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 425bc9188aSMichel Lespinasse * nodes will be lowercase. 435bc9188aSMichel Lespinasse */ 445bc9188aSMichel Lespinasse 45bf7ad8eeSMichel Lespinasse #define RB_RED 0 46bf7ad8eeSMichel Lespinasse #define RB_BLACK 1 47bf7ad8eeSMichel Lespinasse 48bf7ad8eeSMichel Lespinasse #define rb_color(r) ((r)->__rb_parent_color & 1) 49bf7ad8eeSMichel Lespinasse #define rb_is_red(r) (!rb_color(r)) 50bf7ad8eeSMichel Lespinasse #define rb_is_black(r) rb_color(r) 51bf7ad8eeSMichel Lespinasse #define rb_set_red(r) do { (r)->__rb_parent_color &= ~1; } while (0) 52bf7ad8eeSMichel Lespinasse #define rb_set_black(r) do { (r)->__rb_parent_color |= 1; } while (0) 53bf7ad8eeSMichel Lespinasse 54bf7ad8eeSMichel Lespinasse static inline void rb_set_parent(struct rb_node *rb, struct rb_node *p) 55bf7ad8eeSMichel Lespinasse { 56bf7ad8eeSMichel Lespinasse rb->__rb_parent_color = rb_color(rb) | (unsigned long)p; 57bf7ad8eeSMichel Lespinasse } 58bf7ad8eeSMichel Lespinasse static inline void rb_set_color(struct rb_node *rb, int color) 59bf7ad8eeSMichel Lespinasse { 60bf7ad8eeSMichel Lespinasse rb->__rb_parent_color = (rb->__rb_parent_color & ~1) | color; 61bf7ad8eeSMichel Lespinasse } 62bf7ad8eeSMichel Lespinasse 635bc9188aSMichel Lespinasse static inline void rb_set_parent_color(struct rb_node *rb, 645bc9188aSMichel Lespinasse struct rb_node *p, int color) 655bc9188aSMichel Lespinasse { 665bc9188aSMichel Lespinasse rb->__rb_parent_color = (unsigned long)p | color; 675bc9188aSMichel Lespinasse } 685bc9188aSMichel Lespinasse 695bc9188aSMichel Lespinasse static inline struct rb_node *rb_red_parent(struct rb_node *red) 705bc9188aSMichel Lespinasse { 715bc9188aSMichel Lespinasse return (struct rb_node *)red->__rb_parent_color; 725bc9188aSMichel Lespinasse } 735bc9188aSMichel Lespinasse 741da177e4SLinus Torvalds static void __rb_rotate_left(struct rb_node *node, struct rb_root *root) 751da177e4SLinus Torvalds { 761da177e4SLinus Torvalds struct rb_node *right = node->rb_right; 7755a98102SDavid Woodhouse struct rb_node *parent = rb_parent(node); 781da177e4SLinus Torvalds 791da177e4SLinus Torvalds if ((node->rb_right = right->rb_left)) 8055a98102SDavid Woodhouse rb_set_parent(right->rb_left, node); 811da177e4SLinus Torvalds right->rb_left = node; 821da177e4SLinus Torvalds 8355a98102SDavid Woodhouse rb_set_parent(right, parent); 8455a98102SDavid Woodhouse 8555a98102SDavid Woodhouse if (parent) 861da177e4SLinus Torvalds { 8755a98102SDavid Woodhouse if (node == parent->rb_left) 8855a98102SDavid Woodhouse parent->rb_left = right; 891da177e4SLinus Torvalds else 9055a98102SDavid Woodhouse parent->rb_right = right; 911da177e4SLinus Torvalds } 921da177e4SLinus Torvalds else 931da177e4SLinus Torvalds root->rb_node = right; 9455a98102SDavid Woodhouse rb_set_parent(node, right); 951da177e4SLinus Torvalds } 961da177e4SLinus Torvalds 971da177e4SLinus Torvalds static void __rb_rotate_right(struct rb_node *node, struct rb_root *root) 981da177e4SLinus Torvalds { 991da177e4SLinus Torvalds struct rb_node *left = node->rb_left; 10055a98102SDavid Woodhouse struct rb_node *parent = rb_parent(node); 1011da177e4SLinus Torvalds 1021da177e4SLinus Torvalds if ((node->rb_left = left->rb_right)) 10355a98102SDavid Woodhouse rb_set_parent(left->rb_right, node); 1041da177e4SLinus Torvalds left->rb_right = node; 1051da177e4SLinus Torvalds 10655a98102SDavid Woodhouse rb_set_parent(left, parent); 10755a98102SDavid Woodhouse 10855a98102SDavid Woodhouse if (parent) 1091da177e4SLinus Torvalds { 11055a98102SDavid Woodhouse if (node == parent->rb_right) 11155a98102SDavid Woodhouse parent->rb_right = left; 1121da177e4SLinus Torvalds else 11355a98102SDavid Woodhouse parent->rb_left = left; 1141da177e4SLinus Torvalds } 1151da177e4SLinus Torvalds else 1161da177e4SLinus Torvalds root->rb_node = left; 11755a98102SDavid Woodhouse rb_set_parent(node, left); 1181da177e4SLinus Torvalds } 1191da177e4SLinus Torvalds 1205bc9188aSMichel Lespinasse /* 1215bc9188aSMichel Lespinasse * Helper function for rotations: 1225bc9188aSMichel Lespinasse * - old's parent and color get assigned to new 1235bc9188aSMichel Lespinasse * - old gets assigned new as a parent and 'color' as a color. 1245bc9188aSMichel Lespinasse */ 1255bc9188aSMichel Lespinasse static inline void 1265bc9188aSMichel Lespinasse __rb_rotate_set_parents(struct rb_node *old, struct rb_node *new, 1275bc9188aSMichel Lespinasse struct rb_root *root, int color) 1285bc9188aSMichel Lespinasse { 1295bc9188aSMichel Lespinasse struct rb_node *parent = rb_parent(old); 1305bc9188aSMichel Lespinasse new->__rb_parent_color = old->__rb_parent_color; 1315bc9188aSMichel Lespinasse rb_set_parent_color(old, new, color); 1325bc9188aSMichel Lespinasse if (parent) { 1335bc9188aSMichel Lespinasse if (parent->rb_left == old) 1345bc9188aSMichel Lespinasse parent->rb_left = new; 1355bc9188aSMichel Lespinasse else 1365bc9188aSMichel Lespinasse parent->rb_right = new; 1375bc9188aSMichel Lespinasse } else 1385bc9188aSMichel Lespinasse root->rb_node = new; 1395bc9188aSMichel Lespinasse } 1405bc9188aSMichel Lespinasse 1411da177e4SLinus Torvalds void rb_insert_color(struct rb_node *node, struct rb_root *root) 1421da177e4SLinus Torvalds { 1435bc9188aSMichel Lespinasse struct rb_node *parent = rb_red_parent(node), *gparent, *tmp; 1441da177e4SLinus Torvalds 1456d58452dSMichel Lespinasse while (true) { 1466d58452dSMichel Lespinasse /* 1476d58452dSMichel Lespinasse * Loop invariant: node is red 1486d58452dSMichel Lespinasse * 1496d58452dSMichel Lespinasse * If there is a black parent, we are done. 1506d58452dSMichel Lespinasse * Otherwise, take some corrective action as we don't 1516d58452dSMichel Lespinasse * want a red root or two consecutive red nodes. 1526d58452dSMichel Lespinasse */ 1536d58452dSMichel Lespinasse if (!parent) { 1545bc9188aSMichel Lespinasse rb_set_parent_color(node, NULL, RB_BLACK); 1556d58452dSMichel Lespinasse break; 1566d58452dSMichel Lespinasse } else if (rb_is_black(parent)) 1576d58452dSMichel Lespinasse break; 1586d58452dSMichel Lespinasse 1595bc9188aSMichel Lespinasse gparent = rb_red_parent(parent); 1601da177e4SLinus Torvalds 1615bc9188aSMichel Lespinasse if (parent == gparent->rb_left) { 1625bc9188aSMichel Lespinasse tmp = gparent->rb_right; 1635bc9188aSMichel Lespinasse if (tmp && rb_is_red(tmp)) { 1645bc9188aSMichel Lespinasse /* 1655bc9188aSMichel Lespinasse * Case 1 - color flips 1665bc9188aSMichel Lespinasse * 1675bc9188aSMichel Lespinasse * G g 1685bc9188aSMichel Lespinasse * / \ / \ 1695bc9188aSMichel Lespinasse * p u --> P U 1705bc9188aSMichel Lespinasse * / / 1715bc9188aSMichel Lespinasse * n N 1725bc9188aSMichel Lespinasse * 1735bc9188aSMichel Lespinasse * However, since g's parent might be red, and 1745bc9188aSMichel Lespinasse * 4) does not allow this, we need to recurse 1755bc9188aSMichel Lespinasse * at g. 1765bc9188aSMichel Lespinasse */ 1775bc9188aSMichel Lespinasse rb_set_parent_color(tmp, gparent, RB_BLACK); 1785bc9188aSMichel Lespinasse rb_set_parent_color(parent, gparent, RB_BLACK); 1791da177e4SLinus Torvalds node = gparent; 1805bc9188aSMichel Lespinasse parent = rb_parent(node); 1815bc9188aSMichel Lespinasse rb_set_parent_color(node, parent, RB_RED); 1821da177e4SLinus Torvalds continue; 1831da177e4SLinus Torvalds } 1841da177e4SLinus Torvalds 1851f052865SMichel Lespinasse if (parent->rb_right == node) { 1865bc9188aSMichel Lespinasse /* 1875bc9188aSMichel Lespinasse * Case 2 - left rotate at parent 1885bc9188aSMichel Lespinasse * 1895bc9188aSMichel Lespinasse * G G 1905bc9188aSMichel Lespinasse * / \ / \ 1915bc9188aSMichel Lespinasse * p U --> n U 1925bc9188aSMichel Lespinasse * \ / 1935bc9188aSMichel Lespinasse * n p 1945bc9188aSMichel Lespinasse * 1955bc9188aSMichel Lespinasse * This still leaves us in violation of 4), the 1965bc9188aSMichel Lespinasse * continuation into Case 3 will fix that. 1975bc9188aSMichel Lespinasse */ 1985bc9188aSMichel Lespinasse parent->rb_right = tmp = node->rb_left; 1995bc9188aSMichel Lespinasse node->rb_left = parent; 2005bc9188aSMichel Lespinasse if (tmp) 2015bc9188aSMichel Lespinasse rb_set_parent_color(tmp, parent, 2025bc9188aSMichel Lespinasse RB_BLACK); 2035bc9188aSMichel Lespinasse rb_set_parent_color(parent, node, RB_RED); 2041da177e4SLinus Torvalds parent = node; 2051da177e4SLinus Torvalds } 2061da177e4SLinus Torvalds 2075bc9188aSMichel Lespinasse /* 2085bc9188aSMichel Lespinasse * Case 3 - right rotate at gparent 2095bc9188aSMichel Lespinasse * 2105bc9188aSMichel Lespinasse * G P 2115bc9188aSMichel Lespinasse * / \ / \ 2125bc9188aSMichel Lespinasse * p U --> n g 2135bc9188aSMichel Lespinasse * / \ 2145bc9188aSMichel Lespinasse * n U 2155bc9188aSMichel Lespinasse */ 2165bc9188aSMichel Lespinasse gparent->rb_left = tmp = parent->rb_right; 2175bc9188aSMichel Lespinasse parent->rb_right = gparent; 2185bc9188aSMichel Lespinasse if (tmp) 2195bc9188aSMichel Lespinasse rb_set_parent_color(tmp, gparent, RB_BLACK); 2205bc9188aSMichel Lespinasse __rb_rotate_set_parents(gparent, parent, root, RB_RED); 2211f052865SMichel Lespinasse break; 2221da177e4SLinus Torvalds } else { 2235bc9188aSMichel Lespinasse tmp = gparent->rb_left; 2245bc9188aSMichel Lespinasse if (tmp && rb_is_red(tmp)) { 2255bc9188aSMichel Lespinasse /* Case 1 - color flips */ 2265bc9188aSMichel Lespinasse rb_set_parent_color(tmp, gparent, RB_BLACK); 2275bc9188aSMichel Lespinasse rb_set_parent_color(parent, gparent, RB_BLACK); 2281da177e4SLinus Torvalds node = gparent; 2295bc9188aSMichel Lespinasse parent = rb_parent(node); 2305bc9188aSMichel Lespinasse rb_set_parent_color(node, parent, RB_RED); 2311da177e4SLinus Torvalds continue; 2321da177e4SLinus Torvalds } 2331da177e4SLinus Torvalds 2341f052865SMichel Lespinasse if (parent->rb_left == node) { 2355bc9188aSMichel Lespinasse /* Case 2 - right rotate at parent */ 2365bc9188aSMichel Lespinasse parent->rb_left = tmp = node->rb_right; 2375bc9188aSMichel Lespinasse node->rb_right = parent; 2385bc9188aSMichel Lespinasse if (tmp) 2395bc9188aSMichel Lespinasse rb_set_parent_color(tmp, parent, 2405bc9188aSMichel Lespinasse RB_BLACK); 2415bc9188aSMichel Lespinasse rb_set_parent_color(parent, node, RB_RED); 2421da177e4SLinus Torvalds parent = node; 2431da177e4SLinus Torvalds } 2441da177e4SLinus Torvalds 2455bc9188aSMichel Lespinasse /* Case 3 - left rotate at gparent */ 2465bc9188aSMichel Lespinasse gparent->rb_right = tmp = parent->rb_left; 2475bc9188aSMichel Lespinasse parent->rb_left = gparent; 2485bc9188aSMichel Lespinasse if (tmp) 2495bc9188aSMichel Lespinasse rb_set_parent_color(tmp, gparent, RB_BLACK); 2505bc9188aSMichel Lespinasse __rb_rotate_set_parents(gparent, parent, root, RB_RED); 2511f052865SMichel Lespinasse break; 2521da177e4SLinus Torvalds } 2531da177e4SLinus Torvalds } 2541da177e4SLinus Torvalds } 2551da177e4SLinus Torvalds EXPORT_SYMBOL(rb_insert_color); 2561da177e4SLinus Torvalds 2571da177e4SLinus Torvalds static void __rb_erase_color(struct rb_node *node, struct rb_node *parent, 2581da177e4SLinus Torvalds struct rb_root *root) 2591da177e4SLinus Torvalds { 2601da177e4SLinus Torvalds struct rb_node *other; 2611da177e4SLinus Torvalds 262d6ff1273SMichel Lespinasse while (true) { 263d6ff1273SMichel Lespinasse /* 264d6ff1273SMichel Lespinasse * Loop invariant: all leaf paths going through node have a 265d6ff1273SMichel Lespinasse * black node count that is 1 lower than other leaf paths. 266d6ff1273SMichel Lespinasse * 267d6ff1273SMichel Lespinasse * If node is red, we can flip it to black to adjust. 268d6ff1273SMichel Lespinasse * If node is the root, all leaf paths go through it. 269d6ff1273SMichel Lespinasse * Otherwise, we need to adjust the tree through color flips 270d6ff1273SMichel Lespinasse * and tree rotations as per one of the 4 cases below. 271d6ff1273SMichel Lespinasse */ 272d6ff1273SMichel Lespinasse if (node && rb_is_red(node)) { 273d6ff1273SMichel Lespinasse rb_set_black(node); 274d6ff1273SMichel Lespinasse break; 275d6ff1273SMichel Lespinasse } else if (!parent) { 276d6ff1273SMichel Lespinasse break; 277d6ff1273SMichel Lespinasse } else if (parent->rb_left == node) { 2781da177e4SLinus Torvalds other = parent->rb_right; 27955a98102SDavid Woodhouse if (rb_is_red(other)) 2801da177e4SLinus Torvalds { 28155a98102SDavid Woodhouse rb_set_black(other); 28255a98102SDavid Woodhouse rb_set_red(parent); 2831da177e4SLinus Torvalds __rb_rotate_left(parent, root); 2841da177e4SLinus Torvalds other = parent->rb_right; 2851da177e4SLinus Torvalds } 286*e125d147SMichel Lespinasse if (!other->rb_right || rb_is_black(other->rb_right)) { 287*e125d147SMichel Lespinasse if (!other->rb_left || 288*e125d147SMichel Lespinasse rb_is_black(other->rb_left)) { 28955a98102SDavid Woodhouse rb_set_red(other); 2901da177e4SLinus Torvalds node = parent; 29155a98102SDavid Woodhouse parent = rb_parent(node); 292*e125d147SMichel Lespinasse continue; 2931da177e4SLinus Torvalds } 29455a63998SWolfram Strepp rb_set_black(other->rb_left); 29555a98102SDavid Woodhouse rb_set_red(other); 2961da177e4SLinus Torvalds __rb_rotate_right(other, root); 2971da177e4SLinus Torvalds other = parent->rb_right; 2981da177e4SLinus Torvalds } 2992f3243aeSDavid Woodhouse rb_set_color(other, rb_color(parent)); 30055a98102SDavid Woodhouse rb_set_black(parent); 30155a98102SDavid Woodhouse rb_set_black(other->rb_right); 3021da177e4SLinus Torvalds __rb_rotate_left(parent, root); 3031da177e4SLinus Torvalds break; 304d6ff1273SMichel Lespinasse } else { 3051da177e4SLinus Torvalds other = parent->rb_left; 30655a98102SDavid Woodhouse if (rb_is_red(other)) 3071da177e4SLinus Torvalds { 30855a98102SDavid Woodhouse rb_set_black(other); 30955a98102SDavid Woodhouse rb_set_red(parent); 3101da177e4SLinus Torvalds __rb_rotate_right(parent, root); 3111da177e4SLinus Torvalds other = parent->rb_left; 3121da177e4SLinus Torvalds } 313*e125d147SMichel Lespinasse if (!other->rb_left || rb_is_black(other->rb_left)) { 314*e125d147SMichel Lespinasse if (!other->rb_right || 315*e125d147SMichel Lespinasse rb_is_black(other->rb_right)) { 31655a98102SDavid Woodhouse rb_set_red(other); 3171da177e4SLinus Torvalds node = parent; 31855a98102SDavid Woodhouse parent = rb_parent(node); 319*e125d147SMichel Lespinasse continue; 3201da177e4SLinus Torvalds } 32155a63998SWolfram Strepp rb_set_black(other->rb_right); 32255a98102SDavid Woodhouse rb_set_red(other); 3231da177e4SLinus Torvalds __rb_rotate_left(other, root); 3241da177e4SLinus Torvalds other = parent->rb_left; 3251da177e4SLinus Torvalds } 3262f3243aeSDavid Woodhouse rb_set_color(other, rb_color(parent)); 32755a98102SDavid Woodhouse rb_set_black(parent); 32855a98102SDavid Woodhouse rb_set_black(other->rb_left); 3291da177e4SLinus Torvalds __rb_rotate_right(parent, root); 3301da177e4SLinus Torvalds break; 3311da177e4SLinus Torvalds } 3321da177e4SLinus Torvalds } 3331da177e4SLinus Torvalds } 3341da177e4SLinus Torvalds 3351da177e4SLinus Torvalds void rb_erase(struct rb_node *node, struct rb_root *root) 3361da177e4SLinus Torvalds { 3371da177e4SLinus Torvalds struct rb_node *child, *parent; 3381da177e4SLinus Torvalds int color; 3391da177e4SLinus Torvalds 3401da177e4SLinus Torvalds if (!node->rb_left) 3411da177e4SLinus Torvalds child = node->rb_right; 3421da177e4SLinus Torvalds else if (!node->rb_right) 3431da177e4SLinus Torvalds child = node->rb_left; 3441da177e4SLinus Torvalds else 3451da177e4SLinus Torvalds { 3461da177e4SLinus Torvalds struct rb_node *old = node, *left; 3471da177e4SLinus Torvalds 3481da177e4SLinus Torvalds node = node->rb_right; 3491da177e4SLinus Torvalds while ((left = node->rb_left) != NULL) 3501da177e4SLinus Torvalds node = left; 35116c047adSWolfram Strepp 35216c047adSWolfram Strepp if (rb_parent(old)) { 35316c047adSWolfram Strepp if (rb_parent(old)->rb_left == old) 35416c047adSWolfram Strepp rb_parent(old)->rb_left = node; 35516c047adSWolfram Strepp else 35616c047adSWolfram Strepp rb_parent(old)->rb_right = node; 35716c047adSWolfram Strepp } else 35816c047adSWolfram Strepp root->rb_node = node; 35916c047adSWolfram Strepp 3601da177e4SLinus Torvalds child = node->rb_right; 36155a98102SDavid Woodhouse parent = rb_parent(node); 3622f3243aeSDavid Woodhouse color = rb_color(node); 3631da177e4SLinus Torvalds 3644c601178SWolfram Strepp if (parent == old) { 3654c601178SWolfram Strepp parent = node; 3664c601178SWolfram Strepp } else { 3671da177e4SLinus Torvalds if (child) 36855a98102SDavid Woodhouse rb_set_parent(child, parent); 3691975e593SDavid Woodhouse parent->rb_left = child; 3704b324126SWolfram Strepp 3714b324126SWolfram Strepp node->rb_right = old->rb_right; 3724b324126SWolfram Strepp rb_set_parent(old->rb_right, node); 3734c601178SWolfram Strepp } 3741975e593SDavid Woodhouse 375bf7ad8eeSMichel Lespinasse node->__rb_parent_color = old->__rb_parent_color; 3761da177e4SLinus Torvalds node->rb_left = old->rb_left; 37755a98102SDavid Woodhouse rb_set_parent(old->rb_left, node); 3784b324126SWolfram Strepp 3791da177e4SLinus Torvalds goto color; 3801da177e4SLinus Torvalds } 3811da177e4SLinus Torvalds 38255a98102SDavid Woodhouse parent = rb_parent(node); 3832f3243aeSDavid Woodhouse color = rb_color(node); 3841da177e4SLinus Torvalds 3851da177e4SLinus Torvalds if (child) 38655a98102SDavid Woodhouse rb_set_parent(child, parent); 387b945d6b2SPeter Zijlstra if (parent) 388b945d6b2SPeter Zijlstra { 3891da177e4SLinus Torvalds if (parent->rb_left == node) 3901da177e4SLinus Torvalds parent->rb_left = child; 3911da177e4SLinus Torvalds else 3921da177e4SLinus Torvalds parent->rb_right = child; 39317d9ddc7SPallipadi, Venkatesh } 394b945d6b2SPeter Zijlstra else 395b945d6b2SPeter Zijlstra root->rb_node = child; 3961da177e4SLinus Torvalds 3971da177e4SLinus Torvalds color: 3981da177e4SLinus Torvalds if (color == RB_BLACK) 3991da177e4SLinus Torvalds __rb_erase_color(child, parent, root); 4001da177e4SLinus Torvalds } 4011da177e4SLinus Torvalds EXPORT_SYMBOL(rb_erase); 4021da177e4SLinus Torvalds 403b945d6b2SPeter Zijlstra static void rb_augment_path(struct rb_node *node, rb_augment_f func, void *data) 404b945d6b2SPeter Zijlstra { 405b945d6b2SPeter Zijlstra struct rb_node *parent; 406b945d6b2SPeter Zijlstra 407b945d6b2SPeter Zijlstra up: 408b945d6b2SPeter Zijlstra func(node, data); 409b945d6b2SPeter Zijlstra parent = rb_parent(node); 410b945d6b2SPeter Zijlstra if (!parent) 411b945d6b2SPeter Zijlstra return; 412b945d6b2SPeter Zijlstra 413b945d6b2SPeter Zijlstra if (node == parent->rb_left && parent->rb_right) 414b945d6b2SPeter Zijlstra func(parent->rb_right, data); 415b945d6b2SPeter Zijlstra else if (parent->rb_left) 416b945d6b2SPeter Zijlstra func(parent->rb_left, data); 417b945d6b2SPeter Zijlstra 418b945d6b2SPeter Zijlstra node = parent; 419b945d6b2SPeter Zijlstra goto up; 420b945d6b2SPeter Zijlstra } 421b945d6b2SPeter Zijlstra 422b945d6b2SPeter Zijlstra /* 423b945d6b2SPeter Zijlstra * after inserting @node into the tree, update the tree to account for 424b945d6b2SPeter Zijlstra * both the new entry and any damage done by rebalance 425b945d6b2SPeter Zijlstra */ 426b945d6b2SPeter Zijlstra void rb_augment_insert(struct rb_node *node, rb_augment_f func, void *data) 427b945d6b2SPeter Zijlstra { 428b945d6b2SPeter Zijlstra if (node->rb_left) 429b945d6b2SPeter Zijlstra node = node->rb_left; 430b945d6b2SPeter Zijlstra else if (node->rb_right) 431b945d6b2SPeter Zijlstra node = node->rb_right; 432b945d6b2SPeter Zijlstra 433b945d6b2SPeter Zijlstra rb_augment_path(node, func, data); 434b945d6b2SPeter Zijlstra } 4350b6bb66dSAndreas Gruenbacher EXPORT_SYMBOL(rb_augment_insert); 436b945d6b2SPeter Zijlstra 437b945d6b2SPeter Zijlstra /* 438b945d6b2SPeter Zijlstra * before removing the node, find the deepest node on the rebalance path 439b945d6b2SPeter Zijlstra * that will still be there after @node gets removed 440b945d6b2SPeter Zijlstra */ 441b945d6b2SPeter Zijlstra struct rb_node *rb_augment_erase_begin(struct rb_node *node) 442b945d6b2SPeter Zijlstra { 443b945d6b2SPeter Zijlstra struct rb_node *deepest; 444b945d6b2SPeter Zijlstra 445b945d6b2SPeter Zijlstra if (!node->rb_right && !node->rb_left) 446b945d6b2SPeter Zijlstra deepest = rb_parent(node); 447b945d6b2SPeter Zijlstra else if (!node->rb_right) 448b945d6b2SPeter Zijlstra deepest = node->rb_left; 449b945d6b2SPeter Zijlstra else if (!node->rb_left) 450b945d6b2SPeter Zijlstra deepest = node->rb_right; 451b945d6b2SPeter Zijlstra else { 452b945d6b2SPeter Zijlstra deepest = rb_next(node); 453b945d6b2SPeter Zijlstra if (deepest->rb_right) 454b945d6b2SPeter Zijlstra deepest = deepest->rb_right; 455b945d6b2SPeter Zijlstra else if (rb_parent(deepest) != node) 456b945d6b2SPeter Zijlstra deepest = rb_parent(deepest); 457b945d6b2SPeter Zijlstra } 458b945d6b2SPeter Zijlstra 459b945d6b2SPeter Zijlstra return deepest; 460b945d6b2SPeter Zijlstra } 4610b6bb66dSAndreas Gruenbacher EXPORT_SYMBOL(rb_augment_erase_begin); 462b945d6b2SPeter Zijlstra 463b945d6b2SPeter Zijlstra /* 464b945d6b2SPeter Zijlstra * after removal, update the tree to account for the removed entry 465b945d6b2SPeter Zijlstra * and any rebalance damage. 466b945d6b2SPeter Zijlstra */ 467b945d6b2SPeter Zijlstra void rb_augment_erase_end(struct rb_node *node, rb_augment_f func, void *data) 468b945d6b2SPeter Zijlstra { 469b945d6b2SPeter Zijlstra if (node) 470b945d6b2SPeter Zijlstra rb_augment_path(node, func, data); 471b945d6b2SPeter Zijlstra } 4720b6bb66dSAndreas Gruenbacher EXPORT_SYMBOL(rb_augment_erase_end); 473b945d6b2SPeter Zijlstra 4741da177e4SLinus Torvalds /* 4751da177e4SLinus Torvalds * This function returns the first node (in sort order) of the tree. 4761da177e4SLinus Torvalds */ 477f4b477c4SArtem Bityutskiy struct rb_node *rb_first(const struct rb_root *root) 4781da177e4SLinus Torvalds { 4791da177e4SLinus Torvalds struct rb_node *n; 4801da177e4SLinus Torvalds 4811da177e4SLinus Torvalds n = root->rb_node; 4821da177e4SLinus Torvalds if (!n) 4831da177e4SLinus Torvalds return NULL; 4841da177e4SLinus Torvalds while (n->rb_left) 4851da177e4SLinus Torvalds n = n->rb_left; 4861da177e4SLinus Torvalds return n; 4871da177e4SLinus Torvalds } 4881da177e4SLinus Torvalds EXPORT_SYMBOL(rb_first); 4891da177e4SLinus Torvalds 490f4b477c4SArtem Bityutskiy struct rb_node *rb_last(const struct rb_root *root) 4911da177e4SLinus Torvalds { 4921da177e4SLinus Torvalds struct rb_node *n; 4931da177e4SLinus Torvalds 4941da177e4SLinus Torvalds n = root->rb_node; 4951da177e4SLinus Torvalds if (!n) 4961da177e4SLinus Torvalds return NULL; 4971da177e4SLinus Torvalds while (n->rb_right) 4981da177e4SLinus Torvalds n = n->rb_right; 4991da177e4SLinus Torvalds return n; 5001da177e4SLinus Torvalds } 5011da177e4SLinus Torvalds EXPORT_SYMBOL(rb_last); 5021da177e4SLinus Torvalds 503f4b477c4SArtem Bityutskiy struct rb_node *rb_next(const struct rb_node *node) 5041da177e4SLinus Torvalds { 50555a98102SDavid Woodhouse struct rb_node *parent; 50655a98102SDavid Woodhouse 5074c199a93SMichel Lespinasse if (RB_EMPTY_NODE(node)) 50810fd48f2SJens Axboe return NULL; 50910fd48f2SJens Axboe 5101da177e4SLinus Torvalds /* If we have a right-hand child, go down and then left as far 5111da177e4SLinus Torvalds as we can. */ 5121da177e4SLinus Torvalds if (node->rb_right) { 5131da177e4SLinus Torvalds node = node->rb_right; 5141da177e4SLinus Torvalds while (node->rb_left) 5151da177e4SLinus Torvalds node=node->rb_left; 516f4b477c4SArtem Bityutskiy return (struct rb_node *)node; 5171da177e4SLinus Torvalds } 5181da177e4SLinus Torvalds 5191da177e4SLinus Torvalds /* No right-hand children. Everything down and left is 5201da177e4SLinus Torvalds smaller than us, so any 'next' node must be in the general 5211da177e4SLinus Torvalds direction of our parent. Go up the tree; any time the 5221da177e4SLinus Torvalds ancestor is a right-hand child of its parent, keep going 5231da177e4SLinus Torvalds up. First time it's a left-hand child of its parent, said 5241da177e4SLinus Torvalds parent is our 'next' node. */ 52555a98102SDavid Woodhouse while ((parent = rb_parent(node)) && node == parent->rb_right) 52655a98102SDavid Woodhouse node = parent; 5271da177e4SLinus Torvalds 52855a98102SDavid Woodhouse return parent; 5291da177e4SLinus Torvalds } 5301da177e4SLinus Torvalds EXPORT_SYMBOL(rb_next); 5311da177e4SLinus Torvalds 532f4b477c4SArtem Bityutskiy struct rb_node *rb_prev(const struct rb_node *node) 5331da177e4SLinus Torvalds { 53455a98102SDavid Woodhouse struct rb_node *parent; 53555a98102SDavid Woodhouse 5364c199a93SMichel Lespinasse if (RB_EMPTY_NODE(node)) 53710fd48f2SJens Axboe return NULL; 53810fd48f2SJens Axboe 5391da177e4SLinus Torvalds /* If we have a left-hand child, go down and then right as far 5401da177e4SLinus Torvalds as we can. */ 5411da177e4SLinus Torvalds if (node->rb_left) { 5421da177e4SLinus Torvalds node = node->rb_left; 5431da177e4SLinus Torvalds while (node->rb_right) 5441da177e4SLinus Torvalds node=node->rb_right; 545f4b477c4SArtem Bityutskiy return (struct rb_node *)node; 5461da177e4SLinus Torvalds } 5471da177e4SLinus Torvalds 5481da177e4SLinus Torvalds /* No left-hand children. Go up till we find an ancestor which 5491da177e4SLinus Torvalds is a right-hand child of its parent */ 55055a98102SDavid Woodhouse while ((parent = rb_parent(node)) && node == parent->rb_left) 55155a98102SDavid Woodhouse node = parent; 5521da177e4SLinus Torvalds 55355a98102SDavid Woodhouse return parent; 5541da177e4SLinus Torvalds } 5551da177e4SLinus Torvalds EXPORT_SYMBOL(rb_prev); 5561da177e4SLinus Torvalds 5571da177e4SLinus Torvalds void rb_replace_node(struct rb_node *victim, struct rb_node *new, 5581da177e4SLinus Torvalds struct rb_root *root) 5591da177e4SLinus Torvalds { 56055a98102SDavid Woodhouse struct rb_node *parent = rb_parent(victim); 5611da177e4SLinus Torvalds 5621da177e4SLinus Torvalds /* Set the surrounding nodes to point to the replacement */ 5631da177e4SLinus Torvalds if (parent) { 5641da177e4SLinus Torvalds if (victim == parent->rb_left) 5651da177e4SLinus Torvalds parent->rb_left = new; 5661da177e4SLinus Torvalds else 5671da177e4SLinus Torvalds parent->rb_right = new; 5681da177e4SLinus Torvalds } else { 5691da177e4SLinus Torvalds root->rb_node = new; 5701da177e4SLinus Torvalds } 5711da177e4SLinus Torvalds if (victim->rb_left) 57255a98102SDavid Woodhouse rb_set_parent(victim->rb_left, new); 5731da177e4SLinus Torvalds if (victim->rb_right) 57455a98102SDavid Woodhouse rb_set_parent(victim->rb_right, new); 5751da177e4SLinus Torvalds 5761da177e4SLinus Torvalds /* Copy the pointers/colour from the victim to the replacement */ 5771da177e4SLinus Torvalds *new = *victim; 5781da177e4SLinus Torvalds } 5791da177e4SLinus Torvalds EXPORT_SYMBOL(rb_replace_node); 580