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Description | |||||||||||||||||||||||||

AVL tree related test and verification utilities. The functions defined
here are not exported by the main Data.Tree.AVL module. You need to
import this module explicitly if you want to use any of them.
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Synopsis | |||||||||||||||||||||||||

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Correctness checking. | |||||||||||||||||||||||||

isBalanced :: AVL e -> Bool | |||||||||||||||||||||||||

Verify that a tree is height balanced and that the BF of each node is correct. Complexity: O(n) | |||||||||||||||||||||||||

checkHeight :: AVL e -> Maybe Int | |||||||||||||||||||||||||

Verify that a tree is balanced and the BF of each node is correct. Returns (Just height) if so, otherwise Nothing. Complexity: O(n) | |||||||||||||||||||||||||

isSorted :: (e -> e -> Ordering) -> AVL e -> Bool | |||||||||||||||||||||||||

Verify that a tree is sorted. Complexity: O(n) | |||||||||||||||||||||||||

isSortedOK :: (e -> e -> Ordering) -> AVL e -> Bool | |||||||||||||||||||||||||

Verify that a tree is sorted, height balanced and the BF of each node is correct. Complexity: O(n) | |||||||||||||||||||||||||

Test data generation. | |||||||||||||||||||||||||

type TestTrees = [(Int, [(AVL Int, Int)])] | |||||||||||||||||||||||||

AVL Tree test data. Each element of a the list is a pair consisting of a height, and list of all possible sorted trees of the same height, paired with their sizes. The elements of each tree of size s are 0..s-1. | |||||||||||||||||||||||||

allAVL :: TestTrees | |||||||||||||||||||||||||

All possible sorted AVL trees. | |||||||||||||||||||||||||

allNonEmptyAVL :: TestTrees | |||||||||||||||||||||||||

Same as allAVL, but excluding the empty tree (of height 0).
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numTrees :: Int -> Integer | |||||||||||||||||||||||||

Returns the number of possible AVL trees of a given height. Behaves as if defined.. numTrees h = (\(_,xs) -> length xs) (allAVL !! h) and satisfies this recurrence relation.. numTrees 0 = 1 numTrees 1 = 1 numTrees h = (2*(numTrees (h-2)) + (numTrees (h-1))) * (numTrees (h-1)) | |||||||||||||||||||||||||

flatAVL :: Int -> AVL Int | |||||||||||||||||||||||||

Generates a flat AVL tree of n elements [0..n-1]. | |||||||||||||||||||||||||

Exhaustive tests. | |||||||||||||||||||||||||

exhaustiveTest :: (Int -> Int -> AVL Int -> Bool) -> TestTrees -> IO () | |||||||||||||||||||||||||

Apply the test function to each AVL tree in the TestTrees argument, and report progress as test proceeds. The first two arguments of the test function are tree height and size respectively. | |||||||||||||||||||||||||

Tree parameter utilities. | |||||||||||||||||||||||||

minElements :: Int -> Integer | |||||||||||||||||||||||||

Detetermine the minimum number of elements in an AVL tree of given height. This function satisfies this recurrence relation.. minElements 0 = 0 minElements 1 = 1 minElements h = 1 + minElements (h-1) + minElements (h-2) -- = Some weird expression involving the golden ratio | |||||||||||||||||||||||||

maxElements :: Int -> Integer | |||||||||||||||||||||||||

Detetermine the maximum number of elements in an AVL tree of given height. This function satisfies this recurrence relation.. maxElements 0 = 0 maxElements h = 1 + 2 * maxElements (h-1) -- = 2^h-1 | |||||||||||||||||||||||||

Testing BinPath module. | |||||||||||||||||||||||||

pathTree :: AVL Int | |||||||||||||||||||||||||

Infinite test tree. Used for test purposes for BinPath module. Value at each node is the path to that node. | |||||||||||||||||||||||||

Produced by Haddock version 0.7 |