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

  * - 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 <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)
+{
     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)) {
         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);
     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]) {
                 node->subtree[j + 1] = node->subtree[j];
+            }
             break;
+        }
+    }
     node->key[i] = key;
     node->value[i] = value;
     node->subtree[i + 1] = rsubtree;
     node->keys++;
     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);
     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.

Subversion Repositories HelenOS-historic

(root)/kernel/trunk/generic/src/adt/btree.c – Rev 1134 → 1136