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  1. /*
  2.  * Copyright (C) 2006 Jakub Jermar
  3.  * All rights reserved.
  4.  *
  5.  * Redistribution and use in source and binary forms, with or without
  6.  * modification, are permitted provided that the following conditions
  7.  * are met:
  8.  *
  9.  * - Redistributions of source code must retain the above copyright
  10.  *   notice, this list of conditions and the following disclaimer.
  11.  * - Redistributions in binary form must reproduce the above copyright
  12.  *   notice, this list of conditions and the following disclaimer in the
  13.  *   documentation and/or other materials provided with the distribution.
  14.  * - The name of the author may not be used to endorse or promote products
  15.  *   derived from this software without specific prior written permission.
  16.  *
  17.  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
  18.  * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
  19.  * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
  20.  * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
  21.  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
  22.  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
  23.  * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
  24.  * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
  25.  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
  26.  * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  27.  */
  28.  
  29. /*
  30.  * This B-tree has the following properties:
  31.  * - it is a ballanced 2-3-4 tree (i.e. M = 4)
  32.  * - values (i.e. pointers to values) are stored only in leaves
  33.  * - leaves are linked in a list
  34.  * - technically, it is a B+-tree (because of the previous properties)
  35.  *
  36.  * Some of the functions below take pointer to the right-hand
  37.  * side subtree pointer as parameter. Note that this is sufficient
  38.  * because:
  39.  *  - New root node is passed the left-hand side subtree pointer
  40.  *    directly.
  41.  *  - node_split() always creates the right sibling and preserves
  42.  *    the original node (which becomes the left sibling).
  43.  *    There is always pointer to the left-hand side subtree
  44.  *    (i.e. left sibling) in the parent node.
  45.  */
  46.  
  47. #include <adt/btree.h>
  48. #include <adt/list.h>
  49. #include <mm/slab.h>
  50. #include <debug.h>
  51. #include <panic.h>
  52. #include <typedefs.h>
  53. #include <print.h>
  54.  
  55. static void _btree_insert(btree_t *t, __native key, void *value, btree_node_t *rsubtree, btree_node_t *node);
  56. static void node_initialize(btree_node_t *node);
  57. static void node_insert_key(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree);
  58. static btree_node_t *node_split(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree, __native *median);
  59.  
  60. #define ROOT_NODE(n)        (!(n)->parent)
  61. #define INDEX_NODE(n)       ((n)->subtree[0] != NULL)
  62. #define LEAF_NODE(n)        ((n)->subtree[0] == NULL)
  63.  
  64. #define MEDIAN_LOW_INDEX(n) (((n)->keys-1)/2)
  65. #define MEDIAN_HIGH_INDEX(n)    ((n)->keys/2)
  66. #define MEDIAN_LOW(n)       ((n)->key[MEDIAN_LOW_INDEX((n))]);
  67. #define MEDIAN_HIGH(n)      ((n)->key[MEDIAN_HIGH_INDEX((n))]);
  68.  
  69. /** Create empty B-tree.
  70.  *
  71.  * @param t B-tree.
  72.  */
  73. void btree_create(btree_t *t)
  74. {
  75.     list_initialize(&t->leaf_head);
  76.     t->root = (btree_node_t *) malloc(sizeof(btree_node_t), 0);
  77.     node_initialize(t->root);
  78.     list_append(&t->root->leaf_link, &t->leaf_head);
  79. }
  80.  
  81. /** Destroy empty B-tree. */
  82. void btree_destroy(btree_t *t)
  83. {
  84.     ASSERT(!t->root->keys);
  85.     free(t->root);
  86. }
  87.  
  88. /** Insert key-value pair into B-tree.
  89.  *
  90.  * @param t B-tree.
  91.  * @param key Key to be inserted.
  92.  * @param value Value to be inserted.
  93.  * @param leaf_node Leaf node where the insertion should begin.
  94.  */
  95. void btree_insert(btree_t *t, __native key, void *value, btree_node_t *leaf_node)
  96. {
  97.     btree_node_t *lnode;
  98.    
  99.     ASSERT(value);
  100.    
  101.     lnode = leaf_node;
  102.     if (!lnode) {
  103.         if (btree_search(t, key, &lnode)) {
  104.             panic("B-tree %P already contains key %d\n", t, key);
  105.         }
  106.     }
  107.    
  108.     _btree_insert(t, key, value, NULL, lnode);
  109. }
  110.  
  111. /** Recursively insert into B-tree.
  112.  *
  113.  * @param t B-tree.
  114.  * @param key Key to be inserted.
  115.  * @param value Value to be inserted.
  116.  * @param rsubtree Right subtree of the inserted key.
  117.  * @param node Start inserting into this node.
  118.  */
  119. void _btree_insert(btree_t *t, __native key, void *value, btree_node_t *rsubtree, btree_node_t *node)
  120. {
  121.     if (node->keys < BTREE_MAX_KEYS) {
  122.         /*
  123.          * Node conatins enough space, the key can be stored immediately.
  124.          */
  125.         node_insert_key(node, key, value, rsubtree);
  126.     } else {
  127.         btree_node_t *rnode;
  128.         __native median;
  129.        
  130.         /*
  131.          * Node is full.
  132.          * Split it and insert the smallest key from the node containing
  133.          * bigger keys (i.e. the original node) into its parent.
  134.          */
  135.  
  136.         rnode = node_split(node, key, value, rsubtree, &median);
  137.  
  138.         if (LEAF_NODE(node)) {
  139.             list_append(&rnode->leaf_link, &node->leaf_link);
  140.         }
  141.        
  142.         if (ROOT_NODE(node)) {
  143.             /*
  144.              * We split the root node. Create new root.
  145.              */
  146.        
  147.             t->root = (btree_node_t *) malloc(sizeof(btree_node_t), 0);
  148.             node->parent = t->root;
  149.             rnode->parent = t->root;
  150.             node_initialize(t->root);
  151.            
  152.             /*
  153.              * Left-hand side subtree will be the old root (i.e. node).
  154.              * Right-hand side subtree will be rnode.
  155.              */        
  156.             t->root->subtree[0] = node;
  157.  
  158.             t->root->depth = node->depth + 1;
  159.         }
  160.         _btree_insert(t, median, NULL, rnode, node->parent);
  161.     }  
  162.        
  163. }
  164.  
  165. /* TODO */
  166. void btree_remove(btree_t *t, __native key)
  167. {
  168. }
  169.  
  170. /** Search key in a B-tree.
  171.  *
  172.  * @param t B-tree.
  173.  * @param key Key to be searched.
  174.  * @param leaf_node Address where to put pointer to visited leaf node.
  175.  *
  176.  * @return Pointer to value or NULL if there is no such key.
  177.  */
  178. void *btree_search(btree_t *t, __native key, btree_node_t **leaf_node)
  179. {
  180.     btree_node_t *cur, *next;
  181.     void *val = NULL;
  182.    
  183.     /*
  184.      * Iteratively descend to the leaf that can contain searched key.
  185.      */
  186.     for (cur = t->root; cur; cur = next) {
  187.         int i;
  188.    
  189.         /* Last iteration will set this with proper leaf node address. */
  190.         *leaf_node = cur;
  191.         for (i = 0; i < cur->keys; i++) {
  192.             if (key <= cur->key[i]) {
  193.                 val = cur->value[i];
  194.                 next = cur->subtree[i];
  195.                
  196.                 /*
  197.                  * Check if there is anywhere to descend.
  198.                  */
  199.                 if (!next) {
  200.                     /*
  201.                      * Leaf-level.
  202.                      */
  203.                     return (key == cur->key[i]) ? val : NULL;
  204.                 }
  205.                 goto descend;
  206.             }
  207.         }
  208.         next = cur->subtree[i];
  209.     descend:
  210.         ;
  211.     }
  212.  
  213.     /*
  214.      * The key was not found in the *leaf_node and is greater than any of its keys.
  215.      */
  216.     return NULL;
  217. }
  218.  
  219. /** Get pointer to value with the smallest key within the node.
  220.  *
  221.  * Can be only used on leaf-level nodes.
  222.  *
  223.  * @param node B-tree node.
  224.  *
  225.  * @return Pointer to value assiciated with the smallest key.
  226.  */
  227. void *btree_node_min(btree_node_t *node)
  228. {
  229.     ASSERT(LEAF_NODE(node));
  230.     ASSERT(node->keys);
  231.     return node->value[0];
  232. }
  233.  
  234. /** Get pointer to value with the biggest key within the node.
  235.  *
  236.  * Can be only used on leaf-level nodes.
  237.  *
  238.  * @param node B-tree node.
  239.  *
  240.  * @return Pointer to value assiciated with the biggest key.
  241.  */
  242. void *btree_node_max(btree_node_t *node)
  243. {
  244.     ASSERT(LEAF_NODE(node));
  245.     ASSERT(node->keys);
  246.     return node->value[node->keys - 1];
  247. }
  248.  
  249. /** Initialize B-tree node.
  250.  *
  251.  * @param node B-tree node.
  252.  */
  253. void node_initialize(btree_node_t *node)
  254. {
  255.     int i;
  256.  
  257.     node->keys = 0;
  258.    
  259.     /* Clean also space for the extra key. */
  260.     for (i = 0; i < BTREE_MAX_KEYS + 1; i++) {
  261.         node->key[i] = 0;
  262.         node->value[i] = NULL;
  263.         node->subtree[i] = NULL;
  264.     }
  265.     node->subtree[i] = NULL;
  266.    
  267.     node->parent = NULL;
  268.    
  269.     link_initialize(&node->leaf_link);
  270.  
  271.     link_initialize(&node->bfs_link);
  272.     node->depth = 0;
  273. }
  274.  
  275. /** Insert key-value-left-subtree triplet into B-tree non-full node.
  276.  *
  277.  * It is actually possible to have more keys than BTREE_MAX_KEYS.
  278.  * This feature is used during splitting the node when the
  279.  * number of keys is BTREE_MAX_KEYS + 1.
  280.  *
  281.  * @param node B-tree node into wich the new key is to be inserted.
  282.  * @param key The key to be inserted.
  283.  * @param value Pointer to value to be inserted.
  284.  * @param rsubtree Pointer to the right subtree.
  285.  */
  286. void node_insert_key(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree)
  287. {
  288.     int i;
  289.  
  290.     for (i = 0; i < node->keys; i++) {
  291.         if (key < node->key[i]) {
  292.             int j;
  293.        
  294.             for (j = node->keys; j > i; j--) {
  295.                 node->key[j] = node->key[j - 1];
  296.                 node->value[j] = node->value[j - 1];
  297.                 node->subtree[j + 1] = node->subtree[j];
  298.             }
  299.             break; 
  300.         }
  301.     }
  302.  
  303.     node->key[i] = key;
  304.     node->value[i] = value;
  305.     node->subtree[i + 1] = rsubtree;
  306.            
  307.     node->keys++;
  308. }
  309.  
  310. /** Split full B-tree node and insert new key-value-left-subtree triplet.
  311.  *
  312.  * This function will split a node and return pointer to a newly created
  313.  * node containing keys greater than the lesser of medians (or median)
  314.  * of the old keys and the newly added key. It will also write the
  315.  * median key to a memory address supplied by the caller.
  316.  *
  317.  * If the node being split is an index node, the median will be
  318.  * removed from the original node. If the node is a leaf node,
  319.  * the median will be preserved.
  320.  *
  321.  * @param node B-tree node wich is going to be split.
  322.  * @param key The key to be inserted.
  323.  * @param value Pointer to the value to be inserted.
  324.  * @param rsubtree Pointer to the right subtree of the key being added.
  325.  * @param median Address in memory, where the median key will be stored.
  326.  *
  327.  * @return Newly created right sibling of node.
  328.  */
  329. btree_node_t *node_split(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree, __native *median)
  330. {
  331.     btree_node_t *rnode;
  332.     int i, j;
  333.  
  334.     ASSERT(median);
  335.     ASSERT(node->keys == BTREE_MAX_KEYS);
  336.    
  337.     /*
  338.      * Use the extra space to store the extra node.
  339.      */
  340.     node_insert_key(node, key, value, rsubtree);
  341.  
  342.     /*
  343.      * Compute median of keys.
  344.      */
  345.     *median = MEDIAN_LOW(node);
  346.        
  347.     rnode = (btree_node_t *) malloc(sizeof(btree_node_t), 0);
  348.     node_initialize(rnode);
  349.     rnode->parent = node->parent;
  350.     rnode->depth = node->depth;
  351.    
  352.     /*
  353.      * Copy big keys, values and subtree pointers to the new right sibling.
  354.      */
  355.     for (i = MEDIAN_LOW_INDEX(node) + 1, j = 0; i < node->keys; i++, j++) {
  356.         rnode->key[j] = node->key[i];
  357.         rnode->value[j] = node->value[i];
  358.         rnode->subtree[j] = node->subtree[i];
  359.        
  360.         /*
  361.          * Fix parent links in subtrees.
  362.          */
  363.         if (rnode->subtree[j])
  364.             rnode->subtree[j]->parent = rnode;
  365.            
  366.     }
  367.     rnode->subtree[j] = node->subtree[i];
  368.     if (rnode->subtree[j])
  369.         rnode->subtree[j]->parent = rnode;
  370.     rnode->keys = j;
  371.    
  372.     /*
  373.      * Shrink the old node.
  374.      * If this is an index node, remove the median.
  375.      */
  376.     node->keys = MEDIAN_LOW_INDEX(node) + 1;
  377.     if (INDEX_NODE(node))
  378.         node->keys--;
  379.        
  380.     return rnode;
  381. }
  382.  
  383. /** Print B-tree.
  384.  *
  385.  * @param t Print out B-tree.
  386.  */
  387. void btree_print(btree_t *t)
  388. {
  389.     int i, depth = t->root->depth;
  390.     link_t head;
  391.    
  392.     list_initialize(&head);
  393.     list_append(&t->root->bfs_link, &head);
  394.  
  395.     /*
  396.      * Use BFS search to print out the tree.
  397.      * Levels are distinguished from one another by node->depth.
  398.      */
  399.     while (!list_empty(&head)) {
  400.         link_t *hlp;
  401.         btree_node_t *node;
  402.        
  403.         hlp = head.next;
  404.         ASSERT(hlp != &head);
  405.         node = list_get_instance(hlp, btree_node_t, bfs_link);
  406.         list_remove(hlp);
  407.        
  408.         ASSERT(node);
  409.        
  410.         if (node->depth != depth) {
  411.             printf("\n");
  412.             depth = node->depth;
  413.         }
  414.  
  415.         printf("(");
  416.         for (i = 0; i < node->keys; i++) {
  417.             printf("%d,", node->key[i]);
  418.             if (node->depth && node->subtree[i]) {
  419.                 list_append(&node->subtree[i]->bfs_link, &head);
  420.             }
  421.         }
  422.         if (node->depth && node->subtree[i]) {
  423.             list_append(&node->subtree[i]->bfs_link, &head);
  424.         }
  425.         printf(")");
  426.     }
  427.     printf("\n");
  428. }
  429.