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#
#
# The Nim Compiler
# (c) Copyright 2018 Andreas Rumpf
#
# See the file "copying.txt", included in this
# distribution, for details about the copyright.
#
## BTree implementation with few features, but good enough for the
## Nim compiler's needs.
when defined(nimPreviewSlimSystem):
import std/assertions
const
M = 512 # max children per B-tree node = M-1
# (must be even and greater than 2)
Mhalf = M div 2
type
Node[Key, Val] {.acyclic.} = ref object
entries: int
keys: array[M, Key]
case isInternal: bool
of false:
vals: array[M, Val]
of true:
links: array[M, Node[Key, Val]]
BTree*[Key, Val] = object
root: Node[Key, Val]
entries: int ## number of key-value pairs
proc initBTree*[Key, Val](): BTree[Key, Val] =
BTree[Key, Val](root: Node[Key, Val](entries: 0, isInternal: false))
template less(a, b): bool = cmp(a, b) < 0
template eq(a, b): bool = cmp(a, b) == 0
proc getOrDefault*[Key, Val](b: BTree[Key, Val], key: Key): Val =
result = default(Val)
var x = b.root
while x.isInternal:
for j in 0..<x.entries:
if j+1 == x.entries or less(key, x.keys[j+1]):
x = x.links[j]
break
assert(not x.isInternal)
for j in 0..<x.entries:
if eq(key, x.keys[j]): return x.vals[j]
proc contains*[Key, Val](b: BTree[Key, Val], key: Key): bool =
var x = b.root
while x.isInternal:
for j in 0..<x.entries:
if j+1 == x.entries or less(key, x.keys[j+1]):
x = x.links[j]
break
assert(not x.isInternal)
for j in 0..<x.entries:
if eq(key, x.keys[j]): return true
return false
proc copyHalf[Key, Val](h, result: Node[Key, Val]) =
for j in 0..<Mhalf:
result.keys[j] = h.keys[Mhalf + j]
if h.isInternal:
for j in 0..<Mhalf:
result.links[j] = h.links[Mhalf + j]
else:
for j in 0..<Mhalf:
when defined(gcArc) or defined(gcOrc) or defined(gcAtomicArc):
result.vals[j] = move h.vals[Mhalf + j]
else:
shallowCopy(result.vals[j], h.vals[Mhalf + j])
proc split[Key, Val](h: Node[Key, Val]): Node[Key, Val] =
## split node in half
result = Node[Key, Val](entries: Mhalf, isInternal: h.isInternal)
h.entries = Mhalf
copyHalf(h, result)
proc insert[Key, Val](h: Node[Key, Val], key: Key, val: Val): Node[Key, Val] =
#var t = Entry(key: key, val: val, next: nil)
var newKey = key
var j = 0
if not h.isInternal:
while j < h.entries:
if eq(key, h.keys[j]):
h.vals[j] = val
return
if less(key, h.keys[j]): break
inc j
for i in countdown(h.entries, j+1):
when defined(gcArc) or defined(gcOrc) or defined(gcAtomicArc):
h.vals[i] = move h.vals[i-1]
else:
shallowCopy(h.vals[i], h.vals[i-1])
h.vals[j] = val
else:
var newLink: Node[Key, Val] = nil
while j < h.entries:
if j+1 == h.entries or less(key, h.keys[j+1]):
let u = insert(h.links[j], key, val)
inc j
if u == nil: return nil
newKey = u.keys[0]
newLink = u
break
inc j
for i in countdown(h.entries, j+1):
h.links[i] = h.links[i-1]
h.links[j] = newLink
for i in countdown(h.entries, j+1):
h.keys[i] = h.keys[i-1]
h.keys[j] = newKey
inc h.entries
return if h.entries < M: nil else: split(h)
proc add*[Key, Val](b: var BTree[Key, Val]; key: Key; val: Val) =
let u = insert(b.root, key, val)
inc b.entries
if u == nil: return
# need to split root
let t = Node[Key, Val](entries: 2, isInternal: true)
t.keys[0] = b.root.keys[0]
t.links[0] = b.root
t.keys[1] = u.keys[0]
t.links[1] = u
b.root = t
proc toString[Key, Val](h: Node[Key, Val], indent: string; result: var string) =
if not h.isInternal:
for j in 0..<h.entries:
result.add(indent)
result.add($h.keys[j] & " " & $h.vals[j] & "\n")
else:
for j in 0..<h.entries:
if j > 0: result.add(indent & "(" & $h.keys[j] & ")\n")
toString(h.links[j], indent & " ", result)
proc `$`[Key, Val](b: BTree[Key, Val]): string =
result = ""
toString(b.root, "", result)
proc hasNext*[Key, Val](b: BTree[Key, Val]; index: int): bool = index < b.entries
proc countSubTree[Key, Val](it: Node[Key, Val]): int =
if it.isInternal:
result = 0
for k in 0..<it.entries:
inc result, countSubTree(it.links[k])
else:
result = it.entries
proc next*[Key, Val](b: BTree[Key, Val]; index: int): (Key, Val, int) =
var it = b.root
var i = index
# navigate to the right leaf:
while it.isInternal:
var sum = 0
for k in 0..<it.entries:
let c = countSubTree(it.links[k])
inc sum, c
if sum > i:
it = it.links[k]
dec i, (sum - c)
break
result = (it.keys[i], it.vals[i], index+1)
iterator pairs*[Key, Val](b: BTree[Key, Val]): (Key, Val) =
var i = 0
while hasNext(b, i):
let (k, v, i2) = next(b, i)
i = i2
yield (k, v)
proc len*[Key, Val](b: BTree[Key, Val]): int {.inline.} = b.entries
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