A set of integers.

O(n+m). See difference.

O(1). Is the set empty?

O(1). Cardinality of the set.

O(min(n,W)). Is the value a member of the set?

O(min(n,W)). Is the element not in the set?

O(n+m). Is this a subset? (s1 isSubsetOf s2) tells whether s1 is a subset of s2.

O(n+m). Is this a proper subset? (ie. a subset but not equal).

O(1). The empty set.

O(1). A set of one element.

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.

O(min(n,W)). Delete a value in the set. Returns the original set when the value was not present.

O(n+m). The union of two sets.

The union of a list of sets.

O(n+m). Difference between two sets.

O(n+m). The intersection of two sets.

O(n). Filter all elements that satisfy some predicate.

O(n). partition the set according to some predicate.

O(min(n,W)). The expression (split x set) is a pair (set1,set2) where set1 comprises the elements of set less than x and set2 comprises the elements of set greater than x.

split 3 (fromList [1..5]) == (fromList [1,2], fromList [4,5])

O(min(n,W)). Performs a split but also returns whether the pivot element was found in the original set.

O(min(n,W)). The minimal element of the set.

O(min(n,W)). The maximal element of a set.

O(min(n,W)). Delete the minimal element.

O(min(n,W)). Delete the maximal element.

O(min(n,W)). Delete and find the minimal element.

deleteFindMin set = (findMin set, deleteMin set)

O(min(n,W)). Delete and find the maximal element.

deleteFindMax set = (findMax set, deleteMax set)

O(min(n,W)). Retrieves the maximal key of the set, and the set stripped of that element, or Nothing if passed an empty set.

O(min(n,W)). Retrieves the minimal key of the set, and the set stripped of that element, or Nothing if passed an empty set.

O(n*min(n,W)). map f s is the set obtained by applying f to each element of s.

It's worth noting that the size of the result may be smaller if, for some (x,y), x /= y && f x == f y

O(n). Fold over the elements of a set in an unspecified order.

sum set   == fold (+) 0 set
elems set == fold (:) [] set

O(n). The elements of a set. (For sets, this is equivalent to toList)

O(n). Convert the set to a list of elements.

O(n*min(n,W)). Create a set from a list of integers.

O(n). Convert the set to an ascending list of elements.

O(n). Build a set from an ascending list of elements. The precondition (input list is ascending) is not checked.

O(n). Build a set from an ascending list of distinct elements. The precondition (input list is strictly ascending) is not checked.

O(n). Show the tree that implements the set. The tree is shown in a compressed, hanging format.

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.