intsets

The intsets module implements an efficient int set implemented as a sparse bit set.

Note: Currently the assignment operator = for IntSet performs some rather meaningless shallow copy. Since Nim currently does not allow the assignment operator to be overloaded, use assign proc to get a deep copy.

See also:

• sets module for more general hash sets

Imports

since, hashes, sequtils, algorithm

Types

IntSet = object
  elems: int
  counter, max: int
  head: PTrunk
  data: TrunkSeq
  a: array[0 .. 33, int]

An efficient set of int implemented as a sparse bit set. Source Edit

Procs

proc initIntSet(): IntSet {...}{.raises: [], tags: [].}

Returns an empty IntSet.

See also:

• toIntSet proc

Example:

var a = initIntSet()
assert len(a) == 0

Source Edit

proc contains(s: IntSet; key: int): bool {...}{.raises: [], tags: [].}

Returns true if key is in s.

This allows the usage of in operator.

Example:

var a = initIntSet()
for x in [1, 3, 5]:
  a.incl(x)
assert a.contains(3)
assert 3 in a
assert(not a.contains(8))
assert 8 notin a

Source Edit

proc incl(s: var IntSet; key: int) {...}{.raises: [], tags: [].}

Includes an element key in s.

This doesn't do anything if key is already in s.

See also:

• excl proc for excluding an element
• incl proc for including other set
• containsOrIncl proc

Example:

var a = initIntSet()
a.incl(3)
a.incl(3)
assert len(a) == 1

Source Edit

proc incl(s: var IntSet; other: IntSet) {...}{.raises: [], tags: [].}

Includes all elements from other into s.

This is the in-place version of s + other.

See also:

• excl proc for excluding other set
• incl proc for including an element
• containsOrIncl proc

Example:

var
  a = initIntSet()
  b = initIntSet()
a.incl(1)
b.incl(5)
a.incl(b)
assert len(a) == 2
assert 5 in a

Source Edit

proc toIntSet(x: openArray[int]): IntSet {...}{.raises: [], tags: [].}

Creates a new IntSet that contains the elements of x.

Duplicates are removed.

See also:

• initIntSet proc

Example:

var
  a = toIntSet([5, 6, 7])
  b = toIntSet(@[1, 8, 8, 8])
assert len(a) == 3
assert len(b) == 2

Source Edit

proc containsOrIncl(s: var IntSet; key: int): bool {...}{.raises: [], tags: [].}

Includes key in the set s and tells if key was already in s.

The difference with regards to the incl proc is that this proc returns true if s already contained key. The proc will return false if key was added as a new value to s during this call.

See also:

• incl proc for including an element
• missingOrExcl proc

Example:

var a = initIntSet()
assert a.containsOrIncl(3) == false
assert a.containsOrIncl(3) == true
assert a.containsOrIncl(4) == false

Source Edit

proc excl(s: var IntSet; key: int) {...}{.raises: [], tags: [].}

Excludes key from the set s.

This doesn't do anything if key is not found in s.

See also:

• incl proc for including an element
• excl proc for excluding other set
• missingOrExcl proc

Example:

var a = initIntSet()
a.incl(3)
a.excl(3)
a.excl(3)
a.excl(99)
assert len(a) == 0

Source Edit

proc excl(s: var IntSet; other: IntSet) {...}{.raises: [], tags: [].}

Excludes all elements from other from s.

This is the in-place version of s - other.

See also:

• incl proc for including other set
• excl proc for excluding an element
• missingOrExcl proc

Example:

var
  a = initIntSet()
  b = initIntSet()
a.incl(1)
a.incl(5)
b.incl(5)
a.excl(b)
assert len(a) == 1
assert 5 notin a

Source Edit

proc len(s: IntSet): int {...}{.inline, raises: [], tags: [].}

Returns the number of elements in s. Source Edit

proc missingOrExcl(s: var IntSet; key: int): bool {...}{.raises: [], tags: [].}

Excludes key in the set s and tells if key was already missing from s.

The difference with regards to the excl proc is that this proc returns true if key was missing from s. The proc will return false if key was in s and it was removed during this call.

See also:

• excl proc for excluding an element
• excl proc for excluding other set
• containsOrIncl proc

Example:

var a = initIntSet()
a.incl(5)
assert a.missingOrExcl(5) == false
assert a.missingOrExcl(5) == true

Source Edit

proc clear(result: var IntSet) {...}{.raises: [], tags: [].}

Clears the IntSet back to an empty state.

Example:

var a = initIntSet()
a.incl(5)
a.incl(7)
clear(a)
assert len(a) == 0

Source Edit

proc isNil(x: IntSet): bool {...}{.inline, raises: [], tags: [].}

Source Edit

proc assign(dest: var IntSet; src: IntSet) {...}{.raises: [], tags: [].}

Copies src to dest. dest does not need to be initialized by initIntSet proc.

Example:

var
  a = initIntSet()
  b = initIntSet()
b.incl(5)
b.incl(7)
a.assign(b)
assert len(a) == 2

Source Edit

proc union(s1, s2: IntSet): IntSet {...}{.raises: [], tags: [].}

Returns the union of the sets s1 and s2.

The same as s1 + s2.

Example:

var
  a = initIntSet()
  b = initIntSet()
a.incl(1); a.incl(2); a.incl(3)
b.incl(3); b.incl(4); b.incl(5)
assert union(a, b).len == 5
## {1, 2, 3, 4, 5}

Source Edit

proc intersection(s1, s2: IntSet): IntSet {...}{.raises: [], tags: [].}

Returns the intersection of the sets s1 and s2.

The same as s1 * s2.

Example:

var
  a = initIntSet()
  b = initIntSet()
a.incl(1); a.incl(2); a.incl(3)
b.incl(3); b.incl(4); b.incl(5)
assert intersection(a, b).len == 1
## {3}

Source Edit

proc difference(s1, s2: IntSet): IntSet {...}{.raises: [], tags: [].}

Returns the difference of the sets s1 and s2.

The same as s1 - s2.

Example:

var
  a = initIntSet()
  b = initIntSet()
a.incl(1); a.incl(2); a.incl(3)
b.incl(3); b.incl(4); b.incl(5)
assert difference(a, b).len == 2
## {1, 2}

Source Edit

proc symmetricDifference(s1, s2: IntSet): IntSet {...}{.raises: [], tags: [].}

Returns the symmetric difference of the sets s1 and s2.

Example:

var
  a = initIntSet()
  b = initIntSet()
a.incl(1); a.incl(2); a.incl(3)
b.incl(3); b.incl(4); b.incl(5)
assert symmetricDifference(a, b).len == 4
## {1, 2, 4, 5}

Source Edit

proc `+`(s1, s2: IntSet): IntSet {...}{.inline, raises: [], tags: [].}

Alias for union(s1, s2). Source Edit

proc `*`(s1, s2: IntSet): IntSet {...}{.inline, raises: [], tags: [].}

Alias for intersection(s1, s2). Source Edit

proc `-`(s1, s2: IntSet): IntSet {...}{.inline, raises: [], tags: [].}

Alias for difference(s1, s2). Source Edit

proc disjoint(s1, s2: IntSet): bool {...}{.raises: [], tags: [].}

Returns true if the sets s1 and s2 have no items in common.

Example:

var
  a = initIntSet()
  b = initIntSet()
a.incl(1); a.incl(2)
b.incl(2); b.incl(3)
assert disjoint(a, b) == false
b.excl(2)
assert disjoint(a, b) == true

Source Edit

proc card(s: IntSet): int {...}{.inline, raises: [], tags: [].}

Alias for len(). Source Edit

proc `<=`(s1, s2: IntSet): bool {...}{.raises: [], tags: [].}

Returns true if s1 is subset of s2.

A subset s1 has all of its elements in s2, and s2 doesn't necessarily have more elements than s1. That is, s1 can be equal to s2.

Example:

var
  a = initIntSet()
  b = initIntSet()
a.incl(1)
b.incl(1); b.incl(2)
assert a <= b
a.incl(2)
assert a <= b
a.incl(3)
assert(not (a <= b))

Source Edit

proc `<`(s1, s2: IntSet): bool {...}{.raises: [], tags: [].}

Returns true if s1 is proper subset of s2.

A strict or proper subset s1 has all of its elements in s2, but s2 has more elements than s1.

Example:

var
  a = initIntSet()
  b = initIntSet()
a.incl(1)
b.incl(1); b.incl(2)
assert a < b
a.incl(2)
assert(not (a < b))

Source Edit

proc `==`(s1, s2: IntSet): bool {...}{.raises: [], tags: [].}

Returns true if both s1 and s2 have the same elements and set size. Source Edit

proc `$`(s: IntSet): string {...}{.raises: [], tags: [].}

The $ operator for int sets.

Converts the set s to a string, mostly for logging and printing purposes.

Source Edit

Iterators

iterator items(s: IntSet): int {...}{.inline, raises: [], tags: [].}

Iterates over any included element of s. Source Edit