/* * Ouroboros - Copyright (C) 2016 - 2017 * * B-trees * * Dimitri Staessens <dimitri.staessens@ugent.be> * Sander Vrijders <sander.vrijders@ugent.be> * * This library is free software; you can redistribute it and/or * modify it under the terms of the GNU Lesser General Public License * version 2.1 as published by the Free Software Foundation. * * This library is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU * Lesser General Public License for more details. * * You should have received a copy of the GNU Lesser General Public * License along with this library; if not, write to the Free Software * Foundation, Inc., http://www.fsf.org/about/contact/. */ #include <ouroboros/errno.h> #include <ouroboros/btree.h> #include <stdlib.h> #include <stdbool.h> #include <assert.h> #include <string.h> #include <sys/types.h> /* Reasonable limit to avoid overflow of ssize_t */ #define BTREE_MAX_ORDER (1 << 20) struct key_val { uint32_t key; void * val; }; /* Node in btree of order k. */ struct btnode { size_t k; size_t used; bool leaf; struct key_val * keyvals; struct btnode ** children; }; struct btree { struct btnode * root; size_t k; }; /* Binary search for arr[i].key <= key. */ static size_t search_key(const struct key_val * arr, size_t len, uint32_t key) { ssize_t lft = -1; ssize_t rgt = len; ssize_t mid; while (lft + 1 < rgt) { mid = (lft + rgt) / 2; if (arr[mid].key == key) return mid; else if (arr[mid].key < key) lft = mid; else rgt = mid; } return rgt; } static struct btnode * btnode_create(size_t k) { struct btnode * node; size_t i = 0; node = malloc(sizeof(*node)); if (node == NULL) return NULL; node->keyvals = malloc(sizeof(*node->keyvals) * k); if (node->keyvals == NULL) { free(node); return NULL; } node->children = malloc(sizeof(*node->children) * (k + 1)); if (node->children == NULL) { free(node->keyvals); free(node); return NULL; } for (i = 0; i < k; ++i) { node->children[i] = NULL; node->keyvals[i].key = 0; node->keyvals[i].val = NULL; } node->k = k; node->used = 0; node->leaf = true; return node; } static void btnode_destroy(struct btnode * node) { assert(node); free(node->children); free(node->keyvals); free(node); } static void btnode_destroy_subtree(struct btnode * node) { size_t i; for (i = 0; !node->leaf && i <= node->used; ++i) btnode_destroy_subtree(node->children[i]); btnode_destroy(node); } static int btnode_insert(struct btnode * node, struct key_val kv, struct key_val * med, struct btnode ** split) { size_t p; assert(node); assert(split); assert(kv.val); p = search_key(node->keyvals, node->used, kv.key); if (p < node->used && node->keyvals[p].key == kv.key) return -EPERM; assert(p < node->k); if (node->leaf) { memmove(&node->keyvals[p + 1], &node->keyvals[p], sizeof(*node->keyvals) * (node->used - p)); node->keyvals[p] = kv; node->used++; } else { struct btnode * rgt_s = NULL; struct key_val m; if (btnode_insert(node->children[p], kv, &m, &rgt_s)) return -1; if (rgt_s != NULL) { memmove(&node->keyvals[p + 1], &node->keyvals[p], sizeof(*node->keyvals) * (node->used - p)); node->keyvals[p] = m; memmove(&node->children[p + 2], &node->children[p + 1], sizeof(*node->children) * (node->used - p)); node->children[p + 1] = rgt_s; node->used++; } } if (node->used == node->k) { size_t mid = node->used / 2; *med = node->keyvals[mid]; *split = btnode_create(node->k); if (*split == NULL) return -ENOMEM; (*split)->used = node->used - mid - 1; (*split)->leaf = node->leaf; memmove((*split)->keyvals, &node->keyvals[mid + 1], sizeof(*node->keyvals) * (*split)->used); if (!node->leaf) memmove((*split)->children, &node->children[mid + 1], sizeof(*node->children) * ((*split)->used + 1)); node->used = mid; } return 0; } /* Merge child i with child i + 1 */ void merge(struct btnode * node, size_t i) { struct btnode * chld = node->children[i]; struct btnode * next = node->children[i + 1]; chld->keyvals[node->k / 2 - 1] = node->keyvals[i]; memmove(&chld->keyvals[node->k / 2], &next->keyvals[0], sizeof(*next->keyvals) * next->used); if (!chld->leaf) memmove(&chld->children[node->k / 2], &next->children[0], sizeof(*next->children) * (next->used + 1)); memmove(&node->keyvals[i], &node->keyvals[i + 1], sizeof(*node->keyvals) * (node->used - i - 1)); memmove(&node->children[i + 1], &node->children[i + 2], sizeof(*node->children) * (node->used - i)); chld->used += next->used + 1; node->used--; btnode_destroy(next); } /* Handle starving child at index i. */ static void fill(struct btnode * node, size_t i) { struct btnode * chld = node->children[i]; /* Feed from previous sibling. */ if (i != 0 && node->children[i - 1]->used >= node->k / 2) { struct btnode * prev = node->children[i - 1]; memmove(&chld->keyvals[1], &chld->keyvals[0], sizeof(*chld->keyvals) * chld->used); chld->keyvals[0] = node->keyvals[i - 1]; if (!chld->leaf) memmove(&chld->children[1], &chld->children[0], sizeof(*chld->children) * (chld->used + 1)); if (!node->leaf) chld->children[0] = prev->children[prev->used]; node->keyvals[i - 1] = prev->keyvals[prev->used - 1]; ++chld->used; --prev->used; return; } /* Feed from next sibling. */ if (i != node->used && node->children[i + 1]->used >= node->k / 2) { struct btnode * next = node->children[i + 1]; chld->keyvals[chld->used] = node->keyvals[i]; if (!chld->leaf) chld->children[chld->used + 1] = next->children[0]; node->keyvals[i] = next->keyvals[0]; memmove(&next->keyvals[0], &next->keyvals[1], sizeof(*next->keyvals) * next->used); if (!next->leaf) memmove(&next->children[0], &next->children[1], sizeof(*next->children) * next->used); ++chld->used; --next->used; return; } /* Cannibalize sibling. */ if (i != node->used) merge(node, i); else merge(node, i - 1); } static struct key_val btnode_pred(struct btnode * node, size_t i) { struct btnode * pred = node->children[i]; while (!pred->leaf) pred = pred->children[pred->used]; return pred->keyvals[pred->used - 1]; } static struct key_val btnode_succ(struct btnode * node, size_t i) { struct btnode * succ = node->children[i + 1]; while (!succ->leaf) succ = succ->children[0]; return succ->keyvals[0]; } static int btnode_delete(struct btnode * node, uint32_t key) { size_t i; int ret = 0; assert(node); i = search_key(node->keyvals, node->used, key); if (i < node->used && node->keyvals[i].key == key) { if (node->leaf) { memmove(&node->keyvals[i], &node->keyvals[i + 1], sizeof(*node->keyvals) * (node->used - i - 1)); --node->used; } else { if (node->children[i]->used >= node->k / 2) { node->keyvals[i] = btnode_pred(node, i); ret = btnode_delete(node->children[i], node->keyvals[i].key); } else if (node->children[i + 1]->used >= node->k / 2) { node->keyvals[i] = btnode_succ(node, i); ret = btnode_delete(node->children[i + 1], node->keyvals[i].key); } else { merge(node, i); ret = btnode_delete(node, key); } } } else { if (node->leaf) { return -1; /* value not in tree */ } else { bool flag = (i == node->used ? true : false); if (node->children[i]->used < node->children[i]->k / 2) fill(node, i); if (flag && i > node->used) ret = btnode_delete(node->children[i - 1], key); else ret = btnode_delete(node->children[i], key); } } return ret; } struct btree * btree_create(size_t k) { struct btree * tree = malloc(sizeof(*tree)); if (tree == NULL) return NULL; if (k > BTREE_MAX_ORDER) return NULL; tree->k = k; tree->root = NULL; return tree; } void btree_destroy(struct btree * tree) { if (tree == NULL) return; if (tree->root != NULL) btnode_destroy_subtree(tree->root); free(tree); } int btree_insert(struct btree * tree, uint32_t key, void * val) { struct btnode * rgt = NULL; struct key_val kv; struct key_val med; kv.key = key; kv.val = val; if (tree == NULL || val == NULL) return -EINVAL; if (tree->root == NULL) tree->root = btnode_create(tree->k); if (tree->root == NULL) return -ENOMEM; if (btnode_insert(tree->root, kv, &med, &rgt)) return -1; if (rgt != NULL) { struct btnode * lft = btnode_create(tree->root->k); if (lft == NULL) return -ENOMEM; lft->used = tree->root->used; lft->leaf = tree->root->leaf; memmove(lft->keyvals, tree->root->keyvals, sizeof(*tree->root->keyvals) * tree->root->used); memmove(lft->children, tree->root->children, sizeof(*tree->root->children) * (tree->root->used + 1)); tree->root->used = 1; tree->root->leaf = false; tree->root->keyvals[0] = med; tree->root->children[0] = lft; tree->root->children[1] = rgt; } return 0; } int btree_remove(struct btree * tree, uint32_t key) { struct btnode * prev_root; if (tree == NULL) return -EINVAL; if (tree->root == NULL) return 0; if (btnode_delete(tree->root, key)) return -1; if (tree->root->used == 0) { if (tree->root->leaf) { btnode_destroy(tree->root); tree->root = NULL; } else { prev_root = tree->root; tree->root = tree->root->children[0]; btnode_destroy(prev_root); } } return 0; } static void * btnode_search(struct btnode * node, uint32_t key) { size_t i; assert(node); i = search_key(node->keyvals, node->used, key); if (node->keyvals[i].key == key) return node->keyvals[i].val; if (node->children[i]) return btnode_search(node->children[i], key); return NULL; } void * btree_search(struct btree * tree, uint32_t key) { if (tree == NULL || tree->root == NULL) return NULL; return btnode_search(tree->root, key); }