#
#
# Nim's Runtime Library
# (c) Copyright 2012 Andreas Rumpf
#
# See the file "copying.txt", included in this
# distribution, for details about the copyright.
#
## The ``intsets`` module implements an efficient `int` set implemented as a
## `sparse bit set`:idx:.
##
## **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
## <#assign,IntSet,IntSet>`_ to get a deep copy.
##
## **See also:**
## * `sets module <sets.html>`_ for more general hash sets
import
hashes
type
BitScalar = uint
const
InitIntSetSize = 8 # must be a power of two!
TrunkShift = 9
BitsPerTrunk = 1 shl TrunkShift # needs to be a power of 2 and
# divisible by 64
TrunkMask = BitsPerTrunk - 1
IntsPerTrunk = BitsPerTrunk div (sizeof(BitScalar) * 8)
IntShift = 5 + ord(sizeof(BitScalar) == 8) # 5 or 6, depending on int width
IntMask = 1 shl IntShift - 1
type
PTrunk = ref Trunk
Trunk = object
next: PTrunk # all nodes are connected with this pointer
key: int # start address at bit 0
bits: array[0..IntsPerTrunk - 1, BitScalar] # a bit vector
TrunkSeq = seq[PTrunk]
IntSet* = object ## An efficient set of `int` implemented as a sparse bit set.
elems: int # only valid for small numbers
counter, max: int
head: PTrunk
data: TrunkSeq
a: array[0..33, int] # profiling shows that 34 elements are enough
proc mustRehash[T](t: T): bool {.inline.} =
let length = t.max + 1
assert length > t.counter
result = (length * 2 < t.counter * 3) or (length - t.counter < 4)
proc nextTry(h, maxHash: Hash, perturb: var Hash): Hash {.inline.} =
const PERTURB_SHIFT = 5
var perturb2 = cast[uint](perturb) shr PERTURB_SHIFT
perturb = cast[Hash](perturb2)
result = ((5*h) + 1 + perturb) and maxHash
proc intSetGet(t: IntSet, key: int): PTrunk =
var h = key and t.max
var perturb = key
while t.data[h] != nil:
if t.data[h].key == key:
return t.data[h]
h = nextTry(h, t.max, perturb)
result = nil
proc intSetRawInsert(t: IntSet, data: var TrunkSeq, desc: PTrunk) =
var h = desc.key and t.max
var perturb = desc.key
while data[h] != nil:
assert(data[h] != desc)
h = nextTry(h, t.max, perturb)
assert(data[h] == nil)
data[h] = desc
proc intSetEnlarge(t: var IntSet) =
var n: TrunkSeq
var oldMax = t.max
t.max = ((t.max + 1) * 2) - 1
newSeq(n, t.max + 1)
for i in countup(0, oldMax):
if t.data[i] != nil: intSetRawInsert(t, n, t.data[i])
swap(t.data, n)
proc intSetPut(t: var IntSet, key: int): PTrunk =
var h = key and t.max
var perturb = key
while t.data[h] != nil:
if t.data[h].key == key:
return t.data[h]
h = nextTry(h, t.max, perturb)
if mustRehash(t): intSetEnlarge(t)
inc(t.counter)
h = key and t.max
perturb = key
while t.data[h] != nil: h = nextTry(h, t.max, perturb)
assert(t.data[h] == nil)
new(result)
result.next = t.head
result.key = key
t.head = result
t.data[h] = result
proc bitincl(s: var IntSet, key: int) {.inline.} =
var ret: PTrunk
var t = intSetPut(s, `shr`(key, TrunkShift))
var u = key and TrunkMask
t.bits[u shr IntShift] = t.bits[u shr IntShift] or
(BitScalar(1) shl (u and IntMask))
proc exclImpl(s: var IntSet, key: int) =
if s.elems <= s.a.len:
for i in 0..<s.elems:
if s.a[i] == key:
s.a[i] = s.a[s.elems-1]
dec s.elems
return
else:
var t = intSetGet(s, key shr TrunkShift)
if t != nil:
var u = key and TrunkMask
t.bits[u shr IntShift] = t.bits[u shr IntShift] and
not(BitScalar(1) shl (u and IntMask))
template dollarImpl(): untyped =
result = "{"
for key in items(s):
if result.len > 1: result.add(", ")
result.add($key)
result.add("}")
iterator items*(s: IntSet): int {.inline.} =
## Iterates over any included element of `s`.
if s.elems <= s.a.len:
for i in 0..<s.elems:
yield s.a[i]
else:
var r = s.head
while r != nil:
var i = 0
while i <= high(r.bits):
var w: uint = r.bits[i]
# taking a copy of r.bits[i] here is correct, because
# modifying operations are not allowed during traversation
var j = 0
while w != 0: # test all remaining bits for zero
if (w and 1) != 0: # the bit is set!
yield (r.key shl TrunkShift) or (i shl IntShift +% j)
inc(j)
w = w shr 1
inc(i)
r = r.next
proc initIntSet*: IntSet =
## Returns an empty IntSet.
runnableExamples:
var a = initIntSet()
assert len(a) == 0
# newSeq(result.data, InitIntSetSize)
# result.max = InitIntSetSize-1
result = IntSet(
elems: 0,
counter: 0,
max: 0,
head: nil,
data: when defined(nimNoNilSeqs): @[] else: nil)
# a: array[0..33, int] # profiling shows that 34 elements are enough
proc contains*(s: IntSet, key: int): bool =
## Returns true if `key` is in `s`.
##
## This allows the usage of `in` operator.
runnableExamples:
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
if s.elems <= s.a.len:
for i in 0..<s.elems:
if s.a[i] == key: return true
else:
var t = intSetGet(s, `shr`(key, TrunkShift))
if t != nil:
var u = key and TrunkMask
result = (t.bits[u shr IntShift] and
(BitScalar(1) shl (u and IntMask))) != 0
else:
result = false
proc incl*(s: var IntSet, key: int) =
## Includes an element `key` in `s`.
##
## This doesn't do anything if `key` is already in `s`.
##
## See also:
## * `excl proc <#excl,IntSet,int>`_ for excluding an element
## * `incl proc <#incl,IntSet,IntSet>`_ for including other set
## * `containsOrIncl proc <#containsOrIncl,IntSet,int>`_
runnableExamples:
var a = initIntSet()
a.incl(3)
a.incl(3)
assert len(a) == 1
if s.elems <= s.a.len:
for i in 0..<s.elems:
if s.a[i] == key: return
if s.elems < s.a.len:
s.a[s.elems] = key
inc s.elems
return
newSeq(s.data, InitIntSetSize)
s.max = InitIntSetSize-1
for i in 0..<s.elems:
bitincl(s, s.a[i])
s.elems = s.a.len + 1
# fall through:
bitincl(s, key)
proc incl*(s: var IntSet, other: IntSet) =
## Includes all elements from `other` into `s`.
##
## This is the in-place version of `s + other <#+,IntSet,IntSet>`_.
##
## See also:
## * `excl proc <#excl,IntSet,IntSet>`_ for excluding other set
## * `incl proc <#incl,IntSet,int>`_ for including an element
## * `containsOrIncl proc <#containsOrIncl,IntSet,int>`_
runnableExamples:
var
a = initIntSet()
b = initIntSet()
a.incl(1)
b.incl(5)
a.incl(b)
assert len(a) == 2
assert 5 in a
for item in other: incl(s, item)
proc containsOrIncl*(s: var IntSet, key: int): bool =
## Includes `key` in the set `s` and tells if `key` was already in `s`.
##
## The difference with regards to the `incl proc <#incl,IntSet,int>`_ 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 <#incl,IntSet,int>`_ for including an element
## * `missingOrExcl proc <#missingOrExcl,IntSet,int>`_
runnableExamples:
var a = initIntSet()
assert a.containsOrIncl(3) == false
assert a.containsOrIncl(3) == true
assert a.containsOrIncl(4) == false
if s.elems <= s.a.len:
for i in 0..<s.elems:
if s.a[i] == key:
return true
incl(s, key)
result = false
else:
var t = intSetGet(s, `shr`(key, TrunkShift))
if t != nil:
var u = key and TrunkMask
result = (t.bits[u shr IntShift] and BitScalar(1) shl (u and IntMask)) != 0
if not result:
t.bits[u shr IntShift] = t.bits[u shr IntShift] or
(BitScalar(1) shl (u and IntMask))
else:
incl(s, key)
result = false
proc excl*(s: var IntSet, key: int) =
## Excludes `key` from the set `s`.
##
## This doesn't do anything if `key` is not found in `s`.
##
## See also:
## * `incl proc <#incl,IntSet,int>`_ for including an element
## * `excl proc <#excl,IntSet,IntSet>`_ for excluding other set
## * `missingOrExcl proc <#missingOrExcl,IntSet,int>`_
runnableExamples:
var a = initIntSet()
a.incl(3)
a.excl(3)
a.excl(3)
a.excl(99)
assert len(a) == 0
exclImpl(s, key)
proc excl*(s: var IntSet, other: IntSet) =
## Excludes all elements from `other` from `s`.
##
## This is the in-place version of `s - other <#-,IntSet,IntSet>`_.
##
## See also:
## * `incl proc <#incl,IntSet,IntSet>`_ for including other set
## * `excl proc <#excl,IntSet,int>`_ for excluding an element
## * `missingOrExcl proc <#missingOrExcl,IntSet,int>`_
runnableExamples:
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
for item in other: excl(s, item)
proc len*(s: IntSet): int {.inline.} =
## Returns the number of elements in `s`.
if s.elems < s.a.len:
result = s.elems
else:
result = 0
for _ in s:
inc(result)
proc missingOrExcl*(s: var IntSet, key: int): bool =
## Excludes `key` in the set `s` and tells if `key` was already missing from `s`.
##
## The difference with regards to the `excl proc <#excl,IntSet,int>`_ 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 <#excl,IntSet,int>`_ for excluding an element
## * `excl proc <#excl,IntSet,IntSet>`_ for excluding other set
## * `containsOrIncl proc <#containsOrIncl,IntSet,int>`_
runnableExamples:
var a = initIntSet()
a.incl(5)
assert a.missingOrExcl(5) == false
assert a.missingOrExcl(5) == true
var count = s.len
exclImpl(s, key)
result = count == s.len
proc clear*(result: var IntSet) =
## Clears the IntSet back to an empty state.
runnableExamples:
var a = initIntSet()
a.incl(5)
a.incl(7)
clear(a)
assert len(a) == 0
# setLen(result.data, InitIntSetSize)
# for i in 0..InitIntSetSize-1: result.data[i] = nil
# result.max = InitIntSetSize-1
when defined(nimNoNilSeqs):
result.data = @[]
else:
result.data = nil
result.max = 0
result.counter = 0
result.head = nil
result.elems = 0
proc isNil*(x: IntSet): bool {.inline.} = x.head.isNil and x.elems == 0
proc assign*(dest: var IntSet, src: IntSet) =
## Copies `src` to `dest`.
## `dest` does not need to be initialized by `initIntSet proc <#initIntSet>`_.
runnableExamples:
var
a = initIntSet()
b = initIntSet()
b.incl(5)
b.incl(7)
a.assign(b)
assert len(a) == 2
if src.elems <= src.a.len:
when defined(nimNoNilSeqs):
dest.data = @[]
else:
dest.data = nil
dest.max = 0
dest.counter = src.counter
dest.head = nil
dest.elems = src.elems
dest.a = src.a
else:
dest.counter = src.counter
dest.max = src.max
dest.elems = src.elems
newSeq(dest.data, src.data.len)
var it = src.head
while it != nil:
var h = it.key and dest.max
var perturb = it.key
while dest.data[h] != nil: h = nextTry(h, dest.max, perturb)
assert(dest.data[h] == nil)
var n: PTrunk
new(n)
n.next = dest.head
n.key = it.key
n.bits = it.bits
dest.head = n
dest.data[h] = n
it = it.next
proc union*(s1, s2: IntSet): IntSet =
## Returns the union of the sets `s1` and `s2`.
##
## The same as `s1 + s2 <#+,IntSet,IntSet>`_.
runnableExamples:
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}
result.assign(s1)
incl(result, s2)
proc intersection*(s1, s2: IntSet): IntSet =
## Returns the intersection of the sets `s1` and `s2`.
##
## The same as `s1 * s2 <#*,IntSet,IntSet>`_.
runnableExamples:
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}
result = initIntSet()
for item in s1:
if contains(s2, item):
incl(result, item)
proc difference*(s1, s2: IntSet): IntSet =
## Returns the difference of the sets `s1` and `s2`.
##
## The same as `s1 - s2 <#-,IntSet,IntSet>`_.
runnableExamples:
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}
result = initIntSet()
for item in s1:
if not contains(s2, item):
incl(result, item)
proc symmetricDifference*(s1, s2: IntSet): IntSet =
## Returns the symmetric difference of the sets `s1` and `s2`.
runnableExamples:
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}
result.assign(s1)
for item in s2:
if containsOrIncl(result, item): excl(result, item)
proc `+`*(s1, s2: IntSet): IntSet {.inline.} =
## Alias for `union(s1, s2) <#union,IntSet,IntSet>`_.
result = union(s1, s2)
proc `*`*(s1, s2: IntSet): IntSet {.inline.} =
## Alias for `intersection(s1, s2) <#intersection,IntSet,IntSet>`_.
result = intersection(s1, s2)
proc `-`*(s1, s2: IntSet): IntSet {.inline.} =
## Alias for `difference(s1, s2) <#difference,IntSet,IntSet>`_.
result = difference(s1, s2)
proc disjoint*(s1, s2: IntSet): bool =
## Returns true if the sets `s1` and `s2` have no items in common.
runnableExamples:
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
for item in s1:
if contains(s2, item):
return false
return true
proc card*(s: IntSet): int {.inline.} =
## Alias for `len() <#len,IntSet>`_.
result = s.len()
proc `<=`*(s1, s2: IntSet): bool =
## 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`.
runnableExamples:
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))
for item in s1:
if not s2.contains(item):
return false
return true
proc `<`*(s1, s2: IntSet): bool =
## 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`.
runnableExamples:
var
a = initIntSet()
b = initIntSet()
a.incl(1)
b.incl(1); b.incl(2)
assert a < b
a.incl(2)
assert(not (a < b))
return s1 <= s2 and not (s2 <= s1)
proc `==`*(s1, s2: IntSet): bool =
## Returns true if both `s1` and `s2` have the same elements and set size.
return s1 <= s2 and s2 <= s1
proc `$`*(s: IntSet): string =
## The `$` operator for int sets.
##
## Converts the set `s` to a string, mostly for logging and printing purposes.
dollarImpl()
when isMainModule:
import sequtils, algorithm
var x = initIntSet()
x.incl(1)
x.incl(2)
x.incl(7)
x.incl(1056)
x.incl(1044)
x.excl(1044)
assert x.containsOrIncl(888) == false
assert 888 in x
assert x.containsOrIncl(888) == true
assert x.missingOrExcl(888) == false
assert 888 notin x
assert x.missingOrExcl(888) == true
var xs = toSeq(items(x))
xs.sort(cmp[int])
assert xs == @[1, 2, 7, 1056]
var y: IntSet
assign(y, x)
var ys = toSeq(items(y))
ys.sort(cmp[int])
assert ys == @[1, 2, 7, 1056]
assert x == y
var z: IntSet
for i in 0..1000:
incl z, i
assert z.len() == i+1
for i in 0..1000:
assert z.contains(i)
var w = initIntSet()
w.incl(1)
w.incl(4)
w.incl(50)
w.incl(1001)
w.incl(1056)
var xuw = x.union(w)
var xuws = toSeq(items(xuw))
xuws.sort(cmp[int])
assert xuws == @[1, 2, 4, 7, 50, 1001, 1056]
var xiw = x.intersection(w)
var xiws = toSeq(items(xiw))
xiws.sort(cmp[int])
assert xiws == @[1, 1056]
var xdw = x.difference(w)
var xdws = toSeq(items(xdw))
xdws.sort(cmp[int])
assert xdws == @[2, 7]
var xsw = x.symmetricDifference(w)
var xsws = toSeq(items(xsw))
xsws.sort(cmp[int])
assert xsws == @[2, 4, 7, 50, 1001]
x.incl(w)
xs = toSeq(items(x))
xs.sort(cmp[int])
assert xs == @[1, 2, 4, 7, 50, 1001, 1056]
assert w <= x
assert w < x
assert(not disjoint(w, x))
var u = initIntSet()
u.incl(3)
u.incl(5)
u.incl(500)
assert disjoint(u, x)
var v = initIntSet()
v.incl(2)
v.incl(50)
x.excl(v)
xs = toSeq(items(x))
xs.sort(cmp[int])
assert xs == @[1, 4, 7, 1001, 1056]
proc bug12366 =
var
x = initIntSet()
y = initIntSet()
n = 3584
for i in 0..n:
x.incl(i)
y.incl(i)
let z = symmetricDifference(x, y)
doAssert z.len == 0
doAssert $z == "{}"
bug12366()