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The packedsets module implements an efficient Ordinal set implemented as a sparse bit set.

Supports any Ordinal type.

See also

• sets module for more general hash sets

Imports

since, hashes

Types

PackedSet[A] = object

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

Procs

proc `$`[A](s: PackedSet[A]): string

Converts s to a string.

Example:

let a = [1, 2, 3].toPackedSet
assert $a == "{1, 2, 3}"

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proc `*`[A](s1, s2: PackedSet[A]): PackedSet[A] {.inline.}

Alias for intersection(s1, s2). Source Edit

proc `+`[A](s1, s2: PackedSet[A]): PackedSet[A] {.inline.}

Alias for union(s1, s2). Source Edit

proc `-`[A](s1, s2: PackedSet[A]): PackedSet[A] {.inline.}

Alias for difference(s1, s2). Source Edit

proc `<`[A](s1, s2: PackedSet[A]): bool

Returns true if s1 is a 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:

let
  a = [1].toPackedSet
  b = [1, 2].toPackedSet
  c = [1, 3].toPackedSet
assert a < b
assert not (b < b)
assert not (c < b)

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proc `<=`[A](s1, s2: PackedSet[A]): bool

Returns true if s1 is a subset of s2.

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

Example:

let
  a = [1].toPackedSet
  b = [1, 2].toPackedSet
  c = [1, 3].toPackedSet
assert a <= b
assert b <= b
assert not (c <= b)

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proc `==`[A](s1, s2: PackedSet[A]): bool

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

Example:

assert [1, 2].toPackedSet == [2, 1].toPackedSet
assert [1, 2].toPackedSet == [2, 1, 2].toPackedSet

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proc `=copy`[A](dest: var PackedSet[A]; src: PackedSet[A])

Copies src to dest. dest does not need to be initialized by the initPackedSet proc. Source Edit

proc assign[A](dest: var PackedSet[A]; src: PackedSet[A]) {.inline, ...deprecated.}

Deprecated

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

Example:

var
  a = initPackedSet[int]()
  b = initPackedSet[int]()
b.incl(5)
b.incl(7)
a.assign(b)
assert len(a) == 2

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proc card[A](s: PackedSet[A]): int {.inline.}

Alias for len().

Card stands for the cardinality of a set.

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proc clear[A](result: var PackedSet[A])

Clears the PackedSet[A] back to an empty state.

Example:

var a = [5, 7].toPackedSet
clear(a)
assert len(a) == 0

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proc contains[A](s: PackedSet[A]; key: A): bool

Returns true if key is in s.

This allows the usage of the in operator.

Example:

type ABCD = enum A, B, C, D
let a = [1, 3, 5].toPackedSet
assert a.contains(3)
assert 3 in a
assert not a.contains(8)
assert 8 notin a
let letters = [A, C].toPackedSet
assert A in letters
assert C in letters
assert B notin letters

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proc containsOrIncl[A](s: var PackedSet[A]; key: A): bool

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 = initPackedSet[int]()
assert a.containsOrIncl(3) == false
assert a.containsOrIncl(3) == true
assert a.containsOrIncl(4) == false

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proc difference[A](s1, s2: PackedSet[A]): PackedSet[A]

Returns the difference of the sets s1 and s2.

The same as s1 - s2.

Example:

let
  a = [1, 2, 3].toPackedSet
  b = [3, 4, 5].toPackedSet
  c = difference(a, b)
assert c.len == 2
assert c == [1, 2].toPackedSet

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proc disjoint[A](s1, s2: PackedSet[A]): bool

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

Example:

let
  a = [1, 2].toPackedSet
  b = [2, 3].toPackedSet
  c = [3, 4].toPackedSet
assert disjoint(a, b) == false
assert disjoint(a, c) == true

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proc excl[A](s: var PackedSet[A]; key: A)

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 a set
• missingOrExcl proc

Example:

var a = [3].toPackedSet
a.excl(3)
a.excl(3)
a.excl(99)
assert len(a) == 0

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proc excl[A](s: var PackedSet[A]; other: PackedSet[A])

Excludes all elements from other from s.

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

See also:

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

Example:

var a = [1, 5].toPackedSet
a.excl([5].toPackedSet)
assert len(a) == 1
assert 5 notin a

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proc incl[A](s: var PackedSet[A]; key: A)

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 a set
• containsOrIncl proc

Example:

var a = initPackedSet[int]()
a.incl(3)
a.incl(3)
assert len(a) == 1

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proc incl[A](s: var PackedSet[A]; other: PackedSet[A])

Includes all elements from other into s.

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

See also:

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

Example:

var a = [1].toPackedSet
a.incl([5].toPackedSet)
assert len(a) == 2
assert 5 in a

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proc initPackedSet[A](): PackedSet[A]

Returns an empty PackedSet[A]. A must be Ordinal.

See also:

• toPackedSet proc

Example:

let a = initPackedSet[int]()
assert len(a) == 0
type Id = distinct int
var ids = initPackedSet[Id]()
ids.incl(3.Id)

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proc intersection[A](s1, s2: PackedSet[A]): PackedSet[A]

Returns the intersection of the sets s1 and s2.

The same as s1 * s2.

Example:

let
  a = [1, 2, 3].toPackedSet
  b = [3, 4, 5].toPackedSet
  c = intersection(a, b)
assert c.len == 1
assert c == [3].toPackedSet

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proc isNil[A](x: PackedSet[A]): bool {.inline.}

Returns true if x is empty, false otherwise.

Example:

var a = initPackedSet[int]()
assert a.isNil
a.incl(2)
assert not a.isNil
a.excl(2)
assert a.isNil

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proc len[A](s: PackedSet[A]): int {.inline.}

Returns the number of elements in s.

Example:

let a = [1, 3, 5].toPackedSet
assert len(a) == 3

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proc missingOrExcl[A](s: var PackedSet[A]; key: A): bool

Excludes key from 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 a set
• containsOrIncl proc

Example:

var a = [5].toPackedSet
assert a.missingOrExcl(5) == false
assert a.missingOrExcl(5) == true

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proc symmetricDifference[A](s1, s2: PackedSet[A]): PackedSet[A]

Returns the symmetric difference of the sets s1 and s2.

Example:

let
  a = [1, 2, 3].toPackedSet
  b = [3, 4, 5].toPackedSet
  c = symmetricDifference(a, b)
assert c.len == 4
assert c == [1, 2, 4, 5].toPackedSet

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proc toPackedSet[A](x: openArray[A]): PackedSet[A]

Creates a new PackedSet[A] that contains the elements of x.

Duplicates are removed.

See also:

• initPackedSet proc

Example:

let a = [5, 6, 7, 8, 8].toPackedSet
assert len(a) == 4
assert $a == "{5, 6, 7, 8}"

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proc union[A](s1, s2: PackedSet[A]): PackedSet[A]

Returns the union of the sets s1 and s2.

The same as s1 + s2.

Example:

let
  a = [1, 2, 3].toPackedSet
  b = [3, 4, 5].toPackedSet
  c = union(a, b)
assert c.len == 5
assert c == [1, 2, 3, 4, 5].toPackedSet

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Iterators

iterator items[A](s: PackedSet[A]): A {.inline.}

Iterates over any included element of s. Source Edit