11da177e4SLinus Torvalds /* 21da177e4SLinus Torvalds Red Black Trees 31da177e4SLinus Torvalds (C) 1999 Andrea Arcangeli <andrea@suse.de> 41da177e4SLinus Torvalds (C) 2002 David Woodhouse <dwmw2@infradead.org> 51da177e4SLinus Torvalds 61da177e4SLinus Torvalds This program is free software; you can redistribute it and/or modify 71da177e4SLinus Torvalds it under the terms of the GNU General Public License as published by 81da177e4SLinus Torvalds the Free Software Foundation; either version 2 of the License, or 91da177e4SLinus Torvalds (at your option) any later version. 101da177e4SLinus Torvalds 111da177e4SLinus Torvalds This program is distributed in the hope that it will be useful, 121da177e4SLinus Torvalds but WITHOUT ANY WARRANTY; without even the implied warranty of 131da177e4SLinus Torvalds MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 141da177e4SLinus Torvalds GNU General Public License for more details. 151da177e4SLinus Torvalds 161da177e4SLinus Torvalds You should have received a copy of the GNU General Public License 171da177e4SLinus Torvalds along with this program; if not, write to the Free Software 181da177e4SLinus Torvalds Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA 191da177e4SLinus Torvalds 201da177e4SLinus Torvalds linux/lib/rbtree.c 211da177e4SLinus Torvalds */ 221da177e4SLinus Torvalds 231da177e4SLinus Torvalds #include <linux/rbtree.h> 248bc3bcc9SPaul Gortmaker #include <linux/export.h> 251da177e4SLinus Torvalds 265bc9188aSMichel Lespinasse /* 275bc9188aSMichel Lespinasse * red-black trees properties: http://en.wikipedia.org/wiki/Rbtree 285bc9188aSMichel Lespinasse * 295bc9188aSMichel Lespinasse * 1) A node is either red or black 305bc9188aSMichel Lespinasse * 2) The root is black 315bc9188aSMichel Lespinasse * 3) All leaves (NULL) are black 325bc9188aSMichel Lespinasse * 4) Both children of every red node are black 335bc9188aSMichel Lespinasse * 5) Every simple path from root to leaves contains the same number 345bc9188aSMichel Lespinasse * of black nodes. 355bc9188aSMichel Lespinasse * 365bc9188aSMichel Lespinasse * 4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two 375bc9188aSMichel Lespinasse * consecutive red nodes in a path and every red node is therefore followed by 385bc9188aSMichel Lespinasse * a black. So if B is the number of black nodes on every simple path (as per 395bc9188aSMichel Lespinasse * 5), then the longest possible path due to 4 is 2B. 405bc9188aSMichel Lespinasse * 415bc9188aSMichel Lespinasse * We shall indicate color with case, where black nodes are uppercase and red 42*6280d235SMichel Lespinasse * nodes will be lowercase. Unknown color nodes shall be drawn as red within 43*6280d235SMichel Lespinasse * parentheses and have some accompanying text comment. 445bc9188aSMichel Lespinasse */ 455bc9188aSMichel Lespinasse 46bf7ad8eeSMichel Lespinasse #define RB_RED 0 47bf7ad8eeSMichel Lespinasse #define RB_BLACK 1 48bf7ad8eeSMichel Lespinasse 49bf7ad8eeSMichel Lespinasse #define rb_color(r) ((r)->__rb_parent_color & 1) 50bf7ad8eeSMichel Lespinasse #define rb_is_red(r) (!rb_color(r)) 51bf7ad8eeSMichel Lespinasse #define rb_is_black(r) rb_color(r) 52bf7ad8eeSMichel Lespinasse 53bf7ad8eeSMichel Lespinasse static inline void rb_set_parent(struct rb_node *rb, struct rb_node *p) 54bf7ad8eeSMichel Lespinasse { 55bf7ad8eeSMichel Lespinasse rb->__rb_parent_color = rb_color(rb) | (unsigned long)p; 56bf7ad8eeSMichel Lespinasse } 57bf7ad8eeSMichel Lespinasse 585bc9188aSMichel Lespinasse static inline void rb_set_parent_color(struct rb_node *rb, 595bc9188aSMichel Lespinasse struct rb_node *p, int color) 605bc9188aSMichel Lespinasse { 615bc9188aSMichel Lespinasse rb->__rb_parent_color = (unsigned long)p | color; 625bc9188aSMichel Lespinasse } 635bc9188aSMichel Lespinasse 645bc9188aSMichel Lespinasse static inline struct rb_node *rb_red_parent(struct rb_node *red) 655bc9188aSMichel Lespinasse { 665bc9188aSMichel Lespinasse return (struct rb_node *)red->__rb_parent_color; 675bc9188aSMichel Lespinasse } 685bc9188aSMichel Lespinasse 695bc9188aSMichel Lespinasse /* 705bc9188aSMichel Lespinasse * Helper function for rotations: 715bc9188aSMichel Lespinasse * - old's parent and color get assigned to new 725bc9188aSMichel Lespinasse * - old gets assigned new as a parent and 'color' as a color. 735bc9188aSMichel Lespinasse */ 745bc9188aSMichel Lespinasse static inline void 755bc9188aSMichel Lespinasse __rb_rotate_set_parents(struct rb_node *old, struct rb_node *new, 765bc9188aSMichel Lespinasse struct rb_root *root, int color) 775bc9188aSMichel Lespinasse { 785bc9188aSMichel Lespinasse struct rb_node *parent = rb_parent(old); 795bc9188aSMichel Lespinasse new->__rb_parent_color = old->__rb_parent_color; 805bc9188aSMichel Lespinasse rb_set_parent_color(old, new, color); 815bc9188aSMichel Lespinasse if (parent) { 825bc9188aSMichel Lespinasse if (parent->rb_left == old) 835bc9188aSMichel Lespinasse parent->rb_left = new; 845bc9188aSMichel Lespinasse else 855bc9188aSMichel Lespinasse parent->rb_right = new; 865bc9188aSMichel Lespinasse } else 875bc9188aSMichel Lespinasse root->rb_node = new; 885bc9188aSMichel Lespinasse } 895bc9188aSMichel Lespinasse 901da177e4SLinus Torvalds void rb_insert_color(struct rb_node *node, struct rb_root *root) 911da177e4SLinus Torvalds { 925bc9188aSMichel Lespinasse struct rb_node *parent = rb_red_parent(node), *gparent, *tmp; 931da177e4SLinus Torvalds 946d58452dSMichel Lespinasse while (true) { 956d58452dSMichel Lespinasse /* 966d58452dSMichel Lespinasse * Loop invariant: node is red 976d58452dSMichel Lespinasse * 986d58452dSMichel Lespinasse * If there is a black parent, we are done. 996d58452dSMichel Lespinasse * Otherwise, take some corrective action as we don't 1006d58452dSMichel Lespinasse * want a red root or two consecutive red nodes. 1016d58452dSMichel Lespinasse */ 1026d58452dSMichel Lespinasse if (!parent) { 1035bc9188aSMichel Lespinasse rb_set_parent_color(node, NULL, RB_BLACK); 1046d58452dSMichel Lespinasse break; 1056d58452dSMichel Lespinasse } else if (rb_is_black(parent)) 1066d58452dSMichel Lespinasse break; 1076d58452dSMichel Lespinasse 1085bc9188aSMichel Lespinasse gparent = rb_red_parent(parent); 1091da177e4SLinus Torvalds 1105bc9188aSMichel Lespinasse if (parent == gparent->rb_left) { 1115bc9188aSMichel Lespinasse tmp = gparent->rb_right; 1125bc9188aSMichel Lespinasse if (tmp && rb_is_red(tmp)) { 1135bc9188aSMichel Lespinasse /* 1145bc9188aSMichel Lespinasse * Case 1 - color flips 1155bc9188aSMichel Lespinasse * 1165bc9188aSMichel Lespinasse * G g 1175bc9188aSMichel Lespinasse * / \ / \ 1185bc9188aSMichel Lespinasse * p u --> P U 1195bc9188aSMichel Lespinasse * / / 1205bc9188aSMichel Lespinasse * n N 1215bc9188aSMichel Lespinasse * 1225bc9188aSMichel Lespinasse * However, since g's parent might be red, and 1235bc9188aSMichel Lespinasse * 4) does not allow this, we need to recurse 1245bc9188aSMichel Lespinasse * at g. 1255bc9188aSMichel Lespinasse */ 1265bc9188aSMichel Lespinasse rb_set_parent_color(tmp, gparent, RB_BLACK); 1275bc9188aSMichel Lespinasse rb_set_parent_color(parent, gparent, RB_BLACK); 1281da177e4SLinus Torvalds node = gparent; 1295bc9188aSMichel Lespinasse parent = rb_parent(node); 1305bc9188aSMichel Lespinasse rb_set_parent_color(node, parent, RB_RED); 1311da177e4SLinus Torvalds continue; 1321da177e4SLinus Torvalds } 1331da177e4SLinus Torvalds 1341f052865SMichel Lespinasse if (parent->rb_right == node) { 1355bc9188aSMichel Lespinasse /* 1365bc9188aSMichel Lespinasse * Case 2 - left rotate at parent 1375bc9188aSMichel Lespinasse * 1385bc9188aSMichel Lespinasse * G G 1395bc9188aSMichel Lespinasse * / \ / \ 1405bc9188aSMichel Lespinasse * p U --> n U 1415bc9188aSMichel Lespinasse * \ / 1425bc9188aSMichel Lespinasse * n p 1435bc9188aSMichel Lespinasse * 1445bc9188aSMichel Lespinasse * This still leaves us in violation of 4), the 1455bc9188aSMichel Lespinasse * continuation into Case 3 will fix that. 1465bc9188aSMichel Lespinasse */ 1475bc9188aSMichel Lespinasse parent->rb_right = tmp = node->rb_left; 1485bc9188aSMichel Lespinasse node->rb_left = parent; 1495bc9188aSMichel Lespinasse if (tmp) 1505bc9188aSMichel Lespinasse rb_set_parent_color(tmp, parent, 1515bc9188aSMichel Lespinasse RB_BLACK); 1525bc9188aSMichel Lespinasse rb_set_parent_color(parent, node, RB_RED); 1531da177e4SLinus Torvalds parent = node; 1541da177e4SLinus Torvalds } 1551da177e4SLinus Torvalds 1565bc9188aSMichel Lespinasse /* 1575bc9188aSMichel Lespinasse * Case 3 - right rotate at gparent 1585bc9188aSMichel Lespinasse * 1595bc9188aSMichel Lespinasse * G P 1605bc9188aSMichel Lespinasse * / \ / \ 1615bc9188aSMichel Lespinasse * p U --> n g 1625bc9188aSMichel Lespinasse * / \ 1635bc9188aSMichel Lespinasse * n U 1645bc9188aSMichel Lespinasse */ 1655bc9188aSMichel Lespinasse gparent->rb_left = tmp = parent->rb_right; 1665bc9188aSMichel Lespinasse parent->rb_right = gparent; 1675bc9188aSMichel Lespinasse if (tmp) 1685bc9188aSMichel Lespinasse rb_set_parent_color(tmp, gparent, RB_BLACK); 1695bc9188aSMichel Lespinasse __rb_rotate_set_parents(gparent, parent, root, RB_RED); 1701f052865SMichel Lespinasse break; 1711da177e4SLinus Torvalds } else { 1725bc9188aSMichel Lespinasse tmp = gparent->rb_left; 1735bc9188aSMichel Lespinasse if (tmp && rb_is_red(tmp)) { 1745bc9188aSMichel Lespinasse /* Case 1 - color flips */ 1755bc9188aSMichel Lespinasse rb_set_parent_color(tmp, gparent, RB_BLACK); 1765bc9188aSMichel Lespinasse rb_set_parent_color(parent, gparent, RB_BLACK); 1771da177e4SLinus Torvalds node = gparent; 1785bc9188aSMichel Lespinasse parent = rb_parent(node); 1795bc9188aSMichel Lespinasse rb_set_parent_color(node, parent, RB_RED); 1801da177e4SLinus Torvalds continue; 1811da177e4SLinus Torvalds } 1821da177e4SLinus Torvalds 1831f052865SMichel Lespinasse if (parent->rb_left == node) { 1845bc9188aSMichel Lespinasse /* Case 2 - right rotate at parent */ 1855bc9188aSMichel Lespinasse parent->rb_left = tmp = node->rb_right; 1865bc9188aSMichel Lespinasse node->rb_right = parent; 1875bc9188aSMichel Lespinasse if (tmp) 1885bc9188aSMichel Lespinasse rb_set_parent_color(tmp, parent, 1895bc9188aSMichel Lespinasse RB_BLACK); 1905bc9188aSMichel Lespinasse rb_set_parent_color(parent, node, RB_RED); 1911da177e4SLinus Torvalds parent = node; 1921da177e4SLinus Torvalds } 1931da177e4SLinus Torvalds 1945bc9188aSMichel Lespinasse /* Case 3 - left rotate at gparent */ 1955bc9188aSMichel Lespinasse gparent->rb_right = tmp = parent->rb_left; 1965bc9188aSMichel Lespinasse parent->rb_left = gparent; 1975bc9188aSMichel Lespinasse if (tmp) 1985bc9188aSMichel Lespinasse rb_set_parent_color(tmp, gparent, RB_BLACK); 1995bc9188aSMichel Lespinasse __rb_rotate_set_parents(gparent, parent, root, RB_RED); 2001f052865SMichel Lespinasse break; 2011da177e4SLinus Torvalds } 2021da177e4SLinus Torvalds } 2031da177e4SLinus Torvalds } 2041da177e4SLinus Torvalds EXPORT_SYMBOL(rb_insert_color); 2051da177e4SLinus Torvalds 2061da177e4SLinus Torvalds static void __rb_erase_color(struct rb_node *node, struct rb_node *parent, 2071da177e4SLinus Torvalds struct rb_root *root) 2081da177e4SLinus Torvalds { 209*6280d235SMichel Lespinasse struct rb_node *sibling, *tmp1, *tmp2; 2101da177e4SLinus Torvalds 211d6ff1273SMichel Lespinasse while (true) { 212d6ff1273SMichel Lespinasse /* 213d6ff1273SMichel Lespinasse * Loop invariant: all leaf paths going through node have a 214d6ff1273SMichel Lespinasse * black node count that is 1 lower than other leaf paths. 215d6ff1273SMichel Lespinasse * 216d6ff1273SMichel Lespinasse * If node is red, we can flip it to black to adjust. 217d6ff1273SMichel Lespinasse * If node is the root, all leaf paths go through it. 218d6ff1273SMichel Lespinasse * Otherwise, we need to adjust the tree through color flips 219d6ff1273SMichel Lespinasse * and tree rotations as per one of the 4 cases below. 220d6ff1273SMichel Lespinasse */ 221d6ff1273SMichel Lespinasse if (node && rb_is_red(node)) { 222*6280d235SMichel Lespinasse rb_set_parent_color(node, parent, RB_BLACK); 223d6ff1273SMichel Lespinasse break; 224d6ff1273SMichel Lespinasse } else if (!parent) { 225d6ff1273SMichel Lespinasse break; 226d6ff1273SMichel Lespinasse } else if (parent->rb_left == node) { 227*6280d235SMichel Lespinasse sibling = parent->rb_right; 228*6280d235SMichel Lespinasse if (rb_is_red(sibling)) { 229*6280d235SMichel Lespinasse /* 230*6280d235SMichel Lespinasse * Case 1 - left rotate at parent 231*6280d235SMichel Lespinasse * 232*6280d235SMichel Lespinasse * P S 233*6280d235SMichel Lespinasse * / \ / \ 234*6280d235SMichel Lespinasse * N s --> p Sr 235*6280d235SMichel Lespinasse * / \ / \ 236*6280d235SMichel Lespinasse * Sl Sr N Sl 237*6280d235SMichel Lespinasse */ 238*6280d235SMichel Lespinasse parent->rb_right = tmp1 = sibling->rb_left; 239*6280d235SMichel Lespinasse sibling->rb_left = parent; 240*6280d235SMichel Lespinasse rb_set_parent_color(tmp1, parent, RB_BLACK); 241*6280d235SMichel Lespinasse __rb_rotate_set_parents(parent, sibling, root, 242*6280d235SMichel Lespinasse RB_RED); 243*6280d235SMichel Lespinasse sibling = tmp1; 2441da177e4SLinus Torvalds } 245*6280d235SMichel Lespinasse tmp1 = sibling->rb_right; 246*6280d235SMichel Lespinasse if (!tmp1 || rb_is_black(tmp1)) { 247*6280d235SMichel Lespinasse tmp2 = sibling->rb_left; 248*6280d235SMichel Lespinasse if (!tmp2 || rb_is_black(tmp2)) { 249*6280d235SMichel Lespinasse /* 250*6280d235SMichel Lespinasse * Case 2 - sibling color flip 251*6280d235SMichel Lespinasse * (p could be either color here) 252*6280d235SMichel Lespinasse * 253*6280d235SMichel Lespinasse * (p) (p) 254*6280d235SMichel Lespinasse * / \ / \ 255*6280d235SMichel Lespinasse * N S --> N s 256*6280d235SMichel Lespinasse * / \ / \ 257*6280d235SMichel Lespinasse * Sl Sr Sl Sr 258*6280d235SMichel Lespinasse * 259*6280d235SMichel Lespinasse * This leaves us violating 5), so 260*6280d235SMichel Lespinasse * recurse at p. If p is red, the 261*6280d235SMichel Lespinasse * recursion will just flip it to black 262*6280d235SMichel Lespinasse * and exit. If coming from Case 1, 263*6280d235SMichel Lespinasse * p is known to be red. 264*6280d235SMichel Lespinasse */ 265*6280d235SMichel Lespinasse rb_set_parent_color(sibling, parent, 266*6280d235SMichel Lespinasse RB_RED); 2671da177e4SLinus Torvalds node = parent; 26855a98102SDavid Woodhouse parent = rb_parent(node); 269e125d147SMichel Lespinasse continue; 2701da177e4SLinus Torvalds } 271*6280d235SMichel Lespinasse /* 272*6280d235SMichel Lespinasse * Case 3 - right rotate at sibling 273*6280d235SMichel Lespinasse * (p could be either color here) 274*6280d235SMichel Lespinasse * 275*6280d235SMichel Lespinasse * (p) (p) 276*6280d235SMichel Lespinasse * / \ / \ 277*6280d235SMichel Lespinasse * N S --> N Sl 278*6280d235SMichel Lespinasse * / \ \ 279*6280d235SMichel Lespinasse * sl Sr s 280*6280d235SMichel Lespinasse * \ 281*6280d235SMichel Lespinasse * Sr 282*6280d235SMichel Lespinasse */ 283*6280d235SMichel Lespinasse sibling->rb_left = tmp1 = tmp2->rb_right; 284*6280d235SMichel Lespinasse tmp2->rb_right = sibling; 285*6280d235SMichel Lespinasse parent->rb_right = tmp2; 286*6280d235SMichel Lespinasse if (tmp1) 287*6280d235SMichel Lespinasse rb_set_parent_color(tmp1, sibling, 288*6280d235SMichel Lespinasse RB_BLACK); 289*6280d235SMichel Lespinasse tmp1 = sibling; 290*6280d235SMichel Lespinasse sibling = tmp2; 2911da177e4SLinus Torvalds } 292*6280d235SMichel Lespinasse /* 293*6280d235SMichel Lespinasse * Case 4 - left rotate at parent + color flips 294*6280d235SMichel Lespinasse * (p and sl could be either color here. 295*6280d235SMichel Lespinasse * After rotation, p becomes black, s acquires 296*6280d235SMichel Lespinasse * p's color, and sl keeps its color) 297*6280d235SMichel Lespinasse * 298*6280d235SMichel Lespinasse * (p) (s) 299*6280d235SMichel Lespinasse * / \ / \ 300*6280d235SMichel Lespinasse * N S --> P Sr 301*6280d235SMichel Lespinasse * / \ / \ 302*6280d235SMichel Lespinasse * (sl) sr N (sl) 303*6280d235SMichel Lespinasse */ 304*6280d235SMichel Lespinasse parent->rb_right = tmp2 = sibling->rb_left; 305*6280d235SMichel Lespinasse sibling->rb_left = parent; 306*6280d235SMichel Lespinasse rb_set_parent_color(tmp1, sibling, RB_BLACK); 307*6280d235SMichel Lespinasse if (tmp2) 308*6280d235SMichel Lespinasse rb_set_parent(tmp2, parent); 309*6280d235SMichel Lespinasse __rb_rotate_set_parents(parent, sibling, root, 310*6280d235SMichel Lespinasse RB_BLACK); 3111da177e4SLinus Torvalds break; 312d6ff1273SMichel Lespinasse } else { 313*6280d235SMichel Lespinasse sibling = parent->rb_left; 314*6280d235SMichel Lespinasse if (rb_is_red(sibling)) { 315*6280d235SMichel Lespinasse /* Case 1 - right rotate at parent */ 316*6280d235SMichel Lespinasse parent->rb_left = tmp1 = sibling->rb_right; 317*6280d235SMichel Lespinasse sibling->rb_right = parent; 318*6280d235SMichel Lespinasse rb_set_parent_color(tmp1, parent, RB_BLACK); 319*6280d235SMichel Lespinasse __rb_rotate_set_parents(parent, sibling, root, 320*6280d235SMichel Lespinasse RB_RED); 321*6280d235SMichel Lespinasse sibling = tmp1; 3221da177e4SLinus Torvalds } 323*6280d235SMichel Lespinasse tmp1 = sibling->rb_left; 324*6280d235SMichel Lespinasse if (!tmp1 || rb_is_black(tmp1)) { 325*6280d235SMichel Lespinasse tmp2 = sibling->rb_right; 326*6280d235SMichel Lespinasse if (!tmp2 || rb_is_black(tmp2)) { 327*6280d235SMichel Lespinasse /* Case 2 - sibling color flip */ 328*6280d235SMichel Lespinasse rb_set_parent_color(sibling, parent, 329*6280d235SMichel Lespinasse RB_RED); 3301da177e4SLinus Torvalds node = parent; 33155a98102SDavid Woodhouse parent = rb_parent(node); 332e125d147SMichel Lespinasse continue; 3331da177e4SLinus Torvalds } 334*6280d235SMichel Lespinasse /* Case 3 - right rotate at sibling */ 335*6280d235SMichel Lespinasse sibling->rb_right = tmp1 = tmp2->rb_left; 336*6280d235SMichel Lespinasse tmp2->rb_left = sibling; 337*6280d235SMichel Lespinasse parent->rb_left = tmp2; 338*6280d235SMichel Lespinasse if (tmp1) 339*6280d235SMichel Lespinasse rb_set_parent_color(tmp1, sibling, 340*6280d235SMichel Lespinasse RB_BLACK); 341*6280d235SMichel Lespinasse tmp1 = sibling; 342*6280d235SMichel Lespinasse sibling = tmp2; 3431da177e4SLinus Torvalds } 344*6280d235SMichel Lespinasse /* Case 4 - left rotate at parent + color flips */ 345*6280d235SMichel Lespinasse parent->rb_left = tmp2 = sibling->rb_right; 346*6280d235SMichel Lespinasse sibling->rb_right = parent; 347*6280d235SMichel Lespinasse rb_set_parent_color(tmp1, sibling, RB_BLACK); 348*6280d235SMichel Lespinasse if (tmp2) 349*6280d235SMichel Lespinasse rb_set_parent(tmp2, parent); 350*6280d235SMichel Lespinasse __rb_rotate_set_parents(parent, sibling, root, 351*6280d235SMichel Lespinasse RB_BLACK); 3521da177e4SLinus Torvalds break; 3531da177e4SLinus Torvalds } 3541da177e4SLinus Torvalds } 3551da177e4SLinus Torvalds } 3561da177e4SLinus Torvalds 3571da177e4SLinus Torvalds void rb_erase(struct rb_node *node, struct rb_root *root) 3581da177e4SLinus Torvalds { 3591da177e4SLinus Torvalds struct rb_node *child, *parent; 3601da177e4SLinus Torvalds int color; 3611da177e4SLinus Torvalds 3621da177e4SLinus Torvalds if (!node->rb_left) 3631da177e4SLinus Torvalds child = node->rb_right; 3641da177e4SLinus Torvalds else if (!node->rb_right) 3651da177e4SLinus Torvalds child = node->rb_left; 3661da177e4SLinus Torvalds else 3671da177e4SLinus Torvalds { 3681da177e4SLinus Torvalds struct rb_node *old = node, *left; 3691da177e4SLinus Torvalds 3701da177e4SLinus Torvalds node = node->rb_right; 3711da177e4SLinus Torvalds while ((left = node->rb_left) != NULL) 3721da177e4SLinus Torvalds node = left; 37316c047adSWolfram Strepp 37416c047adSWolfram Strepp if (rb_parent(old)) { 37516c047adSWolfram Strepp if (rb_parent(old)->rb_left == old) 37616c047adSWolfram Strepp rb_parent(old)->rb_left = node; 37716c047adSWolfram Strepp else 37816c047adSWolfram Strepp rb_parent(old)->rb_right = node; 37916c047adSWolfram Strepp } else 38016c047adSWolfram Strepp root->rb_node = node; 38116c047adSWolfram Strepp 3821da177e4SLinus Torvalds child = node->rb_right; 38355a98102SDavid Woodhouse parent = rb_parent(node); 3842f3243aeSDavid Woodhouse color = rb_color(node); 3851da177e4SLinus Torvalds 3864c601178SWolfram Strepp if (parent == old) { 3874c601178SWolfram Strepp parent = node; 3884c601178SWolfram Strepp } else { 3891da177e4SLinus Torvalds if (child) 39055a98102SDavid Woodhouse rb_set_parent(child, parent); 3911975e593SDavid Woodhouse parent->rb_left = child; 3924b324126SWolfram Strepp 3934b324126SWolfram Strepp node->rb_right = old->rb_right; 3944b324126SWolfram Strepp rb_set_parent(old->rb_right, node); 3954c601178SWolfram Strepp } 3961975e593SDavid Woodhouse 397bf7ad8eeSMichel Lespinasse node->__rb_parent_color = old->__rb_parent_color; 3981da177e4SLinus Torvalds node->rb_left = old->rb_left; 39955a98102SDavid Woodhouse rb_set_parent(old->rb_left, node); 4004b324126SWolfram Strepp 4011da177e4SLinus Torvalds goto color; 4021da177e4SLinus Torvalds } 4031da177e4SLinus Torvalds 40455a98102SDavid Woodhouse parent = rb_parent(node); 4052f3243aeSDavid Woodhouse color = rb_color(node); 4061da177e4SLinus Torvalds 4071da177e4SLinus Torvalds if (child) 40855a98102SDavid Woodhouse rb_set_parent(child, parent); 409b945d6b2SPeter Zijlstra if (parent) 410b945d6b2SPeter Zijlstra { 4111da177e4SLinus Torvalds if (parent->rb_left == node) 4121da177e4SLinus Torvalds parent->rb_left = child; 4131da177e4SLinus Torvalds else 4141da177e4SLinus Torvalds parent->rb_right = child; 41517d9ddc7SPallipadi, Venkatesh } 416b945d6b2SPeter Zijlstra else 417b945d6b2SPeter Zijlstra root->rb_node = child; 4181da177e4SLinus Torvalds 4191da177e4SLinus Torvalds color: 4201da177e4SLinus Torvalds if (color == RB_BLACK) 4211da177e4SLinus Torvalds __rb_erase_color(child, parent, root); 4221da177e4SLinus Torvalds } 4231da177e4SLinus Torvalds EXPORT_SYMBOL(rb_erase); 4241da177e4SLinus Torvalds 425b945d6b2SPeter Zijlstra static void rb_augment_path(struct rb_node *node, rb_augment_f func, void *data) 426b945d6b2SPeter Zijlstra { 427b945d6b2SPeter Zijlstra struct rb_node *parent; 428b945d6b2SPeter Zijlstra 429b945d6b2SPeter Zijlstra up: 430b945d6b2SPeter Zijlstra func(node, data); 431b945d6b2SPeter Zijlstra parent = rb_parent(node); 432b945d6b2SPeter Zijlstra if (!parent) 433b945d6b2SPeter Zijlstra return; 434b945d6b2SPeter Zijlstra 435b945d6b2SPeter Zijlstra if (node == parent->rb_left && parent->rb_right) 436b945d6b2SPeter Zijlstra func(parent->rb_right, data); 437b945d6b2SPeter Zijlstra else if (parent->rb_left) 438b945d6b2SPeter Zijlstra func(parent->rb_left, data); 439b945d6b2SPeter Zijlstra 440b945d6b2SPeter Zijlstra node = parent; 441b945d6b2SPeter Zijlstra goto up; 442b945d6b2SPeter Zijlstra } 443b945d6b2SPeter Zijlstra 444b945d6b2SPeter Zijlstra /* 445b945d6b2SPeter Zijlstra * after inserting @node into the tree, update the tree to account for 446b945d6b2SPeter Zijlstra * both the new entry and any damage done by rebalance 447b945d6b2SPeter Zijlstra */ 448b945d6b2SPeter Zijlstra void rb_augment_insert(struct rb_node *node, rb_augment_f func, void *data) 449b945d6b2SPeter Zijlstra { 450b945d6b2SPeter Zijlstra if (node->rb_left) 451b945d6b2SPeter Zijlstra node = node->rb_left; 452b945d6b2SPeter Zijlstra else if (node->rb_right) 453b945d6b2SPeter Zijlstra node = node->rb_right; 454b945d6b2SPeter Zijlstra 455b945d6b2SPeter Zijlstra rb_augment_path(node, func, data); 456b945d6b2SPeter Zijlstra } 4570b6bb66dSAndreas Gruenbacher EXPORT_SYMBOL(rb_augment_insert); 458b945d6b2SPeter Zijlstra 459b945d6b2SPeter Zijlstra /* 460b945d6b2SPeter Zijlstra * before removing the node, find the deepest node on the rebalance path 461b945d6b2SPeter Zijlstra * that will still be there after @node gets removed 462b945d6b2SPeter Zijlstra */ 463b945d6b2SPeter Zijlstra struct rb_node *rb_augment_erase_begin(struct rb_node *node) 464b945d6b2SPeter Zijlstra { 465b945d6b2SPeter Zijlstra struct rb_node *deepest; 466b945d6b2SPeter Zijlstra 467b945d6b2SPeter Zijlstra if (!node->rb_right && !node->rb_left) 468b945d6b2SPeter Zijlstra deepest = rb_parent(node); 469b945d6b2SPeter Zijlstra else if (!node->rb_right) 470b945d6b2SPeter Zijlstra deepest = node->rb_left; 471b945d6b2SPeter Zijlstra else if (!node->rb_left) 472b945d6b2SPeter Zijlstra deepest = node->rb_right; 473b945d6b2SPeter Zijlstra else { 474b945d6b2SPeter Zijlstra deepest = rb_next(node); 475b945d6b2SPeter Zijlstra if (deepest->rb_right) 476b945d6b2SPeter Zijlstra deepest = deepest->rb_right; 477b945d6b2SPeter Zijlstra else if (rb_parent(deepest) != node) 478b945d6b2SPeter Zijlstra deepest = rb_parent(deepest); 479b945d6b2SPeter Zijlstra } 480b945d6b2SPeter Zijlstra 481b945d6b2SPeter Zijlstra return deepest; 482b945d6b2SPeter Zijlstra } 4830b6bb66dSAndreas Gruenbacher EXPORT_SYMBOL(rb_augment_erase_begin); 484b945d6b2SPeter Zijlstra 485b945d6b2SPeter Zijlstra /* 486b945d6b2SPeter Zijlstra * after removal, update the tree to account for the removed entry 487b945d6b2SPeter Zijlstra * and any rebalance damage. 488b945d6b2SPeter Zijlstra */ 489b945d6b2SPeter Zijlstra void rb_augment_erase_end(struct rb_node *node, rb_augment_f func, void *data) 490b945d6b2SPeter Zijlstra { 491b945d6b2SPeter Zijlstra if (node) 492b945d6b2SPeter Zijlstra rb_augment_path(node, func, data); 493b945d6b2SPeter Zijlstra } 4940b6bb66dSAndreas Gruenbacher EXPORT_SYMBOL(rb_augment_erase_end); 495b945d6b2SPeter Zijlstra 4961da177e4SLinus Torvalds /* 4971da177e4SLinus Torvalds * This function returns the first node (in sort order) of the tree. 4981da177e4SLinus Torvalds */ 499f4b477c4SArtem Bityutskiy struct rb_node *rb_first(const struct rb_root *root) 5001da177e4SLinus Torvalds { 5011da177e4SLinus Torvalds struct rb_node *n; 5021da177e4SLinus Torvalds 5031da177e4SLinus Torvalds n = root->rb_node; 5041da177e4SLinus Torvalds if (!n) 5051da177e4SLinus Torvalds return NULL; 5061da177e4SLinus Torvalds while (n->rb_left) 5071da177e4SLinus Torvalds n = n->rb_left; 5081da177e4SLinus Torvalds return n; 5091da177e4SLinus Torvalds } 5101da177e4SLinus Torvalds EXPORT_SYMBOL(rb_first); 5111da177e4SLinus Torvalds 512f4b477c4SArtem Bityutskiy struct rb_node *rb_last(const struct rb_root *root) 5131da177e4SLinus Torvalds { 5141da177e4SLinus Torvalds struct rb_node *n; 5151da177e4SLinus Torvalds 5161da177e4SLinus Torvalds n = root->rb_node; 5171da177e4SLinus Torvalds if (!n) 5181da177e4SLinus Torvalds return NULL; 5191da177e4SLinus Torvalds while (n->rb_right) 5201da177e4SLinus Torvalds n = n->rb_right; 5211da177e4SLinus Torvalds return n; 5221da177e4SLinus Torvalds } 5231da177e4SLinus Torvalds EXPORT_SYMBOL(rb_last); 5241da177e4SLinus Torvalds 525f4b477c4SArtem Bityutskiy struct rb_node *rb_next(const struct rb_node *node) 5261da177e4SLinus Torvalds { 52755a98102SDavid Woodhouse struct rb_node *parent; 52855a98102SDavid Woodhouse 5294c199a93SMichel Lespinasse if (RB_EMPTY_NODE(node)) 53010fd48f2SJens Axboe return NULL; 53110fd48f2SJens Axboe 5321da177e4SLinus Torvalds /* If we have a right-hand child, go down and then left as far 5331da177e4SLinus Torvalds as we can. */ 5341da177e4SLinus Torvalds if (node->rb_right) { 5351da177e4SLinus Torvalds node = node->rb_right; 5361da177e4SLinus Torvalds while (node->rb_left) 5371da177e4SLinus Torvalds node=node->rb_left; 538f4b477c4SArtem Bityutskiy return (struct rb_node *)node; 5391da177e4SLinus Torvalds } 5401da177e4SLinus Torvalds 5411da177e4SLinus Torvalds /* No right-hand children. Everything down and left is 5421da177e4SLinus Torvalds smaller than us, so any 'next' node must be in the general 5431da177e4SLinus Torvalds direction of our parent. Go up the tree; any time the 5441da177e4SLinus Torvalds ancestor is a right-hand child of its parent, keep going 5451da177e4SLinus Torvalds up. First time it's a left-hand child of its parent, said 5461da177e4SLinus Torvalds parent is our 'next' node. */ 54755a98102SDavid Woodhouse while ((parent = rb_parent(node)) && node == parent->rb_right) 54855a98102SDavid Woodhouse node = parent; 5491da177e4SLinus Torvalds 55055a98102SDavid Woodhouse return parent; 5511da177e4SLinus Torvalds } 5521da177e4SLinus Torvalds EXPORT_SYMBOL(rb_next); 5531da177e4SLinus Torvalds 554f4b477c4SArtem Bityutskiy struct rb_node *rb_prev(const struct rb_node *node) 5551da177e4SLinus Torvalds { 55655a98102SDavid Woodhouse struct rb_node *parent; 55755a98102SDavid Woodhouse 5584c199a93SMichel Lespinasse if (RB_EMPTY_NODE(node)) 55910fd48f2SJens Axboe return NULL; 56010fd48f2SJens Axboe 5611da177e4SLinus Torvalds /* If we have a left-hand child, go down and then right as far 5621da177e4SLinus Torvalds as we can. */ 5631da177e4SLinus Torvalds if (node->rb_left) { 5641da177e4SLinus Torvalds node = node->rb_left; 5651da177e4SLinus Torvalds while (node->rb_right) 5661da177e4SLinus Torvalds node=node->rb_right; 567f4b477c4SArtem Bityutskiy return (struct rb_node *)node; 5681da177e4SLinus Torvalds } 5691da177e4SLinus Torvalds 5701da177e4SLinus Torvalds /* No left-hand children. Go up till we find an ancestor which 5711da177e4SLinus Torvalds is a right-hand child of its parent */ 57255a98102SDavid Woodhouse while ((parent = rb_parent(node)) && node == parent->rb_left) 57355a98102SDavid Woodhouse node = parent; 5741da177e4SLinus Torvalds 57555a98102SDavid Woodhouse return parent; 5761da177e4SLinus Torvalds } 5771da177e4SLinus Torvalds EXPORT_SYMBOL(rb_prev); 5781da177e4SLinus Torvalds 5791da177e4SLinus Torvalds void rb_replace_node(struct rb_node *victim, struct rb_node *new, 5801da177e4SLinus Torvalds struct rb_root *root) 5811da177e4SLinus Torvalds { 58255a98102SDavid Woodhouse struct rb_node *parent = rb_parent(victim); 5831da177e4SLinus Torvalds 5841da177e4SLinus Torvalds /* Set the surrounding nodes to point to the replacement */ 5851da177e4SLinus Torvalds if (parent) { 5861da177e4SLinus Torvalds if (victim == parent->rb_left) 5871da177e4SLinus Torvalds parent->rb_left = new; 5881da177e4SLinus Torvalds else 5891da177e4SLinus Torvalds parent->rb_right = new; 5901da177e4SLinus Torvalds } else { 5911da177e4SLinus Torvalds root->rb_node = new; 5921da177e4SLinus Torvalds } 5931da177e4SLinus Torvalds if (victim->rb_left) 59455a98102SDavid Woodhouse rb_set_parent(victim->rb_left, new); 5951da177e4SLinus Torvalds if (victim->rb_right) 59655a98102SDavid Woodhouse rb_set_parent(victim->rb_right, new); 5971da177e4SLinus Torvalds 5981da177e4SLinus Torvalds /* Copy the pointers/colour from the victim to the replacement */ 5991da177e4SLinus Torvalds *new = *victim; 6001da177e4SLinus Torvalds } 6011da177e4SLinus Torvalds EXPORT_SYMBOL(rb_replace_node); 602