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Description |
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Synopsis |
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Set type
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data IntSet |
A set of integers.
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Operators
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(\\) :: IntSet -> IntSet -> IntSet |
O(n+m). See difference.
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Query
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isEmpty :: IntSet -> Bool |
O(1). Is the set empty?
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size :: IntSet -> Int |
O(n). Cardinality of the set.
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member :: Int -> IntSet -> Bool |
O(min(n,W)). Is the value a member of the set?
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subset :: IntSet -> IntSet -> Bool |
O(n+m). Is this a subset?
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properSubset :: IntSet -> IntSet -> Bool |
O(n+m). Is this a proper subset? (ie. a subset but not equal).
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Construction
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empty :: IntSet |
O(1). The empty set.
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single :: Int -> IntSet |
O(1). A set of one element.
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insert :: Int -> IntSet -> IntSet |
O(min(n,W)). Add a value to the set. When the value is already
an element of the set, it is replaced by the new one, ie. insert
is left-biased.
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delete :: Int -> IntSet -> IntSet |
O(min(n,W)). Delete a value in the set. Returns the
original set when the value was not present.
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Combine
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union :: IntSet -> IntSet -> IntSet |
O(n+m). The union of two sets.
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unions :: [IntSet] -> IntSet |
The union of a list of sets.
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difference :: IntSet -> IntSet -> IntSet |
O(n+m). Difference between two sets.
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intersection :: IntSet -> IntSet -> IntSet |
O(n+m). The intersection of two sets.
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Filter
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filter :: (Int -> Bool) -> IntSet -> IntSet |
O(n). Filter all elements that satisfy some predicate.
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partition :: (Int -> Bool) -> IntSet -> (IntSet, IntSet) |
O(n). partition the set according to some predicate.
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split :: Int -> IntSet -> (IntSet, IntSet) |
O(log n). The expression (split x set) is a pair (set1,set2)
where all elements in set1 are lower than x and all elements in
set2 larger than x.
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splitMember :: Int -> IntSet -> (Bool, IntSet, IntSet) |
O(log n). Performs a split but also returns whether the pivot
element was found in the original set.
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Fold
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fold :: (Int -> b -> b) -> b -> IntSet -> b |
O(n). Fold over the elements of a set in an unspecified order.
sum set = fold (+) 0 set
elems set = fold (:) [] set
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Conversion
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List
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elems :: IntSet -> [Int] |
O(n). The elements of a set.
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toList :: IntSet -> [Int] |
O(n). Convert the set to a list of elements.
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fromList :: [Int] -> IntSet |
O(n*min(n,W)). Create a set from a list of integers.
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Ordered list
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toAscList :: IntSet -> [Int] |
O(n). Convert the set to an ascending list of elements.
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fromAscList :: [Int] -> IntSet |
O(n*min(n,W)). Build a set from an ascending list of elements.
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fromDistinctAscList :: [Int] -> IntSet |
O(n*min(n,W)). Build a set from an ascending list of distinct elements.
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Debugging
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showTree :: IntSet -> String |
O(n). Show the tree that implements the set. The tree is shown
in a compressed, hanging format.
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showTreeWith :: Bool -> Bool -> IntSet -> String |
O(n). The expression (showTreeWith hang wide map) shows
the tree that implements the set. If hang is
True, a hanging tree is shown otherwise a rotated tree is shown. If
wide is true, an extra wide version is shown.
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Produced by Haddock version 0.8 |