, and only being able to move to the right and down, there are exactly 6 routes to the bottom right corner.

How many such routes are there through a 20x20 grid?
-}
module Main where

import           Prelude hiding (Right)

main :: IO ()
main = print ans

ans = 42

limit = 2
points = [ (x,y)
  | x <- [0..limit]
  , y <- [0..limit]
  ]

data Direction = Right | Down

move Right (x,y) = (x+1, y  )
move Down  (x,y) = (x  , y+1)

-- solve :: (Int, Int) -> [[(Int, Int)]]
{-
λ> [(0,0)]
[(0,0)]
λ> [(0,0),(1,0),(2,0),(2,1),(2,2)]
[(0,0),(1,0),(2,0),(2,1),(2,2)]
λ> [ [(0,0),(1,0),(2,0),(2,1),(2,2)], [(0,0),(1,0),(1,1),(2,1),(2,2)]]
[[(0,0),(1,0),(2,0),(2,1),(2,2)],[(0,0),(1,0),(1,1),(2,1),(2,2)]]
λ>
-}

data Tree a
  = Leaf a
  | Branch (Tree a) (Tree a)
  deriving (Show)