WebSVN – HelenOS-historic – Diff – /kernel/trunk/generic/src/adt/btree.c


/*
 * Copyright (C) 2006 Jakub Jermar
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 *
 * - Redistributions of source code must retain the above copyright
 *   notice, this list of conditions and the following disclaimer.
 * - Redistributions in binary form must reproduce the above copyright
 *   notice, this list of conditions and the following disclaimer in the
 *   documentation and/or other materials provided with the distribution.
 * - The name of the author may not be used to endorse or promote products
 *   derived from this software without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */
 
/*
 * This B-tree has the following properties:
 * - it is a ballanced 2-3-4-5 tree (i.e. BTREE_M = 5)
 * - values (i.e. pointers to values) are stored only in leaves
 * - leaves are linked in a list
 * - technically, it is a B+-tree (because of the previous properties)
 *
 * Be carefull when using these trees. They need to allocate
 * and deallocate memory for their index nodes and as such
 * can sleep.
 */
 
#include <adt/btree.h>
#include <adt/list.h>
#include <mm/slab.h>
#include <debug.h>
#include <panic.h>
#include <typedefs.h>
#include <print.h>
 
static void _btree_insert(btree_t *t, __native key, void *value, btree_node_t *rsubtree, btree_node_t *node);
static void node_initialize(btree_node_t *node);
static void node_insert_key_left(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree);
static void node_insert_key_right(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree);
static btree_node_t *node_split(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree, __native *median);
static void node_remove_key_left(btree_node_t *node, __native key);
static void node_remove_key_right(btree_node_t *node, __native key);
static index_t find_key_by_subtree(btree_node_t *node, btree_node_t *subtree, bool right);
static bool try_insert_by_left_rotation(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree);
static bool try_insert_by_right_rotation(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree);
 
#define ROOT_NODE(n)        (!(n)->parent)
#define INDEX_NODE(n)       ((n)->subtree[0] != NULL)
#define LEAF_NODE(n)        ((n)->subtree[0] == NULL)
 
#define FILL_FACTOR     ((BTREE_M-1)/2)
 
#define MEDIAN_LOW_INDEX(n) (((n)->keys-1)/2)
#define MEDIAN_HIGH_INDEX(n)    ((n)->keys/2)
#define MEDIAN_LOW(n)       ((n)->key[MEDIAN_LOW_INDEX((n))]);
#define MEDIAN_HIGH(n)      ((n)->key[MEDIAN_HIGH_INDEX((n))]);
 
/** Create empty B-tree.
 *
 * @param t B-tree.
 */
void btree_create(btree_t *t)
{
    list_initialize(&t->leaf_head);
    t->root = (btree_node_t *) malloc(sizeof(btree_node_t), 0);
    node_initialize(t->root);
    list_append(&t->root->leaf_link, &t->leaf_head);
}
 
/** Destroy empty B-tree. */
void btree_destroy(btree_t *t)
{
    ASSERT(!t->root->keys);
    free(t->root);
}
 
/** Insert key-value pair into B-tree.
 *
 * @param t B-tree.
 * @param key Key to be inserted.
 * @param value Value to be inserted.
 * @param leaf_node Leaf node where the insertion should begin.
 */
void btree_insert(btree_t *t, __native key, void *value, btree_node_t *leaf_node)
{
    btree_node_t *lnode;
   
    ASSERT(value);
   
    lnode = leaf_node;
    if (!lnode) {
        if (btree_search(t, key, &lnode)) {
            panic("B-tree %P already contains key %d\n", t, key);
        }
    }
   
    _btree_insert(t, key, value, NULL, lnode);
}
 
/** Recursively insert into B-tree.
 *
 * @param t B-tree.
 * @param key Key to be inserted.
 * @param value Value to be inserted.
 * @param rsubtree Right subtree of the inserted key.
 * @param node Start inserting into this node.
 */
void _btree_insert(btree_t *t, __native key, void *value, btree_node_t *rsubtree, btree_node_t *node)
{
    if (node->keys < BTREE_MAX_KEYS) {
        /*
         * Node conatins enough space, the key can be stored immediately.
         */
        node_insert_key_right(node, key, value, rsubtree);
    } else if (try_insert_by_left_rotation(node, key, value, rsubtree)) {
        /*
         * The key-value-rsubtree triplet has been inserted because
         * some keys could have been moved to the left sibling.
         */
    } else if (try_insert_by_right_rotation(node, key, value, rsubtree)) {
        /*
         * The key-value-rsubtree triplet has been inserted because
         * some keys could have been moved to the right sibling.
         */
    } else {
        btree_node_t *rnode;
        __native median;
       
        /*
         * Node is full and both siblings (if both exist) are full too.
         * Split the node and insert the smallest key from the node containing
         * bigger keys (i.e. the new node) into its parent.
         */
 
        rnode = node_split(node, key, value, rsubtree, &median);
 
        if (LEAF_NODE(node)) {
            list_append(&rnode->leaf_link, &node->leaf_link);
        }
       
        if (ROOT_NODE(node)) {
            /*
             * We split the root node. Create new root.
             */
            t->root = (btree_node_t *) malloc(sizeof(btree_node_t), 0);
            node->parent = t->root;
            rnode->parent = t->root;
            node_initialize(t->root);
           
            /*
             * Left-hand side subtree will be the old root (i.e. node).
             * Right-hand side subtree will be rnode.
             */        
            t->root->subtree[0] = node;
 
            t->root->depth = node->depth + 1;
        }
        _btree_insert(t, median, NULL, rnode, node->parent);
    }  
       
}
 
/** Remove B-tree node.
 *
 * @param B-tree.
 * @param key Key to be removed from the B-tree along with its associated value.
 * @param leaf_node If not NULL, pointer to the leaf node where the key is found.
 */
void btree_remove(btree_t *t, __native key, btree_node_t *leaf_node)
{
    btree_node_t *lnode;
   
    lnode = leaf_node;
    if (!lnode) {
        if (!btree_search(t, key, &lnode)) {
            panic("B-tree %P does not contain key %d\n", t, key);
        }
    }
   
    /* TODO */
 
}
 
/** Search key in a B-tree.
 *
 * @param t B-tree.
 * @param key Key to be searched.
 * @param leaf_node Address where to put pointer to visited leaf node.
 *
 * @return Pointer to value or NULL if there is no such key.
 */
void *btree_search(btree_t *t, __native key, btree_node_t **leaf_node)
{
    btree_node_t *cur, *next;
   
    /*
     * Iteratively descend to the leaf that can contain the searched key.
     */
    for (cur = t->root; cur; cur = next) {
 
        /* Last iteration will set this with proper leaf node address. */
        *leaf_node = cur;
       
        /*
         * The key can be in the leftmost subtree.
         * Test it separately.
         */
        if (key < cur->key[0]) {
            next = cur->subtree[0];
            continue;
        } else {
            void *val;
            int i;
       
            /*
             * Now if the key is smaller than cur->key[i]
             * it can only mean that the value is in cur->subtree[i]
             * or it is not in the tree at all.
             */
            for (i = 1; i < cur->keys; i++) {
                if (key < cur->key[i]) {
                    next = cur->subtree[i];
                    val = cur->value[i - 1];
 
                    if (LEAF_NODE(cur))
                        return key == cur->key[i - 1] ? val : NULL;
 
                    goto descend;
                }
            }
           
            /*
             * Last possibility is that the key is in the rightmost subtree.
             */
            next = cur->subtree[i];
            val = cur->value[i - 1];
            if (LEAF_NODE(cur))
                return key == cur->key[i - 1] ? val : NULL;
        }
        descend:
            ;
    }
 
    /*
     * The key was not found in the *leaf_node and is smaller than any of its keys.
     */
    return NULL;
}
 
/** Get pointer to value with the smallest key within the node.
 *
 * Can be only used on leaf-level nodes.
 *
 * @param node B-tree node.
 *
 * @return Pointer to value assiciated with the smallest key.
 */
void *btree_node_min(btree_node_t *node)
{
    ASSERT(LEAF_NODE(node));
    ASSERT(node->keys);
    return node->value[0];
}
 
/** Get pointer to value with the biggest key within the node.
 *
 * Can be only used on leaf-level nodes.
 *
 * @param node B-tree node.
 *
 * @return Pointer to value assiciated with the biggest key.
 */
void *btree_node_max(btree_node_t *node)
{
    ASSERT(LEAF_NODE(node));
    ASSERT(node->keys);
    return node->value[node->keys - 1];
}
 
/** Initialize B-tree node.
 *
 * @param node B-tree node.
 */
void node_initialize(btree_node_t *node)
{
    int i;
 
    node->keys = 0;
   
    /* Clean also space for the extra key. */
    for (i = 0; i < BTREE_MAX_KEYS + 1; i++) {
        node->key[i] = 0;
        node->value[i] = NULL;
        node->subtree[i] = NULL;
    }
    node->subtree[i] = NULL;
   
    node->parent = NULL;
   
    link_initialize(&node->leaf_link);
 
    link_initialize(&node->bfs_link);
    node->depth = 0;
}
 
/** Insert key-value-lsubtree triplet into B-tree node.
 *
 * It is actually possible to have more keys than BTREE_MAX_KEYS.
 * This feature is used during insert by right rotation.
 *
 * @param node B-tree node into wich the new key is to be inserted.
 * @param key The key to be inserted.
 * @param value Pointer to value to be inserted.
 * @param lsubtree Pointer to the left subtree.
 */
void node_insert_key_left(btree_node_t *node, __native key, void *value, btree_node_t *lsubtree)
{
    int i;
 
    for (i = 0; i < node->keys; i++) {
        if (key < node->key[i]) {
            int j;
       
            for (j = node->keys; j > i; j--) {
                node->key[j] = node->key[j - 1];
                node->value[j] = node->value[j - 1];
                node->subtree[j + 1] = node->subtree[j];
            }
            node->subtree[j + 1] = node->subtree[j];
            break; 
        }
    }
    node->key[i] = key;
    node->value[i] = value;
    node->subtree[i] = lsubtree;
           
    node->keys++;
}
 
 
/** Insert key-value-rsubtree triplet into B-tree node.
 *
 * It is actually possible to have more keys than BTREE_MAX_KEYS.
 * This feature is used during splitting the node when the
 * number of keys is BTREE_MAX_KEYS + 1. Insert by left rotation
 * also makes use of this feature.
 *
 * @param node B-tree node into wich the new key is to be inserted.
 * @param key The key to be inserted.
 * @param value Pointer to value to be inserted.
 * @param rsubtree Pointer to the right subtree.
 */
void node_insert_key_right(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree)
{
    int i;
 
    for (i = 0; i < node->keys; i++) {
        if (key < node->key[i]) {
            int j;
       
            for (j = node->keys; j > i; j--) {
                node->key[j] = node->key[j - 1];
                node->value[j] = node->value[j - 1];
                node->subtree[j + 1] = node->subtree[j];
            }
            break; 
        }
    }
    node->key[i] = key;
    node->value[i] = value;
    node->subtree[i + 1] = rsubtree;
           
    node->keys++;
}
 
/** Split full B-tree node and insert new key-value-right-subtree triplet.
 *
 * This function will split a node and return pointer to a newly created
 * node containing keys greater than or equal to the greater of medians
 * (or median) of the old keys and the newly added key. It will also write
 * the median key to a memory address supplied by the caller.
 *
 * If the node being split is an index node, the median will not be
 * included in the new node. If the node is a leaf node,
 * the median will be copied there.
 *
 * @param node B-tree node wich is going to be split.
 * @param key The key to be inserted.
 * @param value Pointer to the value to be inserted.
 * @param rsubtree Pointer to the right subtree of the key being added.
 * @param median Address in memory, where the median key will be stored.
 *
 * @return Newly created right sibling of node.
 */
btree_node_t *node_split(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree, __native *median)
{
    btree_node_t *rnode;
    int i, j;
 
    ASSERT(median);
    ASSERT(node->keys == BTREE_MAX_KEYS);
 
    /*
     * Use the extra space to store the extra node.
     */
    node_insert_key_right(node, key, value, rsubtree);
 
    /*
     * Compute median of keys.
     */
    *median = MEDIAN_HIGH(node);
       
    /*
     * Allocate and initialize new right sibling.
     */
    rnode = (btree_node_t *) malloc(sizeof(btree_node_t), 0);
    node_initialize(rnode);
    rnode->parent = node->parent;
    rnode->depth = node->depth;
   
    /*
     * Copy big keys, values and subtree pointers to the new right sibling.
     * If this is an index node, do not copy the median.
     */
    i = (int) INDEX_NODE(node);
    for (i += MEDIAN_HIGH_INDEX(node), j = 0; i < node->keys; i++, j++) {
        rnode->key[j] = node->key[i];
        rnode->value[j] = node->value[i];
        rnode->subtree[j] = node->subtree[i];
       
        /*
         * Fix parent links in subtrees.
         */
        if (rnode->subtree[j])
            rnode->subtree[j]->parent = rnode;
           
    }
    rnode->subtree[j] = node->subtree[i];
    if (rnode->subtree[j])
        rnode->subtree[j]->parent = rnode;
 
    rnode->keys = j;    /* Set number of keys of the new node. */
    node->keys /= 2;    /* Shrink the old node. */
       
    return rnode;
}
 
/** Remove key and its left subtree pointer from B-tree node.
 *
 * Remove the key and eliminate gaps in node->key array.
 * Note that the value pointer and the left subtree pointer
 * is removed from the node as well.
 *
 * @param node B-tree node.
 * @param key Key to be removed.
 */
void node_remove_key_left(btree_node_t *node, __native key)
{
    int i, j;
   
    for (i = 0; i < node->keys; i++) {
        if (key == node->key[i]) {
            for (j = i + 1; j < node->keys; j++) {
                node->key[j - 1] = node->key[j];
                node->value[j - 1] = node->value[j];
                node->subtree[j - 1] = node->subtree[j];
            }
            node->subtree[j - 1] = node->subtree[j];
            node->keys--;
            return;
        }
    }
    panic("node %P does not contain key %d\n", node, key);
}
 
/** Remove key and its right subtree pointer from B-tree node.
 *
 * Remove the key and eliminate gaps in node->key array.
 * Note that the value pointer and the right subtree pointer
 * is removed from the node as well.
 *
 * @param node B-tree node.
 * @param key Key to be removed.
 */
void node_remove_key_right(btree_node_t *node, __native key)
{
    int i, j;
   
    for (i = 0; i < node->keys; i++) {
        if (key == node->key[i]) {
            for (j = i + 1; j < node->keys; j++) {
                node->key[j - 1] = node->key[j];
                node->value[j - 1] = node->value[j];
                node->subtree[j] = node->subtree[j + 1];
            }
            node->keys--;
            return;
        }
    }
    panic("node %P does not contain key %d\n", node, key);
}
 
/** Find key by its left or right subtree.
 *
 * @param node B-tree node.
 * @param subtree Left or right subtree of a key found in node.
 * @param right If true, subtree is a right subtree. If false, subtree is a left subtree.
 *
 * @return Index of the key associated with the subtree.
 */
index_t find_key_by_subtree(btree_node_t *node, btree_node_t *subtree, bool right)
{
    int i;
   
    for (i = 0; i < node->keys + 1; i++) {
        if (subtree == node->subtree[i])
            return i - (int) (right != false);
    }
    panic("node %P does not contain subtree %P\n", node, subtree);
}
 
/** Insert key-value-rsubtree triplet and rotate the node to the left, if this operation can be done.
 *
 * Left sibling of the node (if it exists) is checked for free space.
 * If there is free space, the key is inserted and the smallest key of
 * the node is moved there. The index node which is the parent of both
 * nodes is fixed.
 *
 * @param node B-tree node.
 * @param inskey Key to be inserted.
 * @param insvalue Value to be inserted.
 * @param rsubtree Right subtree of inskey.
 *
 * @return True if the rotation was performed, false otherwise.
 */
bool try_insert_by_left_rotation(btree_node_t *node, __native inskey, void *insvalue, btree_node_t *rsubtree)
{
    index_t idx;
    btree_node_t *lnode;
 
    /*
     * If this is root node, the rotation can not be done.
     */
    if (ROOT_NODE(node))
        return false;
   
    idx = find_key_by_subtree(node->parent, node, true);
    if ((int) idx == -1) {
        /*
         * If this node is the leftmost subtree of its parent,
         * the rotation can not be done.
         */
        return false;
    }
       
    lnode = node->parent->subtree[idx];
 
    if (lnode->keys < BTREE_MAX_KEYS) {
        __native key;
 
        /*
         * The rotaion can be done. The left sibling has free space.
         */
 
        node_insert_key_right(node, inskey, insvalue, rsubtree);
        key = node->key[0];
       
        if (LEAF_NODE(node)) {
            void *value;
 
            value = node->value[0];
            node_remove_key_left(node, key);
            node_insert_key_right(lnode, key, value, NULL);
            node->parent->key[idx] = node->key[0];
        } else {
            btree_node_t *lsubtree;
 
            lsubtree = node->subtree[0];
            node_remove_key_left(node, key);
            node_insert_key_right(lnode, node->parent->key[idx], NULL, lsubtree);
            node->parent->key[idx] = key;
 
            /* Fix parent link of the reconnected left subtree. */
            lsubtree->parent = lnode;
        }
        return true;
    }
 
    return false;
}
 
/** Insert key-value-rsubtree triplet and rotate the node to the right, if this operation can be done.
 *
 * Right sibling of the node (if it exists) is checked for free space.
 * If there is free space, the key is inserted and the biggest key of
 * the node is moved there. The index node which is the parent of both
 * nodes is fixed.
 *
 * @param node B-tree node.
 * @param inskey Key to be inserted.
 * @param insvalue Value to be inserted.
 * @param rsubtree Right subtree of inskey.
 *
 * @return True if the rotation was performed, false otherwise.
 */
bool try_insert_by_right_rotation(btree_node_t *node, __native inskey, void *insvalue, btree_node_t *rsubtree)
{
    index_t idx;
    btree_node_t *rnode;
 
    /*
     * If this is root node, the rotation can not be done.
     */
    if (ROOT_NODE(node))
        return false;
   
    idx = find_key_by_subtree(node->parent, node, false);
    if (idx == node->parent->keys) {
        /*
         * If this node is the rightmost subtree of its parent,
         * the rotation can not be done.
         */
        return false;
    }
       
    rnode = node->parent->subtree[idx + 1];
 
    if (rnode->keys < BTREE_MAX_KEYS) {
        __native key;
 
        /*
         * The rotaion can be done. The right sibling has free space.
         */
 
        node_insert_key_right(node, inskey, insvalue, rsubtree);
        key = node->key[node->keys - 1];
       
        if (LEAF_NODE(node)) {
            void *value;
 
            value = node->value[node->keys - 1];
            node_remove_key_right(node, key);
            node_insert_key_left(rnode, key, value, NULL);
            node->parent->key[idx] = key;
        } else {
            btree_node_t *rsubt;
 
            rsubt = node->subtree[node->keys];
            node_remove_key_right(node, key);
            node_insert_key_left(rnode, node->parent->key[idx], NULL, rsubt);
            node->parent->key[idx] = key;
 
            /* Fix parent link of the reconnected right subtree. */
            rsubt->parent = rnode;
        }
        return true;
    }
 
    return false;
}
 
/** Print B-tree.
 *
 * @param t Print out B-tree.
 */
void btree_print(btree_t *t)
{
    int i, depth = t->root->depth;
    link_t head;
   
    list_initialize(&head);
    list_append(&t->root->bfs_link, &head);
 
    /*
     * Use BFS search to print out the tree.
     * Levels are distinguished from one another by node->depth.
     */
    while (!list_empty(&head)) {
        link_t *hlp;
        btree_node_t *node;
       
        hlp = head.next;
        ASSERT(hlp != &head);
        node = list_get_instance(hlp, btree_node_t, bfs_link);
        list_remove(hlp);
       
        ASSERT(node);
       
        if (node->depth != depth) {
            printf("\n");
            depth = node->depth;
        }
 
        printf("(");
        for (i = 0; i < node->keys; i++) {
            printf("%d,", node->key[i]);
            if (node->depth && node->subtree[i]) {
                list_append(&node->subtree[i]->bfs_link, &head);
            }
        }
        if (node->depth && node->subtree[i]) {
            list_append(&node->subtree[i]->bfs_link, &head);
        }
        printf(")");
    }
    printf("\n");
}
 
Subversion Repositories HelenOS-historic

(root)/kernel/trunk/generic/src/adt/btree.c @ 1757 – Rev 1136 → 1140
