@@ -299,3 +299,46 @@ hanoi 0 _ _ _ = []
299299hanoi 1 start _ end = [(start, end)]
300300hanoi n start temp end =
301301 hanoi (n- 1 ) start end temp ++ [(start, end)] ++ hanoi (n- 1 ) temp start end
302+ 303+ {-
304+ 8.7 and 8.8
305+ 1. Generate all permutations of a unique string
306+
307+ 2. Generate all permutations of an non-unique string
308+
309+ test case: (sort $ permutations "abc") == (sort $ genPerm "abc")
310+
311+ bottom-up solution p356
312+ -}
313+ genPerm :: String -> [String
314+ genPerm = genPermHelper [[] ]
315+ 316+ -- Loop through all possible character
317+ genPermHelper :: [String -> String -> [String
318+ genPermHelper inp [] = inp
319+ genPermHelper inp (x: xs) = genPermHelper newInp xs
320+ where newInp = appendPerm inp x
321+ 322+ -- Accumulate new permutations (not finished)
323+ appendPerm :: [String -> Char -> [String
324+ appendPerm [] _ = []
325+ appendPerm (x: xs) c = newPerm ++ appendPerm xs c
326+ where -- newPerm = appendPermHelper x c 0 -- with duplicates
327+ newPerm = appendPermHelper' x c 0 [] -- without duplicates
328+ 329+ -- Insert the character to every index of the input
330+ appendPermHelper :: String -> Char -> Nat -> [String
331+ appendPermHelper str c ind
332+ | ind > length str = []
333+ | otherwise = (fstHalf ++ [c] ++ sndHalf): appendPermHelper str c (ind+ 1 )
334+ where (fstHalf,sndHalf) = splitAt ind str
335+ 336+ -- Insert the character to every index of the input with no duplicates
337+ appendPermHelper' :: String -> Char -> Nat -> [String -> [String
338+ appendPermHelper' str c ind acc
339+ | ind > length str = acc
340+ | newPerm `elem` acc = appendPermHelper' str c (ind+ 1 ) acc
341+ | otherwise = appendPermHelper' str c (ind+ 1 ) (newPerm: acc)
342+ where (fstHalf,sndHalf) = splitAt ind str
343+ newPerm = fstHalf ++ [c] ++ sndHalf
344+
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