1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
|
import strutils
type
PNode[T,D] = ref TNode[T,D]
TItem {.acyclic, pure, final, shallow.} [T,D] = object
key: T
value: D
node: PNode[T,D]
when not (D is string):
val_set: Bool
TItems[T,D] = seq[ref TItem[T,D]]
TNode {.acyclic, pure, final, shallow.} [T,D] = object
slots: TItems[T,D]
left: PNode[T,D]
count: Int32
RPath[T,D] = tuple[
Xi: Int,
Nd: PNode[T,D] ]
const
cLen1 = 2
cLen2 = 16
cLen3 = 32
cLenCenter = 80
clen4 = 96
cLenMax = 128
cCenter = cLenMax div 2
proc len[T,D] (n:PNode[T,D]): Int {.inline.} =
return n.Count
proc clean[T: TOrdinal|TNumber](o: var T) {.inline.} = nil
proc clean[T: string|seq](o: var T) {.inline.} =
o = nil
proc clean[T,D] (o: ref TItem[T,D]) {.inline.} =
when (D is string) :
o.Value = nil
else :
o.val_set = false
proc isClean[T,D] (it: ref TItem[T,D]): Bool {.inline.} =
when (D is string) :
return it.Value == nil
else :
return not it.val_set
proc isClean[T,D] (n: PNode[T,D], x: Int): Bool {.inline.} =
when (D is string) :
return n.slots[x].Value == nil
else :
return not n.slots[x].val_set
proc setItem[T,D] (AKey: T, AValue: D, ANode: PNode[T,D]): ref TItem[T,D] {.inline.} =
new(Result)
Result.Key = AKey
Result.Value = AValue
Result.Node = ANode
when not (D is string) :
Result.val_set = true
proc cmp[T:Int8|Int16|Int32|Int64|Int] (a,b: T): T {.inline.} =
return a-b
template binSearchImpl *(docmp: expr) {.immediate.} =
var bFound = false
result = 0
var H = haystack.len -1
while result <= H :
var I {.inject.} = (result + H) shr 1
var SW = docmp
if SW < 0: result = I + 1
else:
H = I - 1
if SW == 0 : bFound = True
if bFound: inc(result)
else: result = - result
proc bSearch[T,D] (haystack: PNode[T,D], needle:T): Int {.inline.} =
binSearchImpl(haystack.slots[I].key.cmp(needle))
proc DeleteItem[T,D] (n: PNode[T,D], x: Int): PNode[T,D] {.inline.} =
var w = n.slots[x]
if w.Node != nil :
clean(w)
return n
dec(n.Count)
if n.Count > 0 :
for i in countup(x, n.Count -1) : n.slots[i] = n.slots[i + 1]
n.slots[n.Count] = nil
case n.Count
of cLen1 : setLen(n.slots, cLen1)
of cLen2 : setLen(n.slots, cLen2)
of cLen3 : setLen(n.slots, cLen3)
of cLenCenter : setLen(n.slots, cLenCenter)
of cLen4 : setLen(n.slots, cLen4)
else: nil
Result = n
else :
Result = n.Left
n.slots = nil
n.Left = nil
proc InternalDelete[T,D] (ANode: PNode[T,D], key: T, AValue: var D): PNode[T,D] =
var Path: array[0..20, RPath[T,D]]
var n = ANode
Result = n
clean(AValue)
var h = 0
while n != nil:
var x = bSearch(n, key)
if x <= 0 :
Path[h].Nd = n
Path[h].Xi = - x
inc(h)
if x == 0 :
n = n.Left
else :
x = (-x) -1
if x < n.Count :
n = n.slots[x].Node
else :
n = nil
else :
dec(x)
if isClean(n, x) : return
AValue = n.slots[x].Value
var n2 = DeleteItem(n, x)
dec(h)
while (n2 != n) and (h >=0) :
n = n2
var w = addr Path[h]
x = w.Xi -1
if x >= 0 :
if (n == nil) and isClean(w.Nd, x) :
n = w.Nd
n.slots[x].Node = nil
n2 = DeleteItem(n, x)
else :
w.Nd.slots[x].Node = n
return
else :
w.Nd.Left = n
return
dec(h)
if h < 0:
Result = n2
return
proc InternalFind[T,D] (n: PNode[T,D], key: T): ref TItem[T,D] {.inline.} =
var wn = n
while wn != nil :
var x = bSearch(wn, key)
if x <= 0 :
if x == 0 :
wn = wn.Left
else :
x = (-x) -1
if x < wn.Count :
wn = wn.slots[x].Node
else :
return nil
else :
return wn.slots[x - 1]
return nil
proc traceTree[T,D](root: PNode[T,D]) =
proc traceX(x: Int) =
write stdout, "("
write stdout, x
write stdout, ") "
proc traceEl(el: ref TItem[T,D]) =
write stdout, " key: "
write stdout, el.Key
write stdout, " value: "
write stdout, el.Value
proc traceln(space: string) =
writeln stdout, ""
write stdout, space
proc doTrace(n: PNode[T,D], level: Int) =
var space = repeatChar(2 * level)
traceln(space)
write stdout, "node: "
if n == nil:
writeln stdout, "is empty"
return
write stdout, n.Count
write stdout, " elements: "
if n.Left != nil:
traceln(space)
write stdout, "left: "
doTrace(n.left, level +1)
for i, el in n.slots :
if el != nil and not isClean(el):
traceln(space)
traceX(i)
if i >= n.Count:
write stdout, "error "
else:
traceEl(el)
if el.Node != nil: doTrace(el.Node, level +1)
else : write stdout, " empty "
elif i < n.Count :
traceln(space)
traceX(i)
write stdout, "clean: "
when T is string :
if el.Key != nil: write stdout, el.Key
else : write stdout, el.Key
if el.Node != nil: doTrace(el.Node, level +1)
else : write stdout, " empty "
writeln stdout,""
doTrace(root, 0)
proc InsertItem[T,D](APath: RPath[T,D], ANode:PNode[T,D], AKey: T, AValue: D) =
var x = - APath.Xi
inc(APath.Nd.Count)
case APath.Nd.Count
of cLen1: setLen(APath.Nd.slots, cLen2)
of cLen2: setLen(APath.Nd.slots, cLen3)
of cLen3: setLen(APath.Nd.slots, cLenCenter)
of cLenCenter: setLen(APath.Nd.slots, cLen4)
of cLen4: setLen(APath.Nd.slots, cLenMax)
else: nil
for i in countdown(APath.Nd.Count.int - 1, x + 1): shallowCopy(APath.Nd.slots[i], APath.Nd.slots[i - 1])
APath.Nd.slots[x] = setItem(AKey, AValue, ANode)
proc SplitPage[T,D](n, left: PNode[T,D], xi: Int, AKey:var T, AValue:var D): PNode[T,D] =
var x = -Xi
var it1: TItems[T,D]
it1.newSeq(cLenCenter)
new(Result)
Result.slots.newSeq(cLenCenter)
Result.Count = cCenter
if x == cCenter:
for i in 0..cCenter -1: shallowCopy(it1[i], left.slots[i])
for i in 0..cCenter -1: shallowCopy(Result.slots[i], left.slots[cCenter + i])
Result.Left = n
else :
if x < cCenter :
for i in 0..x-1: shallowCopy(it1[i], left.slots[i])
it1[x] = setItem(AKey, AValue, n)
for i in x+1 .. cCenter -1: shallowCopy(it1[i], left.slots[i-1])
var w = left.slots[cCenter -1]
AKey = w.Key
AValue = w.Value
Result.Left = w.Node
for i in 0..cCenter -1: shallowCopy(Result.slots[i], left.slots[cCenter + i])
else :
for i in 0..cCenter -1: shallowCopy(it1[i], left.slots[i])
x = x - (cCenter + 1)
for i in 0..x-1: shallowCopy(Result.slots[i], left.slots[cCenter + i + 1])
Result.slots[x] = setItem(AKey, AValue, n)
for i in x+1 .. cCenter -1: shallowCopy(Result.slots[i], left.slots[cCenter + i])
var w = left.slots[cCenter]
AKey = w.Key
AValue = w.Value
Result.Left = w.Node
left.Count = cCenter
shallowCopy(left.slots, it1)
proc InternalPut[T,D](ANode: ref TNode[T,D], AKey: T, AValue: D, OldValue: var D): ref TNode[T,D] =
var h: Int
var Path: array[0..30, RPath[T,D]]
var left: PNode[T,D]
var n = ANode
Result = ANode
h = 0
while n != nil:
var x = bSearch[T,D](n, AKey)
if x <= 0 :
Path[h].Nd = n
Path[h].Xi = x
inc(h)
if x == 0 :
n = n.Left
else :
x = (-x) -1
if x < n.Count :
n = n.slots[x].Node
else :
n = nil
else :
var w = n.slots[x - 1]
OldValue = w.Value
w.Value = AValue
return
dec(h)
left = nil
var lKey = AKey
var lValue = AValue
while h >= 0 :
if Path[h].Nd.Count < cLenMax :
InsertItem(Path[h], n, lKey, lValue)
return
else :
left = Path[h].Nd
n = SplitPage(n, left, Path[h].Xi, lKey, lValue)
dec(h)
new(Result)
Result.slots.newSeq(cLen1)
Result.Count = 1
Result.Left = left
Result.slots[0] = setItem(lKey, lValue, n)
proc CleanTree[T,D](n: PNode[T,D]): PNode[T,D] =
if n.Left != nil :
n.Left = CleanTree(n.Left)
for i in 0 .. n.Count - 1 :
var w = n.slots[i]
if w.Node != nil :
w.Node = CleanTree(w.Node)
clean(w.Value)
clean(w.Key)
n.slots = nil
return nil
proc VisitAllNodes[T,D](n: PNode[T,D], visit: proc(n: PNode[T,D]): PNode[T,D] {.closure.} ): PNode[T,D] =
if n != nil :
if n.Left != nil :
n.Left = VisitAllNodes(n.Left, visit)
for i in 0 .. n.Count - 1 :
var w = n.slots[i]
if w.Node != nil :
w.Node = VisitAllNodes(w.Node, visit)
return visit(n)
return nil
proc VisitAllNodes[T,D](n: PNode[T,D], visit: proc(n: PNode[T,D]) {.closure.} ) =
if n != nil:
if n.Left != nil :
VisitAllNodes(n.Left, visit)
for i in 0 .. n.Count - 1 :
var w = n.slots[i]
if w.Node != nil :
VisitAllNodes(w.Node, visit)
visit(n)
proc VisitAll[T,D](n: PNode[T,D], visit: proc(AKey: T, AValue: D) {.closure.} ) =
if n != nil:
if n.Left != nil :
VisitAll(n.Left, visit)
for i in 0 .. n.Count - 1 :
var w = n.slots[i]
if not w.isClean :
visit(w.Key, w.Value)
if w.Node != nil :
VisitAll(w.Node, visit)
proc VisitAll[T,D](n: PNode[T,D], visit: proc(AKey: T, AValue: var D):Bool {.closure.} ): PNode[T,D] =
if n != nil:
var n1 = n.Left
if n1 != nil :
var n2 = VisitAll(n1, visit)
if n1 != n2 :
n.Left = n2
var i = 0
while i < n.Count :
var w = n.slots[i]
if not w.isClean :
if visit(w.Key, w.Value) :
Result = DeleteItem(n, i)
if Result == nil : return
dec(i)
n1 = w.Node
if n1 != nil :
var n2 = VisitAll(n1, visit)
if n1 != n2 :
w.Node = n2
inc(i)
return n
iterator keys* [T,D] (n: PNode[T,D]): T =
if n != nil :
var Path: array[0..20, RPath[T,D]]
var level = 0
var nd = n
var i = -1
while true :
if i < nd.Count :
Path[level].Nd = nd
Path[level].Xi = i
if i < 0 :
if nd.Left != nil :
nd = nd.Left
inc(level)
else : inc(i)
else :
var w = nd.slots[i]
if not w.isClean() :
yield w.Key
if w.Node != nil :
nd = w.Node
i = -1
inc(level)
else : inc(i)
else :
dec(level)
if level < 0 : break
nd = Path[level].Nd
i = Path[level].Xi
inc(i)
when isMainModule:
proc test() =
var oldValue: Int
var root = InternalPut[int, int](nil, 312, 312, oldValue)
var someOtherRoot = InternalPut[string, int](nil, "312", 312, oldValue)
var it1 = InternalFind(root, 312)
echo it1.Value
for i in 1..1_000_000:
root = InternalPut(root, i, i, oldValue)
var cnt = 0
oldValue = -1
when true : # code compiles, when this or the other when is switched to false
for k in root.keys :
if k <= oldValue :
echo k
oldValue = k
inc(cnt)
echo cnt
when true :
cnt = 0
VisitAll(root, proc(key, val: int) = inc(cnt))
echo cnt
when true :
root = VisitAll(root, proc(key: int, value: var int): bool =
return key mod 2 == 0 )
cnt = 0
oldValue = -1
VisitAll(root, proc(key: int, value: int) {.closure.} =
if key <= oldValue :
echo key
oldValue = key
inc(cnt) )
echo cnt
root = VisitAll(root, proc(key: int, value: var int): bool =
return key mod 2 != 0 )
cnt = 0
oldValue = -1
VisitAll(root, proc(key: int, value: int) {.closure.} =
if key <= oldValue :
echo "error ", key
oldValue = key
inc(cnt) )
echo cnt
#traceTree(root)
test()
|