{- |
   Module      :   Cookbook.Recipes.Algorithm
   Copyright   :   (c) 2014 by Nate Pisarski
   License     :   BSD3
   Maintainer  :   nathanpisarski@gmail.com
   Stability   :   Stable
   Portability :   Portable (Cookbook)
Library for interacting with high-evel data structures found in Cookbook.Recipes.DataStructures (Ds). It also implements some data types that would have just been type synonyms if implemented in Ds.
-}

module Cookbook.Recipes.Algorithm where

import Cookbook.Recipes.DataStructures

-- | Get every node of a tree, put it into a list.
climb :: Tree a -> [a]
climb x = case x of (Empty) -> [];(Branch a Empty b) -> a : climb b;
                    (Branch a b Empty) -> a : climb b;
                    (Branch a b d) -> a : climb b ++ climb d 

-- | Apply a function to every node in a tree.
treeMap :: Tree a -> (a -> a) -> Tree a
treeMap tr f = case tr of
  Empty -> Empty
  (Branch _ Empty z@(Branch c _ _)) -> Branch (f c) (treeMap z f) Empty
  (Branch _ z@(Branch b _ _) Empty) -> Branch (f b) Empty $ treeMap z f

-- | Collectively nullify nodes on a tree.
treeFilter :: Tree a -> (a -> Bool) -> Tree a
treeFilter Empty _ = Empty
treeFilter (Branch a Empty z@(Branch _ _ _)) f = if f a then Branch a Empty (treeFilter z f) else Empty
treeFilter (Branch a z@(Branch _ _ _) Empty) f = if f a then Branch a (treeFilter z f) Empty else Empty

-- | Generates a list of points, with the specified null data in the snd of the tupples.
genMatrix :: (Int,Int) -> a -> [((Int,Int),a)]
genMatrix (a,b) c = helper (0,0)
  where helper (d,e)
          | d == a = []
          | e == b = ((d,e),c) : helper (d+1,0)
          | otherwise = ((d,e),c) : helper (d,e+1)