khenaidoo | ffe076b | 2019-01-15 16:08:08 -0500 | [diff] [blame^] | 1 | // Copyright 2016 The etcd Authors |
| 2 | // |
| 3 | // Licensed under the Apache License, Version 2.0 (the "License"); |
| 4 | // you may not use this file except in compliance with the License. |
| 5 | // You may obtain a copy of the License at |
| 6 | // |
| 7 | // http://www.apache.org/licenses/LICENSE-2.0 |
| 8 | // |
| 9 | // Unless required by applicable law or agreed to in writing, software |
| 10 | // distributed under the License is distributed on an "AS IS" BASIS, |
| 11 | // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| 12 | // See the License for the specific language governing permissions and |
| 13 | // limitations under the License. |
| 14 | |
| 15 | package adt |
| 16 | |
| 17 | import ( |
| 18 | "bytes" |
| 19 | "math" |
| 20 | ) |
| 21 | |
| 22 | // Comparable is an interface for trichotomic comparisons. |
| 23 | type Comparable interface { |
| 24 | // Compare gives the result of a 3-way comparison |
| 25 | // a.Compare(b) = 1 => a > b |
| 26 | // a.Compare(b) = 0 => a == b |
| 27 | // a.Compare(b) = -1 => a < b |
| 28 | Compare(c Comparable) int |
| 29 | } |
| 30 | |
| 31 | type rbcolor int |
| 32 | |
| 33 | const ( |
| 34 | black rbcolor = iota |
| 35 | red |
| 36 | ) |
| 37 | |
| 38 | // Interval implements a Comparable interval [begin, end) |
| 39 | // TODO: support different sorts of intervals: (a,b), [a,b], (a, b] |
| 40 | type Interval struct { |
| 41 | Begin Comparable |
| 42 | End Comparable |
| 43 | } |
| 44 | |
| 45 | // Compare on an interval gives == if the interval overlaps. |
| 46 | func (ivl *Interval) Compare(c Comparable) int { |
| 47 | ivl2 := c.(*Interval) |
| 48 | ivbCmpBegin := ivl.Begin.Compare(ivl2.Begin) |
| 49 | ivbCmpEnd := ivl.Begin.Compare(ivl2.End) |
| 50 | iveCmpBegin := ivl.End.Compare(ivl2.Begin) |
| 51 | |
| 52 | // ivl is left of ivl2 |
| 53 | if ivbCmpBegin < 0 && iveCmpBegin <= 0 { |
| 54 | return -1 |
| 55 | } |
| 56 | |
| 57 | // iv is right of iv2 |
| 58 | if ivbCmpEnd >= 0 { |
| 59 | return 1 |
| 60 | } |
| 61 | |
| 62 | return 0 |
| 63 | } |
| 64 | |
| 65 | type intervalNode struct { |
| 66 | // iv is the interval-value pair entry. |
| 67 | iv IntervalValue |
| 68 | // max endpoint of all descendent nodes. |
| 69 | max Comparable |
| 70 | // left and right are sorted by low endpoint of key interval |
| 71 | left, right *intervalNode |
| 72 | // parent is the direct ancestor of the node |
| 73 | parent *intervalNode |
| 74 | c rbcolor |
| 75 | } |
| 76 | |
| 77 | func (x *intervalNode) color() rbcolor { |
| 78 | if x == nil { |
| 79 | return black |
| 80 | } |
| 81 | return x.c |
| 82 | } |
| 83 | |
| 84 | func (n *intervalNode) height() int { |
| 85 | if n == nil { |
| 86 | return 0 |
| 87 | } |
| 88 | ld := n.left.height() |
| 89 | rd := n.right.height() |
| 90 | if ld < rd { |
| 91 | return rd + 1 |
| 92 | } |
| 93 | return ld + 1 |
| 94 | } |
| 95 | |
| 96 | func (x *intervalNode) min() *intervalNode { |
| 97 | for x.left != nil { |
| 98 | x = x.left |
| 99 | } |
| 100 | return x |
| 101 | } |
| 102 | |
| 103 | // successor is the next in-order node in the tree |
| 104 | func (x *intervalNode) successor() *intervalNode { |
| 105 | if x.right != nil { |
| 106 | return x.right.min() |
| 107 | } |
| 108 | y := x.parent |
| 109 | for y != nil && x == y.right { |
| 110 | x = y |
| 111 | y = y.parent |
| 112 | } |
| 113 | return y |
| 114 | } |
| 115 | |
| 116 | // updateMax updates the maximum values for a node and its ancestors |
| 117 | func (x *intervalNode) updateMax() { |
| 118 | for x != nil { |
| 119 | oldmax := x.max |
| 120 | max := x.iv.Ivl.End |
| 121 | if x.left != nil && x.left.max.Compare(max) > 0 { |
| 122 | max = x.left.max |
| 123 | } |
| 124 | if x.right != nil && x.right.max.Compare(max) > 0 { |
| 125 | max = x.right.max |
| 126 | } |
| 127 | if oldmax.Compare(max) == 0 { |
| 128 | break |
| 129 | } |
| 130 | x.max = max |
| 131 | x = x.parent |
| 132 | } |
| 133 | } |
| 134 | |
| 135 | type nodeVisitor func(n *intervalNode) bool |
| 136 | |
| 137 | // visit will call a node visitor on each node that overlaps the given interval |
| 138 | func (x *intervalNode) visit(iv *Interval, nv nodeVisitor) bool { |
| 139 | if x == nil { |
| 140 | return true |
| 141 | } |
| 142 | v := iv.Compare(&x.iv.Ivl) |
| 143 | switch { |
| 144 | case v < 0: |
| 145 | if !x.left.visit(iv, nv) { |
| 146 | return false |
| 147 | } |
| 148 | case v > 0: |
| 149 | maxiv := Interval{x.iv.Ivl.Begin, x.max} |
| 150 | if maxiv.Compare(iv) == 0 { |
| 151 | if !x.left.visit(iv, nv) || !x.right.visit(iv, nv) { |
| 152 | return false |
| 153 | } |
| 154 | } |
| 155 | default: |
| 156 | if !x.left.visit(iv, nv) || !nv(x) || !x.right.visit(iv, nv) { |
| 157 | return false |
| 158 | } |
| 159 | } |
| 160 | return true |
| 161 | } |
| 162 | |
| 163 | type IntervalValue struct { |
| 164 | Ivl Interval |
| 165 | Val interface{} |
| 166 | } |
| 167 | |
| 168 | // IntervalTree represents a (mostly) textbook implementation of the |
| 169 | // "Introduction to Algorithms" (Cormen et al, 2nd ed.) chapter 13 red-black tree |
| 170 | // and chapter 14.3 interval tree with search supporting "stabbing queries". |
| 171 | type IntervalTree struct { |
| 172 | root *intervalNode |
| 173 | count int |
| 174 | } |
| 175 | |
| 176 | // Delete removes the node with the given interval from the tree, returning |
| 177 | // true if a node is in fact removed. |
| 178 | func (ivt *IntervalTree) Delete(ivl Interval) bool { |
| 179 | z := ivt.find(ivl) |
| 180 | if z == nil { |
| 181 | return false |
| 182 | } |
| 183 | |
| 184 | y := z |
| 185 | if z.left != nil && z.right != nil { |
| 186 | y = z.successor() |
| 187 | } |
| 188 | |
| 189 | x := y.left |
| 190 | if x == nil { |
| 191 | x = y.right |
| 192 | } |
| 193 | if x != nil { |
| 194 | x.parent = y.parent |
| 195 | } |
| 196 | |
| 197 | if y.parent == nil { |
| 198 | ivt.root = x |
| 199 | } else { |
| 200 | if y == y.parent.left { |
| 201 | y.parent.left = x |
| 202 | } else { |
| 203 | y.parent.right = x |
| 204 | } |
| 205 | y.parent.updateMax() |
| 206 | } |
| 207 | if y != z { |
| 208 | z.iv = y.iv |
| 209 | z.updateMax() |
| 210 | } |
| 211 | |
| 212 | if y.color() == black && x != nil { |
| 213 | ivt.deleteFixup(x) |
| 214 | } |
| 215 | |
| 216 | ivt.count-- |
| 217 | return true |
| 218 | } |
| 219 | |
| 220 | func (ivt *IntervalTree) deleteFixup(x *intervalNode) { |
| 221 | for x != ivt.root && x.color() == black && x.parent != nil { |
| 222 | if x == x.parent.left { |
| 223 | w := x.parent.right |
| 224 | if w.color() == red { |
| 225 | w.c = black |
| 226 | x.parent.c = red |
| 227 | ivt.rotateLeft(x.parent) |
| 228 | w = x.parent.right |
| 229 | } |
| 230 | if w == nil { |
| 231 | break |
| 232 | } |
| 233 | if w.left.color() == black && w.right.color() == black { |
| 234 | w.c = red |
| 235 | x = x.parent |
| 236 | } else { |
| 237 | if w.right.color() == black { |
| 238 | w.left.c = black |
| 239 | w.c = red |
| 240 | ivt.rotateRight(w) |
| 241 | w = x.parent.right |
| 242 | } |
| 243 | w.c = x.parent.color() |
| 244 | x.parent.c = black |
| 245 | w.right.c = black |
| 246 | ivt.rotateLeft(x.parent) |
| 247 | x = ivt.root |
| 248 | } |
| 249 | } else { |
| 250 | // same as above but with left and right exchanged |
| 251 | w := x.parent.left |
| 252 | if w.color() == red { |
| 253 | w.c = black |
| 254 | x.parent.c = red |
| 255 | ivt.rotateRight(x.parent) |
| 256 | w = x.parent.left |
| 257 | } |
| 258 | if w == nil { |
| 259 | break |
| 260 | } |
| 261 | if w.left.color() == black && w.right.color() == black { |
| 262 | w.c = red |
| 263 | x = x.parent |
| 264 | } else { |
| 265 | if w.left.color() == black { |
| 266 | w.right.c = black |
| 267 | w.c = red |
| 268 | ivt.rotateLeft(w) |
| 269 | w = x.parent.left |
| 270 | } |
| 271 | w.c = x.parent.color() |
| 272 | x.parent.c = black |
| 273 | w.left.c = black |
| 274 | ivt.rotateRight(x.parent) |
| 275 | x = ivt.root |
| 276 | } |
| 277 | } |
| 278 | } |
| 279 | if x != nil { |
| 280 | x.c = black |
| 281 | } |
| 282 | } |
| 283 | |
| 284 | // Insert adds a node with the given interval into the tree. |
| 285 | func (ivt *IntervalTree) Insert(ivl Interval, val interface{}) { |
| 286 | var y *intervalNode |
| 287 | z := &intervalNode{iv: IntervalValue{ivl, val}, max: ivl.End, c: red} |
| 288 | x := ivt.root |
| 289 | for x != nil { |
| 290 | y = x |
| 291 | if z.iv.Ivl.Begin.Compare(x.iv.Ivl.Begin) < 0 { |
| 292 | x = x.left |
| 293 | } else { |
| 294 | x = x.right |
| 295 | } |
| 296 | } |
| 297 | |
| 298 | z.parent = y |
| 299 | if y == nil { |
| 300 | ivt.root = z |
| 301 | } else { |
| 302 | if z.iv.Ivl.Begin.Compare(y.iv.Ivl.Begin) < 0 { |
| 303 | y.left = z |
| 304 | } else { |
| 305 | y.right = z |
| 306 | } |
| 307 | y.updateMax() |
| 308 | } |
| 309 | z.c = red |
| 310 | ivt.insertFixup(z) |
| 311 | ivt.count++ |
| 312 | } |
| 313 | |
| 314 | func (ivt *IntervalTree) insertFixup(z *intervalNode) { |
| 315 | for z.parent != nil && z.parent.parent != nil && z.parent.color() == red { |
| 316 | if z.parent == z.parent.parent.left { |
| 317 | y := z.parent.parent.right |
| 318 | if y.color() == red { |
| 319 | y.c = black |
| 320 | z.parent.c = black |
| 321 | z.parent.parent.c = red |
| 322 | z = z.parent.parent |
| 323 | } else { |
| 324 | if z == z.parent.right { |
| 325 | z = z.parent |
| 326 | ivt.rotateLeft(z) |
| 327 | } |
| 328 | z.parent.c = black |
| 329 | z.parent.parent.c = red |
| 330 | ivt.rotateRight(z.parent.parent) |
| 331 | } |
| 332 | } else { |
| 333 | // same as then with left/right exchanged |
| 334 | y := z.parent.parent.left |
| 335 | if y.color() == red { |
| 336 | y.c = black |
| 337 | z.parent.c = black |
| 338 | z.parent.parent.c = red |
| 339 | z = z.parent.parent |
| 340 | } else { |
| 341 | if z == z.parent.left { |
| 342 | z = z.parent |
| 343 | ivt.rotateRight(z) |
| 344 | } |
| 345 | z.parent.c = black |
| 346 | z.parent.parent.c = red |
| 347 | ivt.rotateLeft(z.parent.parent) |
| 348 | } |
| 349 | } |
| 350 | } |
| 351 | ivt.root.c = black |
| 352 | } |
| 353 | |
| 354 | // rotateLeft moves x so it is left of its right child |
| 355 | func (ivt *IntervalTree) rotateLeft(x *intervalNode) { |
| 356 | y := x.right |
| 357 | x.right = y.left |
| 358 | if y.left != nil { |
| 359 | y.left.parent = x |
| 360 | } |
| 361 | x.updateMax() |
| 362 | ivt.replaceParent(x, y) |
| 363 | y.left = x |
| 364 | y.updateMax() |
| 365 | } |
| 366 | |
| 367 | // rotateLeft moves x so it is right of its left child |
| 368 | func (ivt *IntervalTree) rotateRight(x *intervalNode) { |
| 369 | if x == nil { |
| 370 | return |
| 371 | } |
| 372 | y := x.left |
| 373 | x.left = y.right |
| 374 | if y.right != nil { |
| 375 | y.right.parent = x |
| 376 | } |
| 377 | x.updateMax() |
| 378 | ivt.replaceParent(x, y) |
| 379 | y.right = x |
| 380 | y.updateMax() |
| 381 | } |
| 382 | |
| 383 | // replaceParent replaces x's parent with y |
| 384 | func (ivt *IntervalTree) replaceParent(x *intervalNode, y *intervalNode) { |
| 385 | y.parent = x.parent |
| 386 | if x.parent == nil { |
| 387 | ivt.root = y |
| 388 | } else { |
| 389 | if x == x.parent.left { |
| 390 | x.parent.left = y |
| 391 | } else { |
| 392 | x.parent.right = y |
| 393 | } |
| 394 | x.parent.updateMax() |
| 395 | } |
| 396 | x.parent = y |
| 397 | } |
| 398 | |
| 399 | // Len gives the number of elements in the tree |
| 400 | func (ivt *IntervalTree) Len() int { return ivt.count } |
| 401 | |
| 402 | // Height is the number of levels in the tree; one node has height 1. |
| 403 | func (ivt *IntervalTree) Height() int { return ivt.root.height() } |
| 404 | |
| 405 | // MaxHeight is the expected maximum tree height given the number of nodes |
| 406 | func (ivt *IntervalTree) MaxHeight() int { |
| 407 | return int((2 * math.Log2(float64(ivt.Len()+1))) + 0.5) |
| 408 | } |
| 409 | |
| 410 | // IntervalVisitor is used on tree searches; return false to stop searching. |
| 411 | type IntervalVisitor func(n *IntervalValue) bool |
| 412 | |
| 413 | // Visit calls a visitor function on every tree node intersecting the given interval. |
| 414 | // It will visit each interval [x, y) in ascending order sorted on x. |
| 415 | func (ivt *IntervalTree) Visit(ivl Interval, ivv IntervalVisitor) { |
| 416 | ivt.root.visit(&ivl, func(n *intervalNode) bool { return ivv(&n.iv) }) |
| 417 | } |
| 418 | |
| 419 | // find the exact node for a given interval |
| 420 | func (ivt *IntervalTree) find(ivl Interval) (ret *intervalNode) { |
| 421 | f := func(n *intervalNode) bool { |
| 422 | if n.iv.Ivl != ivl { |
| 423 | return true |
| 424 | } |
| 425 | ret = n |
| 426 | return false |
| 427 | } |
| 428 | ivt.root.visit(&ivl, f) |
| 429 | return ret |
| 430 | } |
| 431 | |
| 432 | // Find gets the IntervalValue for the node matching the given interval |
| 433 | func (ivt *IntervalTree) Find(ivl Interval) (ret *IntervalValue) { |
| 434 | n := ivt.find(ivl) |
| 435 | if n == nil { |
| 436 | return nil |
| 437 | } |
| 438 | return &n.iv |
| 439 | } |
| 440 | |
| 441 | // Intersects returns true if there is some tree node intersecting the given interval. |
| 442 | func (ivt *IntervalTree) Intersects(iv Interval) bool { |
| 443 | x := ivt.root |
| 444 | for x != nil && iv.Compare(&x.iv.Ivl) != 0 { |
| 445 | if x.left != nil && x.left.max.Compare(iv.Begin) > 0 { |
| 446 | x = x.left |
| 447 | } else { |
| 448 | x = x.right |
| 449 | } |
| 450 | } |
| 451 | return x != nil |
| 452 | } |
| 453 | |
| 454 | // Contains returns true if the interval tree's keys cover the entire given interval. |
| 455 | func (ivt *IntervalTree) Contains(ivl Interval) bool { |
| 456 | var maxEnd, minBegin Comparable |
| 457 | |
| 458 | isContiguous := true |
| 459 | ivt.Visit(ivl, func(n *IntervalValue) bool { |
| 460 | if minBegin == nil { |
| 461 | minBegin = n.Ivl.Begin |
| 462 | maxEnd = n.Ivl.End |
| 463 | return true |
| 464 | } |
| 465 | if maxEnd.Compare(n.Ivl.Begin) < 0 { |
| 466 | isContiguous = false |
| 467 | return false |
| 468 | } |
| 469 | if n.Ivl.End.Compare(maxEnd) > 0 { |
| 470 | maxEnd = n.Ivl.End |
| 471 | } |
| 472 | return true |
| 473 | }) |
| 474 | |
| 475 | return isContiguous && minBegin != nil && maxEnd.Compare(ivl.End) >= 0 && minBegin.Compare(ivl.Begin) <= 0 |
| 476 | } |
| 477 | |
| 478 | // Stab returns a slice with all elements in the tree intersecting the interval. |
| 479 | func (ivt *IntervalTree) Stab(iv Interval) (ivs []*IntervalValue) { |
| 480 | if ivt.count == 0 { |
| 481 | return nil |
| 482 | } |
| 483 | f := func(n *IntervalValue) bool { ivs = append(ivs, n); return true } |
| 484 | ivt.Visit(iv, f) |
| 485 | return ivs |
| 486 | } |
| 487 | |
| 488 | // Union merges a given interval tree into the receiver. |
| 489 | func (ivt *IntervalTree) Union(inIvt IntervalTree, ivl Interval) { |
| 490 | f := func(n *IntervalValue) bool { |
| 491 | ivt.Insert(n.Ivl, n.Val) |
| 492 | return true |
| 493 | } |
| 494 | inIvt.Visit(ivl, f) |
| 495 | } |
| 496 | |
| 497 | type StringComparable string |
| 498 | |
| 499 | func (s StringComparable) Compare(c Comparable) int { |
| 500 | sc := c.(StringComparable) |
| 501 | if s < sc { |
| 502 | return -1 |
| 503 | } |
| 504 | if s > sc { |
| 505 | return 1 |
| 506 | } |
| 507 | return 0 |
| 508 | } |
| 509 | |
| 510 | func NewStringInterval(begin, end string) Interval { |
| 511 | return Interval{StringComparable(begin), StringComparable(end)} |
| 512 | } |
| 513 | |
| 514 | func NewStringPoint(s string) Interval { |
| 515 | return Interval{StringComparable(s), StringComparable(s + "\x00")} |
| 516 | } |
| 517 | |
| 518 | // StringAffineComparable treats "" as > all other strings |
| 519 | type StringAffineComparable string |
| 520 | |
| 521 | func (s StringAffineComparable) Compare(c Comparable) int { |
| 522 | sc := c.(StringAffineComparable) |
| 523 | |
| 524 | if len(s) == 0 { |
| 525 | if len(sc) == 0 { |
| 526 | return 0 |
| 527 | } |
| 528 | return 1 |
| 529 | } |
| 530 | if len(sc) == 0 { |
| 531 | return -1 |
| 532 | } |
| 533 | |
| 534 | if s < sc { |
| 535 | return -1 |
| 536 | } |
| 537 | if s > sc { |
| 538 | return 1 |
| 539 | } |
| 540 | return 0 |
| 541 | } |
| 542 | |
| 543 | func NewStringAffineInterval(begin, end string) Interval { |
| 544 | return Interval{StringAffineComparable(begin), StringAffineComparable(end)} |
| 545 | } |
| 546 | func NewStringAffinePoint(s string) Interval { |
| 547 | return NewStringAffineInterval(s, s+"\x00") |
| 548 | } |
| 549 | |
| 550 | func NewInt64Interval(a int64, b int64) Interval { |
| 551 | return Interval{Int64Comparable(a), Int64Comparable(b)} |
| 552 | } |
| 553 | |
| 554 | func NewInt64Point(a int64) Interval { |
| 555 | return Interval{Int64Comparable(a), Int64Comparable(a + 1)} |
| 556 | } |
| 557 | |
| 558 | type Int64Comparable int64 |
| 559 | |
| 560 | func (v Int64Comparable) Compare(c Comparable) int { |
| 561 | vc := c.(Int64Comparable) |
| 562 | cmp := v - vc |
| 563 | if cmp < 0 { |
| 564 | return -1 |
| 565 | } |
| 566 | if cmp > 0 { |
| 567 | return 1 |
| 568 | } |
| 569 | return 0 |
| 570 | } |
| 571 | |
| 572 | // BytesAffineComparable treats empty byte arrays as > all other byte arrays |
| 573 | type BytesAffineComparable []byte |
| 574 | |
| 575 | func (b BytesAffineComparable) Compare(c Comparable) int { |
| 576 | bc := c.(BytesAffineComparable) |
| 577 | |
| 578 | if len(b) == 0 { |
| 579 | if len(bc) == 0 { |
| 580 | return 0 |
| 581 | } |
| 582 | return 1 |
| 583 | } |
| 584 | if len(bc) == 0 { |
| 585 | return -1 |
| 586 | } |
| 587 | |
| 588 | return bytes.Compare(b, bc) |
| 589 | } |
| 590 | |
| 591 | func NewBytesAffineInterval(begin, end []byte) Interval { |
| 592 | return Interval{BytesAffineComparable(begin), BytesAffineComparable(end)} |
| 593 | } |
| 594 | func NewBytesAffinePoint(b []byte) Interval { |
| 595 | be := make([]byte, len(b)+1) |
| 596 | copy(be, b) |
| 597 | be[len(b)] = 0 |
| 598 | return NewBytesAffineInterval(b, be) |
| 599 | } |