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 26*5bc9188aSMichel Lespinasse /* 27*5bc9188aSMichel Lespinasse * red-black trees properties: http://en.wikipedia.org/wiki/Rbtree 28*5bc9188aSMichel Lespinasse * 29*5bc9188aSMichel Lespinasse * 1) A node is either red or black 30*5bc9188aSMichel Lespinasse * 2) The root is black 31*5bc9188aSMichel Lespinasse * 3) All leaves (NULL) are black 32*5bc9188aSMichel Lespinasse * 4) Both children of every red node are black 33*5bc9188aSMichel Lespinasse * 5) Every simple path from root to leaves contains the same number 34*5bc9188aSMichel Lespinasse * of black nodes. 35*5bc9188aSMichel Lespinasse * 36*5bc9188aSMichel Lespinasse * 4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two 37*5bc9188aSMichel Lespinasse * consecutive red nodes in a path and every red node is therefore followed by 38*5bc9188aSMichel Lespinasse * a black. So if B is the number of black nodes on every simple path (as per 39*5bc9188aSMichel Lespinasse * 5), then the longest possible path due to 4 is 2B. 40*5bc9188aSMichel Lespinasse * 41*5bc9188aSMichel Lespinasse * We shall indicate color with case, where black nodes are uppercase and red 42*5bc9188aSMichel Lespinasse * nodes will be lowercase. 43*5bc9188aSMichel Lespinasse */ 44*5bc9188aSMichel 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 63*5bc9188aSMichel Lespinasse static inline void rb_set_parent_color(struct rb_node *rb, 64*5bc9188aSMichel Lespinasse struct rb_node *p, int color) 65*5bc9188aSMichel Lespinasse { 66*5bc9188aSMichel Lespinasse rb->__rb_parent_color = (unsigned long)p | color; 67*5bc9188aSMichel Lespinasse } 68*5bc9188aSMichel Lespinasse 69*5bc9188aSMichel Lespinasse static inline struct rb_node *rb_red_parent(struct rb_node *red) 70*5bc9188aSMichel Lespinasse { 71*5bc9188aSMichel Lespinasse return (struct rb_node *)red->__rb_parent_color; 72*5bc9188aSMichel Lespinasse } 73*5bc9188aSMichel 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 120*5bc9188aSMichel Lespinasse /* 121*5bc9188aSMichel Lespinasse * Helper function for rotations: 122*5bc9188aSMichel Lespinasse * - old's parent and color get assigned to new 123*5bc9188aSMichel Lespinasse * - old gets assigned new as a parent and 'color' as a color. 124*5bc9188aSMichel Lespinasse */ 125*5bc9188aSMichel Lespinasse static inline void 126*5bc9188aSMichel Lespinasse __rb_rotate_set_parents(struct rb_node *old, struct rb_node *new, 127*5bc9188aSMichel Lespinasse struct rb_root *root, int color) 128*5bc9188aSMichel Lespinasse { 129*5bc9188aSMichel Lespinasse struct rb_node *parent = rb_parent(old); 130*5bc9188aSMichel Lespinasse new->__rb_parent_color = old->__rb_parent_color; 131*5bc9188aSMichel Lespinasse rb_set_parent_color(old, new, color); 132*5bc9188aSMichel Lespinasse if (parent) { 133*5bc9188aSMichel Lespinasse if (parent->rb_left == old) 134*5bc9188aSMichel Lespinasse parent->rb_left = new; 135*5bc9188aSMichel Lespinasse else 136*5bc9188aSMichel Lespinasse parent->rb_right = new; 137*5bc9188aSMichel Lespinasse } else 138*5bc9188aSMichel Lespinasse root->rb_node = new; 139*5bc9188aSMichel Lespinasse } 140*5bc9188aSMichel Lespinasse 1411da177e4SLinus Torvalds void rb_insert_color(struct rb_node *node, struct rb_root *root) 1421da177e4SLinus Torvalds { 143*5bc9188aSMichel 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) { 154*5bc9188aSMichel 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 159*5bc9188aSMichel Lespinasse gparent = rb_red_parent(parent); 1601da177e4SLinus Torvalds 161*5bc9188aSMichel Lespinasse if (parent == gparent->rb_left) { 162*5bc9188aSMichel Lespinasse tmp = gparent->rb_right; 163*5bc9188aSMichel Lespinasse if (tmp && rb_is_red(tmp)) { 164*5bc9188aSMichel Lespinasse /* 165*5bc9188aSMichel Lespinasse * Case 1 - color flips 166*5bc9188aSMichel Lespinasse * 167*5bc9188aSMichel Lespinasse * G g 168*5bc9188aSMichel Lespinasse * / \ / \ 169*5bc9188aSMichel Lespinasse * p u --> P U 170*5bc9188aSMichel Lespinasse * / / 171*5bc9188aSMichel Lespinasse * n N 172*5bc9188aSMichel Lespinasse * 173*5bc9188aSMichel Lespinasse * However, since g's parent might be red, and 174*5bc9188aSMichel Lespinasse * 4) does not allow this, we need to recurse 175*5bc9188aSMichel Lespinasse * at g. 176*5bc9188aSMichel Lespinasse */ 177*5bc9188aSMichel Lespinasse rb_set_parent_color(tmp, gparent, RB_BLACK); 178*5bc9188aSMichel Lespinasse rb_set_parent_color(parent, gparent, RB_BLACK); 1791da177e4SLinus Torvalds node = gparent; 180*5bc9188aSMichel Lespinasse parent = rb_parent(node); 181*5bc9188aSMichel Lespinasse rb_set_parent_color(node, parent, RB_RED); 1821da177e4SLinus Torvalds continue; 1831da177e4SLinus Torvalds } 1841da177e4SLinus Torvalds 1851f052865SMichel Lespinasse if (parent->rb_right == node) { 186*5bc9188aSMichel Lespinasse /* 187*5bc9188aSMichel Lespinasse * Case 2 - left rotate at parent 188*5bc9188aSMichel Lespinasse * 189*5bc9188aSMichel Lespinasse * G G 190*5bc9188aSMichel Lespinasse * / \ / \ 191*5bc9188aSMichel Lespinasse * p U --> n U 192*5bc9188aSMichel Lespinasse * \ / 193*5bc9188aSMichel Lespinasse * n p 194*5bc9188aSMichel Lespinasse * 195*5bc9188aSMichel Lespinasse * This still leaves us in violation of 4), the 196*5bc9188aSMichel Lespinasse * continuation into Case 3 will fix that. 197*5bc9188aSMichel Lespinasse */ 198*5bc9188aSMichel Lespinasse parent->rb_right = tmp = node->rb_left; 199*5bc9188aSMichel Lespinasse node->rb_left = parent; 200*5bc9188aSMichel Lespinasse if (tmp) 201*5bc9188aSMichel Lespinasse rb_set_parent_color(tmp, parent, 202*5bc9188aSMichel Lespinasse RB_BLACK); 203*5bc9188aSMichel Lespinasse rb_set_parent_color(parent, node, RB_RED); 2041da177e4SLinus Torvalds parent = node; 2051da177e4SLinus Torvalds } 2061da177e4SLinus Torvalds 207*5bc9188aSMichel Lespinasse /* 208*5bc9188aSMichel Lespinasse * Case 3 - right rotate at gparent 209*5bc9188aSMichel Lespinasse * 210*5bc9188aSMichel Lespinasse * G P 211*5bc9188aSMichel Lespinasse * / \ / \ 212*5bc9188aSMichel Lespinasse * p U --> n g 213*5bc9188aSMichel Lespinasse * / \ 214*5bc9188aSMichel Lespinasse * n U 215*5bc9188aSMichel Lespinasse */ 216*5bc9188aSMichel Lespinasse gparent->rb_left = tmp = parent->rb_right; 217*5bc9188aSMichel Lespinasse parent->rb_right = gparent; 218*5bc9188aSMichel Lespinasse if (tmp) 219*5bc9188aSMichel Lespinasse rb_set_parent_color(tmp, gparent, RB_BLACK); 220*5bc9188aSMichel Lespinasse __rb_rotate_set_parents(gparent, parent, root, RB_RED); 2211f052865SMichel Lespinasse break; 2221da177e4SLinus Torvalds } else { 223*5bc9188aSMichel Lespinasse tmp = gparent->rb_left; 224*5bc9188aSMichel Lespinasse if (tmp && rb_is_red(tmp)) { 225*5bc9188aSMichel Lespinasse /* Case 1 - color flips */ 226*5bc9188aSMichel Lespinasse rb_set_parent_color(tmp, gparent, RB_BLACK); 227*5bc9188aSMichel Lespinasse rb_set_parent_color(parent, gparent, RB_BLACK); 2281da177e4SLinus Torvalds node = gparent; 229*5bc9188aSMichel Lespinasse parent = rb_parent(node); 230*5bc9188aSMichel Lespinasse rb_set_parent_color(node, parent, RB_RED); 2311da177e4SLinus Torvalds continue; 2321da177e4SLinus Torvalds } 2331da177e4SLinus Torvalds 2341f052865SMichel Lespinasse if (parent->rb_left == node) { 235*5bc9188aSMichel Lespinasse /* Case 2 - right rotate at parent */ 236*5bc9188aSMichel Lespinasse parent->rb_left = tmp = node->rb_right; 237*5bc9188aSMichel Lespinasse node->rb_right = parent; 238*5bc9188aSMichel Lespinasse if (tmp) 239*5bc9188aSMichel Lespinasse rb_set_parent_color(tmp, parent, 240*5bc9188aSMichel Lespinasse RB_BLACK); 241*5bc9188aSMichel Lespinasse rb_set_parent_color(parent, node, RB_RED); 2421da177e4SLinus Torvalds parent = node; 2431da177e4SLinus Torvalds } 2441da177e4SLinus Torvalds 245*5bc9188aSMichel Lespinasse /* Case 3 - left rotate at gparent */ 246*5bc9188aSMichel Lespinasse gparent->rb_right = tmp = parent->rb_left; 247*5bc9188aSMichel Lespinasse parent->rb_left = gparent; 248*5bc9188aSMichel Lespinasse if (tmp) 249*5bc9188aSMichel Lespinasse rb_set_parent_color(tmp, gparent, RB_BLACK); 250*5bc9188aSMichel 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 26255a98102SDavid Woodhouse while ((!node || rb_is_black(node)) && node != root->rb_node) 2631da177e4SLinus Torvalds { 2641da177e4SLinus Torvalds if (parent->rb_left == node) 2651da177e4SLinus Torvalds { 2661da177e4SLinus Torvalds other = parent->rb_right; 26755a98102SDavid Woodhouse if (rb_is_red(other)) 2681da177e4SLinus Torvalds { 26955a98102SDavid Woodhouse rb_set_black(other); 27055a98102SDavid Woodhouse rb_set_red(parent); 2711da177e4SLinus Torvalds __rb_rotate_left(parent, root); 2721da177e4SLinus Torvalds other = parent->rb_right; 2731da177e4SLinus Torvalds } 27455a98102SDavid Woodhouse if ((!other->rb_left || rb_is_black(other->rb_left)) && 27555a98102SDavid Woodhouse (!other->rb_right || rb_is_black(other->rb_right))) 2761da177e4SLinus Torvalds { 27755a98102SDavid Woodhouse rb_set_red(other); 2781da177e4SLinus Torvalds node = parent; 27955a98102SDavid Woodhouse parent = rb_parent(node); 2801da177e4SLinus Torvalds } 2811da177e4SLinus Torvalds else 2821da177e4SLinus Torvalds { 28355a98102SDavid Woodhouse if (!other->rb_right || rb_is_black(other->rb_right)) 2841da177e4SLinus Torvalds { 28555a63998SWolfram Strepp rb_set_black(other->rb_left); 28655a98102SDavid Woodhouse rb_set_red(other); 2871da177e4SLinus Torvalds __rb_rotate_right(other, root); 2881da177e4SLinus Torvalds other = parent->rb_right; 2891da177e4SLinus Torvalds } 2902f3243aeSDavid Woodhouse rb_set_color(other, rb_color(parent)); 29155a98102SDavid Woodhouse rb_set_black(parent); 29255a98102SDavid Woodhouse rb_set_black(other->rb_right); 2931da177e4SLinus Torvalds __rb_rotate_left(parent, root); 2941da177e4SLinus Torvalds node = root->rb_node; 2951da177e4SLinus Torvalds break; 2961da177e4SLinus Torvalds } 2971da177e4SLinus Torvalds } 2981da177e4SLinus Torvalds else 2991da177e4SLinus Torvalds { 3001da177e4SLinus Torvalds other = parent->rb_left; 30155a98102SDavid Woodhouse if (rb_is_red(other)) 3021da177e4SLinus Torvalds { 30355a98102SDavid Woodhouse rb_set_black(other); 30455a98102SDavid Woodhouse rb_set_red(parent); 3051da177e4SLinus Torvalds __rb_rotate_right(parent, root); 3061da177e4SLinus Torvalds other = parent->rb_left; 3071da177e4SLinus Torvalds } 30855a98102SDavid Woodhouse if ((!other->rb_left || rb_is_black(other->rb_left)) && 30955a98102SDavid Woodhouse (!other->rb_right || rb_is_black(other->rb_right))) 3101da177e4SLinus Torvalds { 31155a98102SDavid Woodhouse rb_set_red(other); 3121da177e4SLinus Torvalds node = parent; 31355a98102SDavid Woodhouse parent = rb_parent(node); 3141da177e4SLinus Torvalds } 3151da177e4SLinus Torvalds else 3161da177e4SLinus Torvalds { 31755a98102SDavid Woodhouse if (!other->rb_left || rb_is_black(other->rb_left)) 3181da177e4SLinus Torvalds { 31955a63998SWolfram Strepp rb_set_black(other->rb_right); 32055a98102SDavid Woodhouse rb_set_red(other); 3211da177e4SLinus Torvalds __rb_rotate_left(other, root); 3221da177e4SLinus Torvalds other = parent->rb_left; 3231da177e4SLinus Torvalds } 3242f3243aeSDavid Woodhouse rb_set_color(other, rb_color(parent)); 32555a98102SDavid Woodhouse rb_set_black(parent); 32655a98102SDavid Woodhouse rb_set_black(other->rb_left); 3271da177e4SLinus Torvalds __rb_rotate_right(parent, root); 3281da177e4SLinus Torvalds node = root->rb_node; 3291da177e4SLinus Torvalds break; 3301da177e4SLinus Torvalds } 3311da177e4SLinus Torvalds } 3321da177e4SLinus Torvalds } 3331da177e4SLinus Torvalds if (node) 33455a98102SDavid Woodhouse rb_set_black(node); 3351da177e4SLinus Torvalds } 3361da177e4SLinus Torvalds 3371da177e4SLinus Torvalds void rb_erase(struct rb_node *node, struct rb_root *root) 3381da177e4SLinus Torvalds { 3391da177e4SLinus Torvalds struct rb_node *child, *parent; 3401da177e4SLinus Torvalds int color; 3411da177e4SLinus Torvalds 3421da177e4SLinus Torvalds if (!node->rb_left) 3431da177e4SLinus Torvalds child = node->rb_right; 3441da177e4SLinus Torvalds else if (!node->rb_right) 3451da177e4SLinus Torvalds child = node->rb_left; 3461da177e4SLinus Torvalds else 3471da177e4SLinus Torvalds { 3481da177e4SLinus Torvalds struct rb_node *old = node, *left; 3491da177e4SLinus Torvalds 3501da177e4SLinus Torvalds node = node->rb_right; 3511da177e4SLinus Torvalds while ((left = node->rb_left) != NULL) 3521da177e4SLinus Torvalds node = left; 35316c047adSWolfram Strepp 35416c047adSWolfram Strepp if (rb_parent(old)) { 35516c047adSWolfram Strepp if (rb_parent(old)->rb_left == old) 35616c047adSWolfram Strepp rb_parent(old)->rb_left = node; 35716c047adSWolfram Strepp else 35816c047adSWolfram Strepp rb_parent(old)->rb_right = node; 35916c047adSWolfram Strepp } else 36016c047adSWolfram Strepp root->rb_node = node; 36116c047adSWolfram Strepp 3621da177e4SLinus Torvalds child = node->rb_right; 36355a98102SDavid Woodhouse parent = rb_parent(node); 3642f3243aeSDavid Woodhouse color = rb_color(node); 3651da177e4SLinus Torvalds 3664c601178SWolfram Strepp if (parent == old) { 3674c601178SWolfram Strepp parent = node; 3684c601178SWolfram Strepp } else { 3691da177e4SLinus Torvalds if (child) 37055a98102SDavid Woodhouse rb_set_parent(child, parent); 3711975e593SDavid Woodhouse parent->rb_left = child; 3724b324126SWolfram Strepp 3734b324126SWolfram Strepp node->rb_right = old->rb_right; 3744b324126SWolfram Strepp rb_set_parent(old->rb_right, node); 3754c601178SWolfram Strepp } 3761975e593SDavid Woodhouse 377bf7ad8eeSMichel Lespinasse node->__rb_parent_color = old->__rb_parent_color; 3781da177e4SLinus Torvalds node->rb_left = old->rb_left; 37955a98102SDavid Woodhouse rb_set_parent(old->rb_left, node); 3804b324126SWolfram Strepp 3811da177e4SLinus Torvalds goto color; 3821da177e4SLinus Torvalds } 3831da177e4SLinus Torvalds 38455a98102SDavid Woodhouse parent = rb_parent(node); 3852f3243aeSDavid Woodhouse color = rb_color(node); 3861da177e4SLinus Torvalds 3871da177e4SLinus Torvalds if (child) 38855a98102SDavid Woodhouse rb_set_parent(child, parent); 389b945d6b2SPeter Zijlstra if (parent) 390b945d6b2SPeter Zijlstra { 3911da177e4SLinus Torvalds if (parent->rb_left == node) 3921da177e4SLinus Torvalds parent->rb_left = child; 3931da177e4SLinus Torvalds else 3941da177e4SLinus Torvalds parent->rb_right = child; 39517d9ddc7SPallipadi, Venkatesh } 396b945d6b2SPeter Zijlstra else 397b945d6b2SPeter Zijlstra root->rb_node = child; 3981da177e4SLinus Torvalds 3991da177e4SLinus Torvalds color: 4001da177e4SLinus Torvalds if (color == RB_BLACK) 4011da177e4SLinus Torvalds __rb_erase_color(child, parent, root); 4021da177e4SLinus Torvalds } 4031da177e4SLinus Torvalds EXPORT_SYMBOL(rb_erase); 4041da177e4SLinus Torvalds 405b945d6b2SPeter Zijlstra static void rb_augment_path(struct rb_node *node, rb_augment_f func, void *data) 406b945d6b2SPeter Zijlstra { 407b945d6b2SPeter Zijlstra struct rb_node *parent; 408b945d6b2SPeter Zijlstra 409b945d6b2SPeter Zijlstra up: 410b945d6b2SPeter Zijlstra func(node, data); 411b945d6b2SPeter Zijlstra parent = rb_parent(node); 412b945d6b2SPeter Zijlstra if (!parent) 413b945d6b2SPeter Zijlstra return; 414b945d6b2SPeter Zijlstra 415b945d6b2SPeter Zijlstra if (node == parent->rb_left && parent->rb_right) 416b945d6b2SPeter Zijlstra func(parent->rb_right, data); 417b945d6b2SPeter Zijlstra else if (parent->rb_left) 418b945d6b2SPeter Zijlstra func(parent->rb_left, data); 419b945d6b2SPeter Zijlstra 420b945d6b2SPeter Zijlstra node = parent; 421b945d6b2SPeter Zijlstra goto up; 422b945d6b2SPeter Zijlstra } 423b945d6b2SPeter Zijlstra 424b945d6b2SPeter Zijlstra /* 425b945d6b2SPeter Zijlstra * after inserting @node into the tree, update the tree to account for 426b945d6b2SPeter Zijlstra * both the new entry and any damage done by rebalance 427b945d6b2SPeter Zijlstra */ 428b945d6b2SPeter Zijlstra void rb_augment_insert(struct rb_node *node, rb_augment_f func, void *data) 429b945d6b2SPeter Zijlstra { 430b945d6b2SPeter Zijlstra if (node->rb_left) 431b945d6b2SPeter Zijlstra node = node->rb_left; 432b945d6b2SPeter Zijlstra else if (node->rb_right) 433b945d6b2SPeter Zijlstra node = node->rb_right; 434b945d6b2SPeter Zijlstra 435b945d6b2SPeter Zijlstra rb_augment_path(node, func, data); 436b945d6b2SPeter Zijlstra } 4370b6bb66dSAndreas Gruenbacher EXPORT_SYMBOL(rb_augment_insert); 438b945d6b2SPeter Zijlstra 439b945d6b2SPeter Zijlstra /* 440b945d6b2SPeter Zijlstra * before removing the node, find the deepest node on the rebalance path 441b945d6b2SPeter Zijlstra * that will still be there after @node gets removed 442b945d6b2SPeter Zijlstra */ 443b945d6b2SPeter Zijlstra struct rb_node *rb_augment_erase_begin(struct rb_node *node) 444b945d6b2SPeter Zijlstra { 445b945d6b2SPeter Zijlstra struct rb_node *deepest; 446b945d6b2SPeter Zijlstra 447b945d6b2SPeter Zijlstra if (!node->rb_right && !node->rb_left) 448b945d6b2SPeter Zijlstra deepest = rb_parent(node); 449b945d6b2SPeter Zijlstra else if (!node->rb_right) 450b945d6b2SPeter Zijlstra deepest = node->rb_left; 451b945d6b2SPeter Zijlstra else if (!node->rb_left) 452b945d6b2SPeter Zijlstra deepest = node->rb_right; 453b945d6b2SPeter Zijlstra else { 454b945d6b2SPeter Zijlstra deepest = rb_next(node); 455b945d6b2SPeter Zijlstra if (deepest->rb_right) 456b945d6b2SPeter Zijlstra deepest = deepest->rb_right; 457b945d6b2SPeter Zijlstra else if (rb_parent(deepest) != node) 458b945d6b2SPeter Zijlstra deepest = rb_parent(deepest); 459b945d6b2SPeter Zijlstra } 460b945d6b2SPeter Zijlstra 461b945d6b2SPeter Zijlstra return deepest; 462b945d6b2SPeter Zijlstra } 4630b6bb66dSAndreas Gruenbacher EXPORT_SYMBOL(rb_augment_erase_begin); 464b945d6b2SPeter Zijlstra 465b945d6b2SPeter Zijlstra /* 466b945d6b2SPeter Zijlstra * after removal, update the tree to account for the removed entry 467b945d6b2SPeter Zijlstra * and any rebalance damage. 468b945d6b2SPeter Zijlstra */ 469b945d6b2SPeter Zijlstra void rb_augment_erase_end(struct rb_node *node, rb_augment_f func, void *data) 470b945d6b2SPeter Zijlstra { 471b945d6b2SPeter Zijlstra if (node) 472b945d6b2SPeter Zijlstra rb_augment_path(node, func, data); 473b945d6b2SPeter Zijlstra } 4740b6bb66dSAndreas Gruenbacher EXPORT_SYMBOL(rb_augment_erase_end); 475b945d6b2SPeter Zijlstra 4761da177e4SLinus Torvalds /* 4771da177e4SLinus Torvalds * This function returns the first node (in sort order) of the tree. 4781da177e4SLinus Torvalds */ 479f4b477c4SArtem Bityutskiy struct rb_node *rb_first(const struct rb_root *root) 4801da177e4SLinus Torvalds { 4811da177e4SLinus Torvalds struct rb_node *n; 4821da177e4SLinus Torvalds 4831da177e4SLinus Torvalds n = root->rb_node; 4841da177e4SLinus Torvalds if (!n) 4851da177e4SLinus Torvalds return NULL; 4861da177e4SLinus Torvalds while (n->rb_left) 4871da177e4SLinus Torvalds n = n->rb_left; 4881da177e4SLinus Torvalds return n; 4891da177e4SLinus Torvalds } 4901da177e4SLinus Torvalds EXPORT_SYMBOL(rb_first); 4911da177e4SLinus Torvalds 492f4b477c4SArtem Bityutskiy struct rb_node *rb_last(const struct rb_root *root) 4931da177e4SLinus Torvalds { 4941da177e4SLinus Torvalds struct rb_node *n; 4951da177e4SLinus Torvalds 4961da177e4SLinus Torvalds n = root->rb_node; 4971da177e4SLinus Torvalds if (!n) 4981da177e4SLinus Torvalds return NULL; 4991da177e4SLinus Torvalds while (n->rb_right) 5001da177e4SLinus Torvalds n = n->rb_right; 5011da177e4SLinus Torvalds return n; 5021da177e4SLinus Torvalds } 5031da177e4SLinus Torvalds EXPORT_SYMBOL(rb_last); 5041da177e4SLinus Torvalds 505f4b477c4SArtem Bityutskiy struct rb_node *rb_next(const struct rb_node *node) 5061da177e4SLinus Torvalds { 50755a98102SDavid Woodhouse struct rb_node *parent; 50855a98102SDavid Woodhouse 5094c199a93SMichel Lespinasse if (RB_EMPTY_NODE(node)) 51010fd48f2SJens Axboe return NULL; 51110fd48f2SJens Axboe 5121da177e4SLinus Torvalds /* If we have a right-hand child, go down and then left as far 5131da177e4SLinus Torvalds as we can. */ 5141da177e4SLinus Torvalds if (node->rb_right) { 5151da177e4SLinus Torvalds node = node->rb_right; 5161da177e4SLinus Torvalds while (node->rb_left) 5171da177e4SLinus Torvalds node=node->rb_left; 518f4b477c4SArtem Bityutskiy return (struct rb_node *)node; 5191da177e4SLinus Torvalds } 5201da177e4SLinus Torvalds 5211da177e4SLinus Torvalds /* No right-hand children. Everything down and left is 5221da177e4SLinus Torvalds smaller than us, so any 'next' node must be in the general 5231da177e4SLinus Torvalds direction of our parent. Go up the tree; any time the 5241da177e4SLinus Torvalds ancestor is a right-hand child of its parent, keep going 5251da177e4SLinus Torvalds up. First time it's a left-hand child of its parent, said 5261da177e4SLinus Torvalds parent is our 'next' node. */ 52755a98102SDavid Woodhouse while ((parent = rb_parent(node)) && node == parent->rb_right) 52855a98102SDavid Woodhouse node = parent; 5291da177e4SLinus Torvalds 53055a98102SDavid Woodhouse return parent; 5311da177e4SLinus Torvalds } 5321da177e4SLinus Torvalds EXPORT_SYMBOL(rb_next); 5331da177e4SLinus Torvalds 534f4b477c4SArtem Bityutskiy struct rb_node *rb_prev(const struct rb_node *node) 5351da177e4SLinus Torvalds { 53655a98102SDavid Woodhouse struct rb_node *parent; 53755a98102SDavid Woodhouse 5384c199a93SMichel Lespinasse if (RB_EMPTY_NODE(node)) 53910fd48f2SJens Axboe return NULL; 54010fd48f2SJens Axboe 5411da177e4SLinus Torvalds /* If we have a left-hand child, go down and then right as far 5421da177e4SLinus Torvalds as we can. */ 5431da177e4SLinus Torvalds if (node->rb_left) { 5441da177e4SLinus Torvalds node = node->rb_left; 5451da177e4SLinus Torvalds while (node->rb_right) 5461da177e4SLinus Torvalds node=node->rb_right; 547f4b477c4SArtem Bityutskiy return (struct rb_node *)node; 5481da177e4SLinus Torvalds } 5491da177e4SLinus Torvalds 5501da177e4SLinus Torvalds /* No left-hand children. Go up till we find an ancestor which 5511da177e4SLinus Torvalds is a right-hand child of its parent */ 55255a98102SDavid Woodhouse while ((parent = rb_parent(node)) && node == parent->rb_left) 55355a98102SDavid Woodhouse node = parent; 5541da177e4SLinus Torvalds 55555a98102SDavid Woodhouse return parent; 5561da177e4SLinus Torvalds } 5571da177e4SLinus Torvalds EXPORT_SYMBOL(rb_prev); 5581da177e4SLinus Torvalds 5591da177e4SLinus Torvalds void rb_replace_node(struct rb_node *victim, struct rb_node *new, 5601da177e4SLinus Torvalds struct rb_root *root) 5611da177e4SLinus Torvalds { 56255a98102SDavid Woodhouse struct rb_node *parent = rb_parent(victim); 5631da177e4SLinus Torvalds 5641da177e4SLinus Torvalds /* Set the surrounding nodes to point to the replacement */ 5651da177e4SLinus Torvalds if (parent) { 5661da177e4SLinus Torvalds if (victim == parent->rb_left) 5671da177e4SLinus Torvalds parent->rb_left = new; 5681da177e4SLinus Torvalds else 5691da177e4SLinus Torvalds parent->rb_right = new; 5701da177e4SLinus Torvalds } else { 5711da177e4SLinus Torvalds root->rb_node = new; 5721da177e4SLinus Torvalds } 5731da177e4SLinus Torvalds if (victim->rb_left) 57455a98102SDavid Woodhouse rb_set_parent(victim->rb_left, new); 5751da177e4SLinus Torvalds if (victim->rb_right) 57655a98102SDavid Woodhouse rb_set_parent(victim->rb_right, new); 5771da177e4SLinus Torvalds 5781da177e4SLinus Torvalds /* Copy the pointers/colour from the victim to the replacement */ 5791da177e4SLinus Torvalds *new = *victim; 5801da177e4SLinus Torvalds } 5811da177e4SLinus Torvalds EXPORT_SYMBOL(rb_replace_node); 582