Path Count
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
import Test.Hspec | |
main :: IO () | |
main = hspec spec | |
type Point = (Int, Int) | |
data Tree a = Leaf | |
| Node a (Tree a) (Tree a) | |
deriving (Show, Eq) | |
pathCount :: Int -> Int -> Int | |
pathCount m n = leafCount $ fromTree m n | |
where fromTree m n = buildTree (0,m) (n,0) | |
leafCount :: Tree Point -> Int | |
leafCount Leaf = 0 | |
leafCount (Node _ Leaf Leaf) = 1 | |
leafCount (Node _ left right) = leafCount left + leafCount right | |
buildTree :: Point -> Point -> Tree Point | |
buildTree (a,b) end@(c,d) | |
| a > c = Leaf | |
| b < 0 = Leaf | |
| otherwise = Node (a, b) (buildTree (a+1,b) end) (buildTree (a,b-1) end) | |
spec :: Spec | |
spec = | |
describe "Path Count" $ do | |
it "can calculate paths for 1x2 matrix" $ do | |
let tree = | |
Node (0,1) | |
(Node (1,1) | |
(Node (2,1) Leaf | |
(Node (2,0) Leaf Leaf)) | |
(Node (1,0) (Node (2,0) Leaf Leaf) | |
Leaf)) | |
(Node (0,0) | |
(Node (1,0) | |
(Node (2,0) Leaf Leaf) | |
Leaf) | |
Leaf) | |
{- | |
Possible paths: | |
(0,1) - (1,1) - (2,1) - (2,0) | |
(0,1) - (1,1) - (1,0) - (2,0) | |
(0,1) - (0,0) - (1,0) - (2,0) | |
-} | |
buildTree (0,1) (2,0) `shouldBe` tree | |
leafCount(buildTree (0,1) (2,0)) `shouldBe` 3 | |
leafCount(buildTree (0,2) (1,0)) `shouldBe` 3 | |
pathCount 1 2 `shouldBe` 3 | |
pathCount 2 1 `shouldBe` 3 | |
pathCount 1 1 `shouldBe` 2 | |
it "can calculate paths for 2x2 matrix" $ do | |
let tree = | |
Node (0,2) | |
(Node (1,2) | |
(Node (2,2) | |
Leaf | |
(Node (2,1) | |
Leaf | |
(Node (2,0) Leaf Leaf))) | |
(Node (1,1) | |
(Node (2,1) | |
Leaf | |
(Node (2,0) Leaf Leaf)) | |
(Node (1,0) | |
(Node (2,0) Leaf Leaf) | |
Leaf))) | |
(Node (0,1) | |
(Node (1,1) | |
(Node (2,1) | |
Leaf | |
(Node (2,0) Leaf Leaf)) | |
(Node (1,0) | |
(Node (2,0) Leaf Leaf) | |
Leaf)) | |
(Node (0,0) | |
(Node (1,0) | |
(Node (2,0) Leaf Leaf) | |
Leaf) | |
Leaf)) | |
leafCount tree `shouldBe` 6 | |
buildTree (0,2) (2,0) `shouldBe` tree | |
pathCount 2 2 `shouldBe` 6 |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment