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 tree (i.e. BTREE_M = 4)
  * - 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)
+ *
- * Some of the functions below take pointer to the right-hand
- * side subtree pointer as parameter. Note that this is sufficient
- * because:
- *  - New root node is passed the left-hand side subtree pointer
- *    directly.
- *  - node_split() always creates the right sibling and preserves
- *    the original node (which becomes the left sibling).
- *    There is always pointer to the left-hand side subtree
- *    (i.e. left sibling) in the parent node.
- *
  * 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(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree);
+static void node_insert_key_left(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree);
-void node_remove_key(btree_node_t *node, __native key);
+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 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(node, key, value, rsubtree);
+        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.
+         * Node is full and both siblings (if both exist) are full too.
-         * Split it and insert the smallest key from the node containing
+         * Split the node and insert the smallest key from the node containing
-         * bigger keys (i.e. the original node) into its parent.
+         * 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);
+    }
+}
 /* TODO */
 void btree_remove(btree_t *t, __native key)
+{
+}
 /** 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-right-subtree triplet into B-tree non-full node.
+/** 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.
+ * 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(btree_node_t *node, __native key, void *value, btree_node_t *rsubtree)
+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(node, key, value, rsubtree);
+    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
-/** Remove key from B-tree node.
+ * is removed from the node as well.
+ *
  * @param node B-tree node.
  * @param key Key to be removed.
  */
-void node_remove_key(btree_node_t *node, __native key)
+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 1134 → 1136