37 lines
1.1 KiB
Haskell
37 lines
1.1 KiB
Haskell
data Tree a = Empty | Branch a (Tree a) (Tree a)
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deriving (Show, Eq)
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maxNodes :: Int -> Int
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maxNodes = subtract 1 . (2 ^)
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minNodesSeq :: [Int]
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minNodesSeq = 0 : 1 : zipWith ((+) . (1 +)) minNodesSeq (tail minNodesSeq)
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minNodes :: Int -> Int
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minNodes = (!!) minNodesSeq
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maxHeight :: Int -> Int
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maxHeight n = subtract 1 $ length $ takeWhile (<= n) minNodesSeq
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minHeight :: Int -> Int
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minHeight = ceiling . logBase 2 . fromIntegral . (+ 1)
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countNodes :: Tree a -> Int
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countNodes Empty = 0
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countNodes (Branch _ l r) = countNodes l + countNodes r + 1
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hbalTree :: a -> Int -> [Tree a]
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hbalTree _ 0 = [Empty]
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hbalTree x 1 = [Branch x Empty Empty]
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hbalTree x n =
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[Branch x l r | l <- minustwocase, r <- minusonecase]
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++ [Branch x l r | l <- minusonecase, r <- minusonecase]
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++ [Branch x l r | l <- minusonecase, r <- minustwocase]
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where
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minusonecase = hbalTree x (n - 1)
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minustwocase = hbalTree x (n - 2)
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hbalTreeNodes :: a -> Int -> [Tree a]
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hbalTreeNodes _ 0 = [Empty]
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hbalTreeNodes x n = concatMap (filter ((n ==) . countNodes) . hbalTree x) [minHeight n .. maxHeight n]
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