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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043
|
#ifndef INTERVALTREE_H_
#define INTERVALTREE_H_
#include <cmath>
#include <cstdlib>
#include <cassert>
#include <limits>
#include <algorithm>
#include <sstream>
#include <vector>
#include <string>
// The interval_tree.h file contains code for
// interval trees implemented using red-black-trees as described in
// the book _Introduction_To_Algorithms_ by Cormen, Leisserson,
// and Rivest.
// The low should return the lowest point of the interval and
// the high should return the highest point of the interval.
template<typename T, typename N=long>
class IntervalTree {
public:
enum color_t {BLACK, RED};
class Node {
friend class IntervalTree<T,N>;
public:
std::string str(Node *, Node *) const;
Node();
Node(const T&, N, N);
virtual ~Node();
N low() const;
N high() const;
T value() const;
protected:
T value_;
N key;
N high_;
N maxHigh;
color_t color;
Node * left;
Node * right;
Node * parent;
};
IntervalTree();
~IntervalTree();
std::string str() const;
void remove(N, N, std::vector<T>&);
template <class F> void remove(N, N, const F&, std::vector<T>&);
void remove_window(N, N, std::vector<T>&);
template <class F> void remove_window(N, N, const F&, std::vector<T>&);
Node * insert(const T&, N, N);
void fetch(N, N, std::vector<T>&);
void fetch_window(N, N, std::vector<T>&);
T fetch_nearest_up(typename IntervalTree<T,N>::Node* x, N value);
T fetch_nearest_up(N value);
typename IntervalTree<T,N>::Node* fetch_nearest_down(typename IntervalTree<T,N>::Node* x, N value);
T fetch_nearest_down(N value);
protected:
void fetch_node(N, N, std::vector<Node*>&);
void fetch_window_node(N, N, std::vector<Node*>&);
T remove(Node *);
Node * GetPredecessorOf(Node *) const;
Node * GetSuccessorOf(Node *) const;
void check() const;
/* A sentinel is used for root and for nil. These sentinels are */
/* created when ITTreeCreate is caled. root->left should always */
/* point to the node which is the root of the tree. nil points to a */
/* node which should always be black but has aribtrary children and */
/* parent and no key or info. The point of using these sentinels is so */
/* that the root and nil nodes do not require special cases in the code */
Node * root;
Node * nil;
N Overlap(N a1, N a2, N b1, N b2);
N Contain(N a1, N a2, N b1, N b2);
void LeftRotate(Node *);
void RightRotate(Node *);
void TreeInsertHelp(Node *);
void TreePrintHelper(Node *, std::stringstream&) const;
void FixUpMaxHigh(Node *);
void DeleteFixUp(Node *);
void CheckMaxHighFields(Node *) const;
bool CheckMaxHighFieldsHelper(Node * y,
const N currentHigh,
bool match) const;
};
// If the symbol CHECK_INTERVAL_TREE_ASSUMPTIONS is defined then the
// code does a lot of extra checking to make sure certain assumptions
// are satisfied. This only needs to be done if you suspect bugs are
// present or if you make significant changes and want to make sure
// your changes didn't mess anything up.
// #define CHECK_INTERVAL_TREE_ASSUMPTIONS 1
template<typename T, typename N> IntervalTree<T,N>::Node::Node() {
}
template<typename T, typename N>
IntervalTree<T,N>::Node::Node(const T& value__, N lowPoint, N highPoint)
: value_ (value__),
key(lowPoint),
high_(highPoint),
maxHigh(highPoint)
{
}
template<typename T, typename N>
IntervalTree<T,N>::Node::~Node()
{
}
template<typename T, typename N>
IntervalTree<T,N>::IntervalTree()
{
nil = new typename IntervalTree<T,N>::Node();
nil->left = nil->right = nil->parent = nil;
nil->color = BLACK;
nil->key = nil->high_ = nil->maxHigh = std::numeric_limits<N>::min();
root = new typename IntervalTree<T,N>::Node();
root->parent = root->left = root->right = nil;
root->key = root->high_ = root->maxHigh = std::numeric_limits<N>::max();
root->color=BLACK;
}
template<typename T, typename N>
N IntervalTree<T,N>::Node::low() const {
return key;
}
template<typename T, typename N>
N IntervalTree<T,N>::Node::high() const {
return high_;
}
template<typename T, typename N>
T IntervalTree<T,N>::Node::value() const {
return value_;
}
/***********************************************************************/
/* FUNCTION: LeftRotate */
/**/
/* INPUTS: the node to rotate on */
/**/
/* OUTPUT: None */
/**/
/* Modifies Input: this, x */
/**/
/* EFFECTS: Rotates as described in _Introduction_To_Algorithms by */
/* Cormen, Leiserson, Rivest (Chapter 14). Basically this */
/* makes the parent of x be to the left of x, x the parent of */
/* its parent before the rotation and fixes other pointers */
/* accordingly. Also updates the maxHigh fields of x and y */
/* after rotation. */
/***********************************************************************/
template<typename T, typename N>
void IntervalTree<T,N>::LeftRotate(typename IntervalTree<T,N>::Node* x) {
typename IntervalTree<T,N>::Node* y;
/* I originally wrote this function to use the sentinel for */
/* nil to avoid checking for nil. However this introduces a */
/* very subtle bug because sometimes this function modifies */
/* the parent pointer of nil. This can be a problem if a */
/* function which calls LeftRotate also uses the nil sentinel */
/* and expects the nil sentinel's parent pointer to be unchanged */
/* after calling this function. For example, when DeleteFixUP */
/* calls LeftRotate it expects the parent pointer of nil to be */
/* unchanged. */
y=x->right;
x->right=y->left;
if (y->left != nil) y->left->parent=x; /* used to use sentinel here */
/* and do an unconditional assignment instead of testing for nil */
y->parent=x->parent;
/* instead of checking if x->parent is the root as in the book, we */
/* count on the root sentinel to implicitly take care of this case */
if( x == x->parent->left) {
x->parent->left=y;
} else {
x->parent->right=y;
}
y->left=x;
x->parent=y;
x->maxHigh=std::max(x->left->maxHigh,std::max(x->right->maxHigh,x->high_));
y->maxHigh=std::max(x->maxHigh,std::max(y->right->maxHigh,y->high_));
#ifdef CHECK_INTERVAL_TREE_ASSUMPTIONS
check();
#elif defined(DEBUG_ASSERT)
assert(nil->color != RED || !"nil not red in ITLeftRotate");
assert((nil->maxHigh!=std::numeric_limits<N>::min())
|| !"nil->maxHigh != std::numeric_limits<N>::min() in ITLeftRotate");
#endif
}
/***********************************************************************/
/* FUNCTION: RighttRotate */
/**/
/* INPUTS: node to rotate on */
/**/
/* OUTPUT: None */
/**/
/* Modifies Input?: this, y */
/**/
/* EFFECTS: Rotates as described in _Introduction_To_Algorithms by */
/* Cormen, Leiserson, Rivest (Chapter 14). Basically this */
/* makes the parent of x be to the left of x, x the parent of */
/* its parent before the rotation and fixes other pointers */
/* accordingly. Also updates the maxHigh fields of x and y */
/* after rotation. */
/***********************************************************************/
template<typename T, typename N>
void IntervalTree<T,N>::RightRotate(typename IntervalTree<T,N>::Node* y) {
typename IntervalTree<T,N>::Node* x;
/* I originally wrote this function to use the sentinel for */
/* nil to avoid checking for nil. However this introduces a */
/* very subtle bug because sometimes this function modifies */
/* the parent pointer of nil. This can be a problem if a */
/* function which calls LeftRotate also uses the nil sentinel */
/* and expects the nil sentinel's parent pointer to be unchanged */
/* after calling this function. For example, when DeleteFixUP */
/* calls LeftRotate it expects the parent pointer of nil to be */
/* unchanged. */
x=y->left;
y->left=x->right;
if (nil != x->right) x->right->parent=y; /*used to use sentinel here */
/* and do an unconditional assignment instead of testing for nil */
/* instead of checking if x->parent is the root as in the book, we */
/* count on the root sentinel to implicitly take care of this case */
x->parent=y->parent;
if( y == y->parent->left) {
y->parent->left=x;
} else {
y->parent->right=x;
}
x->right=y;
y->parent=x;
y->maxHigh=std::max(y->left->maxHigh,std::max(y->right->maxHigh,y->high_));
x->maxHigh=std::max(x->left->maxHigh,std::max(y->maxHigh,x->high_));
#ifdef CHECK_INTERVAL_TREE_ASSUMPTIONS
check();
#elif defined(DEBUG_ASSERT)
assert(nil->color != RED || !"nil not red in ITRightRotate");
assert((nil->maxHigh!=std::numeric_limits<N>::min())
|| !"nil->maxHigh != std::numeric_limits<N>::min() in ITRightRotate");
#endif
}
/***********************************************************************/
/* FUNCTION: TreeInsertHelp */
/**/
/* INPUTS: z is the node to insert */
/**/
/* OUTPUT: none */
/**/
/* Modifies Input: this, z */
/**/
/* EFFECTS: Inserts z into the tree as if it were a regular binary tree */
/* using the algorithm described in _Introduction_To_Algorithms_ */
/* by Cormen et al. This funciton is only intended to be called */
/* by the InsertTree function and not by the user */
/***********************************************************************/
template<typename T, typename N>
void IntervalTree<T,N>::TreeInsertHelp(typename IntervalTree<T,N>::Node* z) {
/* This function should only be called by InsertITTree (see above) */
typename IntervalTree<T,N>::Node* x;
typename IntervalTree<T,N>::Node* y;
z->left=z->right=nil;
y=root;
x=root->left;
while( x != nil) {
y=x;
if ( x->key > z->key) {
x=x->left;
} else { /* x->key <= z->key */
x=x->right;
}
}
z->parent=y;
if ( (y == root) ||
(y->key > z->key) ) {
y->left=z;
} else {
y->right=z;
}
#if defined(DEBUG_ASSERT)
assert(nil->color != RED || !"nil not red in ITTreeInsertHelp");
assert((nil->maxHigh!=std::numeric_limits<N>::min())
|| !"nil->maxHigh != std::numeric_limits<N>::min() in ITTreeInsertHelp");
#endif
}
/***********************************************************************/
/* FUNCTION: FixUpMaxHigh */
/**/
/* INPUTS: x is the node to start from*/
/**/
/* OUTPUT: none */
/**/
/* Modifies Input: this */
/**/
/* EFFECTS: Travels up to the root fixing the maxHigh fields after */
/* an insertion or deletion */
/***********************************************************************/
template<typename T, typename N>
void IntervalTree<T,N>::FixUpMaxHigh(typename IntervalTree<T,N>::Node * x) {
while(x != root) {
x->maxHigh=std::max(x->high_,std::max(x->left->maxHigh,x->right->maxHigh));
x=x->parent;
}
#ifdef CHECK_INTERVAL_TREE_ASSUMPTIONS
check();
#endif
}
/* Before calling InsertNode the node x should have its key set */
/***********************************************************************/
/* FUNCTION: InsertNode */
/**/
/* INPUTS: newInterval is the interval to insert*/
/**/
/* OUTPUT: This function returns a pointer to the newly inserted node */
/* which is guarunteed to be valid until this node is deleted. */
/* What this means is if another data structure stores this */
/* pointer then the tree does not need to be searched when this */
/* is to be deleted. */
/**/
/* Modifies Input: tree */
/**/
/* EFFECTS: Creates a node node which contains the appropriate key and */
/* info pointers and inserts it into the tree. */
/***********************************************************************/
template <typename T, typename N>
typename IntervalTree<T,N>::Node* IntervalTree<T,N>::insert(const T& newInterval, N low, N high)
{
typename IntervalTree<T,N>::Node * y;
typename IntervalTree<T,N>::Node * x;
typename IntervalTree<T,N>::Node * newNode;
x = new typename IntervalTree<T,N>::Node(newInterval, low, high);
TreeInsertHelp(x);
FixUpMaxHigh(x->parent);
newNode = x;
x->color=RED;
while(x->parent->color == RED) { /* use sentinel instead of checking for root */
if (x->parent == x->parent->parent->left) {
y=x->parent->parent->right;
if (y->color == RED) {
x->parent->color=BLACK;
y->color=BLACK;
x->parent->parent->color=RED;
x=x->parent->parent;
} else {
if (x == x->parent->right) {
x=x->parent;
LeftRotate(x);
}
x->parent->color=BLACK;
x->parent->parent->color=RED;
RightRotate(x->parent->parent);
}
} else { /* case for x->parent == x->parent->parent->right */
/* this part is just like the section above with */
/* left and right interchanged */
y=x->parent->parent->left;
if (y->color == RED) {
x->parent->color=BLACK;
y->color=BLACK;
x->parent->parent->color=RED;
x=x->parent->parent;
} else {
if (x == x->parent->left) {
x=x->parent;
RightRotate(x);
}
x->parent->color=BLACK;
x->parent->parent->color=RED;
LeftRotate(x->parent->parent);
}
}
}
root->left->color=BLACK;
return(newNode);
#ifdef CHECK_INTERVAL_TREE_ASSUMPTIONS
check();
#elif defined(DEBUG_ASSERT)
assert(nil->color != RED || !"nil not red in ITTreeInsert");
assert(root->color != RED || !"root not red in ITTreeInsert");
assert((nil->maxHigh!=std::numeric_limits<N>::min())
|| !"nil->maxHigh != std::numeric_limits<N>::min() in ITTreeInsert");
#endif
}
/***********************************************************************/
/* FUNCTION: GetSuccessorOf */
/**/
/* INPUTS: x is the node we want the succesor of */
/**/
/* OUTPUT: This function returns the successor of x or NULL if no */
/* successor exists. */
/**/
/* Modifies Input: none */
/**/
/* Note: uses the algorithm in _Introduction_To_Algorithms_ */
/***********************************************************************/
template<typename T, typename N>
typename IntervalTree<T,N>::Node * IntervalTree<T,N>::GetSuccessorOf(typename IntervalTree<T,N>::Node * x) const
{
typename IntervalTree<T,N>::Node* y;
if (nil != (y = x->right)) { /* assignment to y is intentional */
while(y->left != nil) { /* returns the minium of the right subtree of x */
y=y->left;
}
return(y);
} else {
y=x->parent;
while(x == y->right) { /* sentinel used instead of checking for nil */
x=y;
y=y->parent;
}
if (y == root) return(nil);
return(y);
}
}
/***********************************************************************/
/* FUNCTION: GetPredecessorOf */
/**/
/* INPUTS: x is the node to get predecessor of */
/**/
/* OUTPUT: This function returns the predecessor of x or NULL if no */
/* predecessor exists. */
/**/
/* Modifies Input: none */
/**/
/* Note: uses the algorithm in _Introduction_To_Algorithms_ */
/***********************************************************************/
template<typename T, typename N>
typename IntervalTree<T,N>::Node * IntervalTree<T,N>::GetPredecessorOf(typename IntervalTree<T,N>::Node * x) const {
typename IntervalTree<T,N>::Node* y;
if (nil != (y = x->left)) { /* assignment to y is intentional */
while(y->right != nil) { /* returns the maximum of the left subtree of x */
y=y->right;
}
return(y);
} else {
y=x->parent;
while(x == y->left) {
if (y == root) return(nil);
x=y;
y=y->parent;
}
return(y);
}
}
/***********************************************************************/
/* FUNCTION: str */
/**/
/* INPUTS: none */
/**/
/* OUTPUT: none */
/**/
/* EFFECTS: This function recursively prints the nodes of the tree */
/* inorder. */
/**/
/* Modifies Input: none */
/**/
/* Note: This function should only be called from ITTreePrint */
/***********************************************************************/
template<typename T, typename N>
std::string IntervalTree<T,N>::Node::str(typename IntervalTree<T,N>::Node * nil,
typename IntervalTree<T,N>::Node * root) const {
std::stringstream s;
s << value_;
s << ", k=" << key << ", h=" << high_ << ", mH=" << maxHigh;
s << " l->key=";
if( left == nil) s << "NULL"; else s << left->key;
s << " r->key=";
if( right == nil) s << "NULL"; else s << right->key;
s << " p->key=";
if( parent == root) s << "NULL"; else s << parent->key;
s << " color=" << (color == RED ? "RED" : "BLACK") << std::endl;
return s.str();
}
template<typename T, typename N>
void IntervalTree<T,N>::TreePrintHelper(typename IntervalTree<T,N>::Node* x, std::stringstream &s) const {
if (x != nil) {
TreePrintHelper(x->left, s);
s << x->str(nil,root);
TreePrintHelper(x->right, s);
}
}
template<typename T, typename N>
IntervalTree<T,N>::~IntervalTree() {
typename IntervalTree<T,N>::Node * x = root->left;
typename std::vector<typename IntervalTree<T,N>::Node *> stuffToFree;
if (x != nil) {
if (x->left != nil) {
stuffToFree.push_back(x->left);
}
if (x->right != nil) {
stuffToFree.push_back(x->right);
}
delete x;
while( !stuffToFree.empty() ) {
x = stuffToFree.back();
stuffToFree.pop_back();
if (x->left != nil) {
stuffToFree.push_back(x->left);
}
if (x->right != nil) {
stuffToFree.push_back(x->right);
}
delete x;
}
}
delete nil;
delete root;
}
/***********************************************************************/
/* FUNCTION: str */
/**/
/* INPUTS: none */
/**/
/* OUTPUT: none */
/**/
/* EFFECT: This function recursively prints the nodes of the tree */
/* inorder. */
/**/
/* Modifies Input: none */
/**/
/***********************************************************************/
template<typename T, typename N>
std::string IntervalTree<T,N>::str() const {
std::stringstream s;
TreePrintHelper(root->left, s);
return s.str();
}
/***********************************************************************/
/* FUNCTION: DeleteFixUp */
/**/
/* INPUTS: x is the child of the spliced */
/* out node in remove. */
/**/
/* OUTPUT: none */
/**/
/* EFFECT: Performs rotations and changes colors to restore red-black */
/* properties after a node is deleted */
/**/
/* Modifies Input: this, x */
/**/
/* The algorithm from this function is from _Introduction_To_Algorithms_ */
/***********************************************************************/
template<typename T,typename N>
void IntervalTree<T,N>::DeleteFixUp(typename IntervalTree<T,N>::Node* x) {
typename IntervalTree<T,N>::Node * w;
typename IntervalTree<T,N>::Node * rootLeft = root->left;
while( (x->color == BLACK) && (rootLeft != x)) {
if (x == x->parent->left) {
w=x->parent->right;
if (w->color == RED) {
w->color=BLACK;
x->parent->color=RED;
LeftRotate(x->parent);
w=x->parent->right;
}
if ( (w->right->color == BLACK) && (w->left->color == BLACK) ) {
w->color=RED;
x=x->parent;
} else {
if (w->right->color == BLACK) {
w->left->color=BLACK;
w->color=RED;
RightRotate(w);
w=x->parent->right;
}
w->color=x->parent->color;
x->parent->color=BLACK;
w->right->color=BLACK;
LeftRotate(x->parent);
x=rootLeft; /* this is to exit while loop */
}
} else { /* the code below is has left and right switched from above */
w=x->parent->left;
if (w->color == RED) {
w->color=BLACK;
x->parent->color=RED;
RightRotate(x->parent);
w=x->parent->left;
}
if ( (w->right->color == BLACK) && (w->left->color == BLACK) ) {
w->color=RED;
x=x->parent;
} else {
if (w->left->color == BLACK) {
w->right->color=BLACK;
w->color=RED;
LeftRotate(w);
w=x->parent->left;
}
w->color=x->parent->color;
x->parent->color=BLACK;
w->left->color=BLACK;
RightRotate(x->parent);
x=rootLeft; /* this is to exit while loop */
}
}
}
x->color=BLACK;
#ifdef CHECK_INTERVAL_TREE_ASSUMPTIONS
check();
#elif defined(DEBUG_ASSERT)
assert(nil->color != BLACK || !"nil not black in ITDeleteFixUp");
assert((nil->maxHigh!=std::numeric_limits<N>::min())
|| !"nil->maxHigh != std::numeric_limits<N>::min() in ITDeleteFixUp");
#endif
}
/***********************************************************************/
/* FUNCTION: remove */
/**/
/* INPUTS: tree is the tree to delete node z from */
/**/
/* OUTPUT: returns the Interval stored at deleted node */
/**/
/* EFFECT: Deletes z from tree and but don't call destructor */
/* Then calls FixUpMaxHigh to fix maxHigh fields then calls */
/* ITDeleteFixUp to restore red-black properties */
/**/
/* Modifies Input: z */
/**/
/* The algorithm from this function is from _Introduction_To_Algorithms_ */
/***********************************************************************/
template<typename T, typename N>
T IntervalTree<T,N>::remove(typename IntervalTree<T,N>::Node * z){
typename IntervalTree<T,N>::Node* y;
typename IntervalTree<T,N>::Node* x;
T returnValue = z->value();
y= ((z->left == nil) || (z->right == nil)) ? z : GetSuccessorOf(z);
x= (y->left == nil) ? y->right : y->left;
if (root == (x->parent = y->parent)) { /* assignment of y->p to x->p is intentional */
root->left=x;
} else {
if (y == y->parent->left) {
y->parent->left=x;
} else {
y->parent->right=x;
}
}
if (y != z) { /* y should not be nil in this case */
#ifdef DEBUG_ASSERT
assert( (y!=nil) || !"y is nil in remove");
#endif
/* y is the node to splice out and x is its child */
y->maxHigh = std::numeric_limits<N>::min();
y->left=z->left;
y->right=z->right;
y->parent=z->parent;
z->left->parent=z->right->parent=y;
if (z == z->parent->left) {
z->parent->left=y;
} else {
z->parent->right=y;
}
FixUpMaxHigh(x->parent);
if (y->color == BLACK) {
y->color = z->color;
DeleteFixUp(x);
} else
y->color = z->color;
delete z;
#ifdef CHECK_INTERVAL_TREE_ASSUMPTIONS
check();
#elif defined(DEBUG_ASSERT)
assert(nil->color != BLACK || !"nil not black in ITDelete");
assert((nil->maxHigh!=std::numeric_limits<N>::min())
&& !"nil->maxHigh != std::numeric_limits<N>::min() in ITDelete");
#endif
} else {
FixUpMaxHigh(x->parent);
if (y->color == BLACK) DeleteFixUp(x);
delete y;
#ifdef CHECK_INTERVAL_TREE_ASSUMPTIONS
check();
#elif defined(DEBUG_ASSERT)
assert(nil->color != BLACK || !"nil not black in ITDelete");
assert((nil->maxHigh!=std::numeric_limits<N>::min())
|| !"nil->maxHigh != std::numeric_limits<N>::min() in ITDelete");
#endif
}
return returnValue;
}
template <typename T, typename N>
void IntervalTree<T,N>::remove(N low, N high, std::vector<T> &removed)
{
typename std::vector<typename IntervalTree<T,N>::Node*> got;
fetch_node(low, high, got);
for (typename std::vector<typename IntervalTree<T,N>::Node*>::const_iterator
i=got.begin(); i!=got.end(); ++i)
{
removed.push_back((*i)->value());
remove(*i);
}
}
template <typename T, typename N> template <typename F>
void IntervalTree<T,N>::remove(N low, N high, const F &removeFunctor, std::vector<T> &removed)
{
typename std::vector<typename IntervalTree<T,N>::Node*> got;
fetch_node(low, high, got);
for (typename std::vector<typename IntervalTree<T,N>::Node*>::const_iterator
i=got.begin(); i!=got.end(); ++i)
{
if (removeFunctor((*i)->value(), (*i)->low(), (*i)->high())) {
removed.push_back((*i)->value());
remove(*i);
}
}
}
template <typename T, typename N>
void IntervalTree<T,N>::remove_window(N low, N high, std::vector<T> &removed)
{
typename std::vector<typename IntervalTree<T,N>::Node*> got;
fetch_window_node(low, high, got);
for (typename std::vector<typename IntervalTree<T,N>::Node*>::const_iterator
i=got.begin(); i!=got.end(); ++i)
{
removed.push_back((*i)->value());
remove(*i);
}
}
template <typename T, typename N> template <typename F>
void IntervalTree<T,N>::remove_window(
N low,
N high,
const F& removeFunctor,
std::vector<T> &removed)
{
typename std::vector<typename IntervalTree<T,N>::Node*> got;
fetch_window_node(low, high, got);
for (typename std::vector<typename IntervalTree<T,N>::Node*>::const_iterator
i=got.begin(); i!=got.end(); ++i)
{
if (removeFunctor((*i)->value(), (*i)->low(), (*i)->high())) {
removed.push_back((*i)->value());
remove(*i);
}
}
}
/***********************************************************************/
/* FUNCTION: Overlap */
/**/
/* INPUTS: [a1,a2) and [b1,b2) are the low and high endpoints of two */
/* intervals. */
/**/
/* OUTPUT: stack containing pointers to the nodes between [low,high) */
/**/
/* Modifies Input: none */
/**/
/* EFFECT: returns 1 if the intervals overlap, and 0 otherwise */
/***********************************************************************/
template<typename T, typename N>
N IntervalTree<T,N>::Overlap(N a1, N a2, N b1, N b2) {
return a1 <= b2 && b1 <= a2;
}
template<typename T, typename N>
N IntervalTree<T,N>::Contain(N a1, N a2, N b1, N b2) {
return a1 <= b1 && b2 <= a2;
}
/***********************************************************************/
/* FUNCTION: fetch */
/**/
/* INPUTS: tree is the tree to look for intervals overlapping the */
/* interval [low,high) */
/**/
/* OUTPUT: stack containing pointers to the nodes overlapping */
/* [low,high) */
/**/
/* Modifies Input: none */
/**/
/* EFFECT: Returns a stack containing pointers to nodes containing */
/* intervals which overlap [low,high) in O(max(N,k*log(N))) */
/* where N is the number of intervals in the tree and k is */
/* the number of overlapping intervals */
/**/
/* Note: This basic idea for this function comes from the */
/* _Introduction_To_Algorithms_ book by Cormen et al, but */
/* modifications were made to return all overlapping intervals */
/* instead of just the first overlapping interval as in the */
/* book. The natural way to do this would require recursive */
/* calls of a basic search function. I translated the */
/* recursive version into an interative version with a stack */
/* as described below. */
/***********************************************************************/
/* The basic idea for the function below is to take the IntervalSearch */
/* function from the book and modify to find all overlapping intervals */
/* instead of just one. */
template<typename T, typename N>
void IntervalTree<T,N>::fetch(N low, N high, std::vector<T> &enumResultStack) {
typename std::vector<typename IntervalTree<T,N>::Node*> got;
fetch_node(low, high, got);
for (typename std::vector<typename IntervalTree<T,N>::Node*>::const_iterator
i = got.begin(); i != got.end(); i++) {
enumResultStack.push_back((*i)->value());
}
}
template<typename T, typename N>
T IntervalTree<T,N>::fetch_nearest_up(typename IntervalTree<T,N>::Node* x, N value) {
if(x == nil)
return T();
if(x->key > value) {
// Maybe there is a better interval candidate in the left subtree
if(x->left != nil) {
T best_left_value = fetch_nearest_up(x->left,value);
if (best_left_value.defined())
return best_left_value;
}
return x->value();
} else {
return fetch_nearest_up(x->right,value);
}
}
template<typename T, typename N>
T IntervalTree<T,N>::fetch_nearest_up(N value) {
return fetch_nearest_up(root->left,value);
}
template<typename T, typename N>
typename IntervalTree<T,N>::Node* IntervalTree<T,N>::fetch_nearest_down(typename IntervalTree<T,N>::Node* x, N value) {
if (x == nil)
return NULL;
if(x->key > value) {
return fetch_nearest_down(x->left,value);
} else {
// There is not a better interval in the subtrees
if(x->high_ == x->maxHigh && x->high_ <= value) {
return x;
} else {
typename IntervalTree<T,N>::Node* best_node = NULL;
if(x->high_ <= value) {
best_node = x;
}
// Is there a closer interval in the left subtree
if(x->left != nil) {
typename IntervalTree<T,N>::Node* best_node_left = fetch_nearest_down(x->left,value);
if(best_node == NULL) {
best_node = best_node_left;
} else if(best_node_left != NULL && best_node_left->high_ > best_node->high_) {
best_node = best_node_left;
}
}
// Is there a closer interval in the right subtree
if(x->right != nil) {
typename IntervalTree<T,N>::Node* best_node_right = fetch_nearest_down(x->right,value);
if(best_node == NULL) {
best_node = best_node_right;
} else if(best_node_right != NULL && best_node_right->high_ > best_node->high_) {
best_node = best_node_right;
}
}
return best_node;
}
}
}
template<typename T, typename N>
T IntervalTree<T,N>::fetch_nearest_down(N value) {
typename IntervalTree<T,N>::Node* best_node = fetch_nearest_down(root->left,value);
if(best_node)
return best_node->value();
else
return T();
}
template<typename T, typename N>
void IntervalTree<T,N>::fetch_node(
N low,
N high,
std::vector<typename IntervalTree<T,N>::Node*> &enumResultStack)
{
std::vector<IntervalTree<T,N>::Node*> stack;
// left first
stack.push_back(root->right);
stack.push_back(root->left);
while (stack.size() > 0) {
IntervalTree<T,N>::Node* x = stack.back();
stack.pop_back();
if (x != nil) {
if (Overlap(low,high,x->key,x->high_) ) {
enumResultStack.push_back(x);
}
stack.push_back(x->right);
if (x->left->maxHigh >= low) {
stack.push_back(x->left);
}
}
}
}
template<typename T, typename N>
void IntervalTree<T,N>::fetch_window(N low, N high, std::vector<T> &enumResultStack)
{
typename std::vector<typename IntervalTree<T,N>::Node*> got;
fetch_window_node(low, high, got);
for (typename std::vector<typename IntervalTree<T,N>::Node*>::const_iterator
i = got.begin(); i != got.end(); i++) {
enumResultStack.push_back((*i)->value());
}
}
template<typename T, typename N>
void IntervalTree<T,N>::fetch_window_node(
N low,
N high,
std::vector<typename IntervalTree<T,N>::Node*> &enumResultStack)
{
std::vector<IntervalTree<T,N>::Node*> stack;
// left first
stack.push_back(root->right);
stack.push_back(root->left);
while (stack.size() > 0) {
IntervalTree<T,N>::Node* x = stack.back();
stack.pop_back();
if (x != nil) {
if (Contain(low,high,x->key,x->high_) ) {
enumResultStack.push_back(x);
}
stack.push_back(x->right);
if (x->left->maxHigh >= low) {
stack.push_back(x->left);
}
}
}
}
template<typename T, typename N>
bool IntervalTree<T,N>::CheckMaxHighFieldsHelper(typename IntervalTree<T,N>::Node * y,
const N currentHigh,
bool match) const
{
if (y != nil) {
match = CheckMaxHighFieldsHelper(y->left,currentHigh,match) ?
true : match;
if (y->high_ == currentHigh)
match = true;
match = CheckMaxHighFieldsHelper(y->right,currentHigh,match) ?
true : match;
}
return match;
}
/* Make sure the maxHigh fields for everything makes sense. *
* If something is wrong, print a warning and exit */
template<typename T, typename N>
void IntervalTree<T,N>::CheckMaxHighFields(typename IntervalTree<T,N>::Node * x) const {
if (x != nil) {
CheckMaxHighFields(x->left);
if(!(CheckMaxHighFieldsHelper(x,x->maxHigh,false) > 0)) {
assert(0);
}
CheckMaxHighFields(x->right);
}
}
template<typename T, typename N>
void IntervalTree<T,N>::check() const {
CheckMaxHighFields(root->left);
}
#endif
|