sets

The sets module implements an efficient hash set and ordered hash set.

Hash sets are different from the built in set type. Sets allow you to store any value that can be hashed and they don't contain duplicate entries.

Common usages of sets:

• removing duplicates from a container by converting it with toHashSet proc (see also sequtils.deduplicate proc)
• membership testing
• mathematical operations on two sets, such as union, intersection, difference, and symmetric difference

echo toHashSet([9, 5, 1])     # {9, 1, 5}
echo toOrderedSet([9, 5, 1])  # {9, 5, 1}

let
  s1 = toHashSet([9, 5, 1])
  s2 = toHashSet([3, 5, 7])

echo s1 + s2    # {9, 1, 3, 5, 7}
echo s1 - s2    # {1, 9}
echo s1 * s2    # {5}
echo s1 -+- s2  # {9, 1, 3, 7}

Note: The data types declared here have value semantics: This means that = performs a copy of the set.

See also:

• intsets module for efficient int sets
• tables module for hash tables

Imports

hashes, math

Types

HashSet[A] {...}{..} = object
  data: KeyValuePairSeq[A]
  counter: int

A generic hash set.

Use init proc or initHashSet proc before calling other procs on it.

Source Edit

OrderedSet[A] {...}{..} = object
  data: OrderedKeyValuePairSeq[A]
  counter, first, last: int

A generic hash set that remembers insertion order.

Use init proc or initOrderedSet proc before calling other procs on it.

Source Edit

SomeSet[A] = HashSet[A] | OrderedSet[A]

Type union representing HashSet or OrderedSet. Source Edit

Consts

defaultInitialSize = 64

Source Edit

Procs

proc rightSize(count: Natural): int {...}{.inline,
                                      deprecated: "Deprecated since 1.4.0",
                                      raises: [], tags: [].}

Deprecated: Deprecated since 1.4.0

Deprecated since Nim v1.4.0, it is not needed anymore because picking the correct size is done internally.

Return the value of initialSize to support count items.

If more items are expected to be added, simply add that expected extra amount to the parameter before calling this.

Source Edit

proc init[A](s: var HashSet[A]; initialSize = defaultInitialSize)

Initializes a hash set.

Starting from Nim v0.20, sets are initialized by default and it is not necessary to call this function explicitly.

You can call this proc on a previously initialized hash set, which will discard all its values. This might be more convenient than iterating over existing values and calling excl() on them.

See also:

• initHashSet proc
• toHashSet proc

Example:

var a: HashSet[int]
init(a)

Source Edit

proc initHashSet[A](initialSize = defaultInitialSize): HashSet[A]

Wrapper around init proc for initialization of hash sets.

Returns an empty hash set you can assign directly in var blocks in a single line.

Starting from Nim v0.20, sets are initialized by default and it is not necessary to call this function explicitly.

See also:

• toHashSet proc

Example:

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

Source Edit

proc `[]`[A](s: var HashSet[A]; key: A): var A

Returns the element that is actually stored in s which has the same value as key or raises the KeyError exception.

This is useful when one overloaded hash and == but still needs reference semantics for sharing.

Source Edit

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

Returns true if key is in s.

This allows the usage of in operator.

See also:

• incl proc
• containsOrIncl proc

Example:

var values = initHashSet[int]()
assert(not values.contains(2))
assert 2 notin values

values.incl(2)
assert values.contains(2)
assert 2 in values

Source Edit

proc incl[A](s: var HashSet[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 other set
• containsOrIncl proc

Example:

var values = initHashSet[int]()
values.incl(2)
values.incl(2)
assert values.len == 1

Source Edit

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

Includes all elements from other set into s (must be declared as var).

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
  values = toHashSet([1, 2, 3])
  others = toHashSet([3, 4, 5])
values.incl(others)
assert values.len == 5

Source Edit

proc toHashSet[A](keys: openArray[A]): HashSet[A]

Creates a new hash set that contains the members of the given collection (seq, array, or string) keys.

Duplicates are removed.

See also:

• initHashSet proc

Example:

let
  a = toHashSet([5, 3, 2])
  b = toHashSet("abracadabra")
assert len(a) == 3
## a == {2, 3, 5}
assert len(b) == 5
## b == {'a', 'b', 'c', 'd', 'r'}

Source Edit

proc containsOrIncl[A](s: var HashSet[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
• incl proc for including other set
• missingOrExcl proc

Example:

var values = initHashSet[int]()
assert values.containsOrIncl(2) == false
assert values.containsOrIncl(2) == true
assert values.containsOrIncl(3) == false

Source Edit

proc excl[A](s: var HashSet[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 other set
• missingOrExcl proc

Example:

var s = toHashSet([2, 3, 6, 7])
s.excl(2)
s.excl(2)
assert s.len == 3

Source Edit

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

Excludes all elements of other set 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
  numbers = toHashSet([1, 2, 3, 4, 5])
  even = toHashSet([2, 4, 6, 8])
numbers.excl(even)
assert len(numbers) == 3
## numbers == {1, 3, 5}

Source Edit

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

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 s = toHashSet([2, 3, 6, 7])
assert s.missingOrExcl(4) == true
assert s.missingOrExcl(6) == false
assert s.missingOrExcl(6) == true

Source Edit

proc pop[A](s: var HashSet[A]): A

Removes and returns an arbitrary element from the set s.

Raises KeyError if the set s is empty.

See also:

• clear proc

Example:

var s = toHashSet([2, 1])
assert [s.pop, s.pop] in [[1, 2], [2,1]] # order unspecified
doAssertRaises(KeyError, echo s.pop)

Source Edit

proc clear[A](s: var HashSet[A])

Clears the HashSet back to an empty state, without shrinking any of the existing storage.

O(n) operation, where n is the size of the hash bucket.

See also:

• pop proc

Example:

var s = toHashSet([3, 5, 7])
clear(s)
assert len(s) == 0

Source Edit

proc len[A](s: HashSet[A]): int

Returns the number of elements in s.

Due to an implementation detail you can call this proc on variables which have not been initialized yet. The proc will return zero as the length then.

Example:

var a: HashSet[string]
assert len(a) == 0
let s = toHashSet([3, 5, 7])
assert len(s) == 3

Source Edit

proc card[A](s: HashSet[A]): int

Alias for len().

Card stands for the cardinality of a set.

Source Edit

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

Returns the union of the sets s1 and s2.

The same as s1 + s2.

The union of two sets is represented mathematically as A ∪ B and is the set of all objects that are members of s1, s2 or both.

See also:

• intersection proc
• difference proc
• symmetricDifference proc

Example:

let
  a = toHashSet(["a", "b"])
  b = toHashSet(["b", "c"])
  c = union(a, b)
assert c == toHashSet(["a", "b", "c"])

Source Edit

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

Returns the intersection of the sets s1 and s2.

The same as s1 * s2.

The intersection of two sets is represented mathematically as A ∩ B and is the set of all objects that are members of s1 and s2 at the same time.

See also:

• union proc
• difference proc
• symmetricDifference proc

Example:

let
  a = toHashSet(["a", "b"])
  b = toHashSet(["b", "c"])
  c = intersection(a, b)
assert c == toHashSet(["b"])

Source Edit

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

Returns the difference of the sets s1 and s2.

The same as s1 - s2.

The difference of two sets is represented mathematically as A ∖ B and is the set of all objects that are members of s1 and not members of s2.

See also:

• union proc
• intersection proc
• symmetricDifference proc

Example:

let
  a = toHashSet(["a", "b"])
  b = toHashSet(["b", "c"])
  c = difference(a, b)
assert c == toHashSet(["a"])

Source Edit

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

Returns the symmetric difference of the sets s1 and s2.

The same as s1 -+- s2.

The symmetric difference of two sets is represented mathematically as A △ B or A ⊖ B and is the set of all objects that are members of s1 or s2 but not both at the same time.

See also:

• union proc
• intersection proc
• difference proc

Example:

let
  a = toHashSet(["a", "b"])
  b = toHashSet(["b", "c"])
  c = symmetricDifference(a, b)
assert c == toHashSet(["a", "c"])

Source Edit

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

Alias for union(s1, s2). Source Edit

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

Alias for intersection(s1, s2). Source Edit

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

Alias for difference(s1, s2). Source Edit

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

Alias for symmetricDifference(s1, s2). Source Edit

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

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

Example:

let
  a = toHashSet(["a", "b"])
  b = toHashSet(["b", "c"])
assert disjoint(a, b) == false
assert disjoint(a, b - a) == true

Source Edit

proc `<`[A](s, t: HashSet[A]): bool

Returns true if s is a strict or proper subset of t.

A strict or proper subset s has all of its members in t but t has more elements than s.

Example:

let
  a = toHashSet(["a", "b"])
  b = toHashSet(["b", "c"])
  c = intersection(a, b)
assert c < a and c < b
assert(not (a < a))

Source Edit

proc `<=`[A](s, t: HashSet[A]): bool

Returns true if s is a subset of t.

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

Example:

let
  a = toHashSet(["a", "b"])
  b = toHashSet(["b", "c"])
  c = intersection(a, b)
assert c <= a and c <= b
assert a <= a

Source Edit

proc `==`[A](s, t: HashSet[A]): bool

Returns true if both s and t have the same members and set size.

Example:

var
  a = toHashSet([1, 2])
  b = toHashSet([2, 1])
assert a == b

Source Edit

proc map[A, B](data: HashSet[A]; op: proc (x: A): B {...}{.closure.}): HashSet[B]

Returns a new set after applying op proc on each of the elements of data set.

You can use this proc to transform the elements from a set.

Example:

let
  a = toHashSet([1, 2, 3])
  b = a.map(proc (x: int): string = $x)
assert b == toHashSet(["1", "2", "3"])

Source Edit

proc hash[A](s: HashSet[A]): Hash

Hashing of HashSet. Source Edit

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

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

Don't use this proc for serialization, the representation may change at any moment and values are not escaped.

Examples:

echo toHashSet([2, 4, 5])
# --> {2, 4, 5}
echo toHashSet(["no", "esc'aping", "is \" provided"])
# --> {no, esc'aping, is " provided}

Source Edit

proc initSet[A](initialSize = defaultInitialSize): HashSet[A] {...}{.
    deprecated: "Deprecated since v0.20, use \'initHashSet\'".}

Deprecated: Deprecated since v0.20, use 'initHashSet'

Source Edit

proc toSet[A](keys: openArray[A]): HashSet[A] {...}{.
    deprecated: "Deprecated since v0.20, use \'toHashSet\'".}

Deprecated: Deprecated since v0.20, use 'toHashSet'

Source Edit

proc isValid[A](s: HashSet[A]): bool {...}{.deprecated: "Deprecated since v0.20; sets are initialized by default".}

Deprecated: Deprecated since v0.20; sets are initialized by default

Returns true if the set has been initialized (with initHashSet proc or init proc).

Examples:

proc savePreferences(options: HashSet[string]) =
  assert options.isValid, "Pass an initialized set!"
  # Do stuff here, may crash in release builds!

Source Edit

proc init[A](s: var OrderedSet[A]; initialSize = defaultInitialSize)

Initializes an ordered hash set.

Starting from Nim v0.20, sets are initialized by default and it is not necessary to call this function explicitly.

You can call this proc on a previously initialized hash set, which will discard all its values. This might be more convenient than iterating over existing values and calling excl() on them.

See also:

• initOrderedSet proc
• toOrderedSet proc

Example:

var a: OrderedSet[int]
init(a)

Source Edit

proc initOrderedSet[A](initialSize = defaultInitialSize): OrderedSet[A]

Wrapper around init proc for initialization of ordered hash sets.

Returns an empty ordered hash set you can assign directly in var blocks in a single line.

Starting from Nim v0.20, sets are initialized by default and it is not necessary to call this function explicitly.

See also:

• toOrderedSet proc

Example:

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

Source Edit

proc toOrderedSet[A](keys: openArray[A]): OrderedSet[A]

Creates a new hash set that contains the members of the given collection (seq, array, or string) keys.

Duplicates are removed.

See also:

• initOrderedSet proc

Example:

let
  a = toOrderedSet([5, 3, 2])
  b = toOrderedSet("abracadabra")
assert len(a) == 3
## a == {5, 3, 2} # different than in HashSet
assert len(b) == 5
## b == {'a', 'b', 'r', 'c', 'd'} # different than in HashSet

Source Edit

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

Returns true if key is in s.

This allows the usage of in operator.

See also:

• incl proc
• containsOrIncl proc

Example:

var values = initOrderedSet[int]()
assert(not values.contains(2))
assert 2 notin values

values.incl(2)
assert values.contains(2)
assert 2 in values

Source Edit

proc incl[A](s: var OrderedSet[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 other set
• containsOrIncl proc

Example:

var values = initOrderedSet[int]()
values.incl(2)
values.incl(2)
assert values.len == 1

Source Edit

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

Includes all elements from the OrderedSet other into HashSet s (must be declared as var).

See also:

• incl proc for including an element
• containsOrIncl proc

Example:

var
  values = toHashSet([1, 2, 3])
  others = toOrderedSet([3, 4, 5])
values.incl(others)
assert values.len == 5

Source Edit

proc containsOrIncl[A](s: var OrderedSet[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 values = initOrderedSet[int]()
assert values.containsOrIncl(2) == false
assert values.containsOrIncl(2) == true
assert values.containsOrIncl(3) == false

Source Edit

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

Excludes key from the set s. Efficiency: O(n).

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

See also:

• incl proc for including an element
• missingOrExcl proc

Example:

var s = toOrderedSet([2, 3, 6, 7])
s.excl(2)
s.excl(2)
assert s.len == 3

Source Edit

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

Excludes key in the set s and tells if key was already missing from s. Efficiency: O(n).

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
• containsOrIncl proc

Example:

var s = toOrderedSet([2, 3, 6, 7])
assert s.missingOrExcl(4) == true
assert s.missingOrExcl(6) == false
assert s.missingOrExcl(6) == true

Source Edit

proc clear[A](s: var OrderedSet[A])

Clears the OrderedSet back to an empty state, without shrinking any of the existing storage.

O(n) operation where n is the size of the hash bucket.

Example:

var s = toOrderedSet([3, 5, 7])
clear(s)
assert len(s) == 0

Source Edit

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

Returns the number of elements in s.

Due to an implementation detail you can call this proc on variables which have not been initialized yet. The proc will return zero as the length then.

Example:

var a: OrderedSet[string]
assert len(a) == 0
let s = toHashSet([3, 5, 7])
assert len(s) == 3

Source Edit

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

Alias for len().

Card stands for the cardinality of a set.

Source Edit

proc `==`[A](s, t: OrderedSet[A]): bool

Equality for ordered sets.

Example:

let
  a = toOrderedSet([1, 2])
  b = toOrderedSet([2, 1])
assert(not (a == b))

Source Edit

proc hash[A](s: OrderedSet[A]): Hash

Hashing of OrderedSet. Source Edit

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

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

Don't use this proc for serialization, the representation may change at any moment and values are not escaped.

Examples:

echo toOrderedSet([2, 4, 5])
# --> {2, 4, 5}
echo toOrderedSet(["no", "esc'aping", "is \" provided"])
# --> {no, esc'aping, is " provided}

Source Edit

Iterators

iterator items[A](s: HashSet[A]): A

Iterates over elements of the set s.

If you need a sequence with the elements you can use sequtils.toSeq template.

type
  pair = tuple[a, b: int]
var
  a, b = initHashSet[pair]()
a.incl((2, 3))
a.incl((3, 2))
a.incl((2, 3))
for x, y in a.items:
  b.incl((x - 2, y + 1))
assert a.len == 2
echo b
# --> {(a: 1, b: 3), (a: 0, b: 4)}

Source Edit

iterator items[A](s: OrderedSet[A]): A

Iterates over keys in the ordered set s in insertion order.

If you need a sequence with the elements you can use sequtils.toSeq template.

var a = initOrderedSet[int]()
for value in [9, 2, 1, 5, 1, 8, 4, 2]:
  a.incl(value)
for value in a.items:
  echo "Got ", value
# --> Got 9
# --> Got 2
# --> Got 1
# --> Got 5
# --> Got 8
# --> Got 4

Source Edit

iterator pairs[A](s: OrderedSet[A]): tuple[a: int, b: A]

Iterates through (position, value) tuples of OrderedSet s.

Example:

let a = toOrderedSet("abracadabra")
var p = newSeq[(int, char)]()
for x in pairs(a):
  p.add(x)
assert p == @[(0, 'a'), (1, 'b'), (2, 'r'), (3, 'c'), (4, 'd')]

Source Edit