/* * bpt.c */ #define Version "1.16.1" /* * * bpt: B+ Tree Implementation * * Copyright (c) 2018 Amittai Aviram http://www.amittai.com * All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions are met: * * 1. Redistributions of source code must retain the above copyright notice, * this list of conditions and the following disclaimer. * * 2. 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. * 3. The name of the copyright holder may not be used to endorse * or promote products derived from this software without specific * prior written permission. * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDER "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 COPYRIGHT HOLDER 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. * Author: Amittai Aviram * http://www.amittai.com * amittai.aviram@gmail.com or afa13@columbia.edu * Original Date: 26 June 2010 * Last modified: 02 September 2018 * * This implementation demonstrates the B+ tree data structure * for educational purposes, includin insertion, deletion, search, and display * of the search path, the leaves, or the whole tree. * * Must be compiled with a C99-compliant C compiler such as the latest GCC. * * Usage: bpt [order] * where order is an optional argument * (integer MIN_ORDER <= order <= MAX_ORDER) * defined as the maximal number of pointers in any node. * */ #include #ifdef _WIN32 #define bool char #define false 0 #define true 1 #endif #include #include #include // Default order is 4. #define DEFAULT_ORDER 4 // Minimum order is necessarily 3. We set the maximum // order arbitrarily. You may change the maximum order. #define MIN_ORDER 3 #define MAX_ORDER 20 // Constant for optional command-line input with "i" command. #define BUFFER_SIZE 256 // TYPES. /* Type representing the record * to which a given key refers. * In a real B+ tree system, the * record would hold data (in a database) * or a file (in an operating system) * or some other information. * Users can rewrite this part of the code * to change the type and content * of the value field. */ typedef struct record { int value; } record; /* Type representing a node in the B+ tree. * This type is general enough to serve for both * the leaf and the internal node. * The heart of the node is the array * of keys and the array of corresponding * pointers. The relation between keys * and pointers differs between leaves and * internal nodes. In a leaf, the index * of each key equals the index of its corresponding * pointer, with a maximum of order - 1 key-pointer * pairs. The last pointer points to the * leaf to the right (or NULL in the case * of the rightmost leaf). * In an internal node, the first pointer * refers to lower nodes with keys less than * the smallest key in the keys array. Then, * with indices i starting at 0, the pointer * at i + 1 points to the subtree with keys * greater than or equal to the key in this * node at index i. * The num_keys field is used to keep * track of the number of valid keys. * In an internal node, the number of valid * pointers is always num_keys + 1. * In a leaf, the number of valid pointers * to data is always num_keys. The * last leaf pointer points to the next leaf. */ typedef struct node { void ** pointers; int * keys; struct node * parent; bool is_leaf; int num_keys; struct node * next; // Used for queue. } node; // GLOBALS. /* The order determines the maximum and minimum * number of entries (keys and pointers) in any * node. Every node has at most order - 1 keys and * at least (roughly speaking) half that number. * Every leaf has as many pointers to data as keys, * and every internal node has one more pointer * to a subtree than the number of keys. * This global variable is initialized to the * default value. */ int order = DEFAULT_ORDER; /* The queue is used to print the tree in * level order, starting from the root * printing each entire rank on a separate * line, finishing with the leaves. */ node * queue = NULL; /* The user can toggle on and off the "verbose" * property, which causes the pointer addresses * to be printed out in hexadecimal notation * next to their corresponding keys. */ bool verbose_output = false; // FUNCTION PROTOTYPES. // Output and utility. void license_notice(void); void usage_1(void); void usage_2(void); void usage_3(void); void enqueue(node * new_node); node * dequeue(void); int height(node * const root); int path_to_root(node * const root, node * child); void print_leaves(node * const root); void print_tree(node * const root); void find_and_print(node * const root, int key, bool verbose); void find_and_print_range(node * const root, int range1, int range2, bool verbose); int find_range(node * const root, int key_start, int key_end, bool verbose, int returned_keys[], void * returned_pointers[]); node * find_leaf(node * const root, int key, bool verbose); record * find(node * root, int key, bool verbose, node ** leaf_out); int cut(int length); // Insertion. record * make_record(int value); node * make_node(void); node * make_leaf(void); int get_left_index(node * parent, node * left); node * insert_into_leaf(node * leaf, int key, record * pointer); node * insert_into_leaf_after_splitting(node * root, node * leaf, int key, record * pointer); node * insert_into_node(node * root, node * parent, int left_index, int key, node * right); node * insert_into_node_after_splitting(node * root, node * parent, int left_index, int key, node * right); node * insert_into_parent(node * root, node * left, int key, node * right); node * insert_into_new_root(node * left, int key, node * right); node * start_new_tree(int key, record * pointer); node * insert(node * root, int key, int value); // Deletion. int get_neighbor_index(node * n); node * adjust_root(node * root); node * coalesce_nodes(node * root, node * n, node * neighbor, int neighbor_index, int k_prime); node * redistribute_nodes(node * root, node * n, node * neighbor, int neighbor_index, int k_prime_index, int k_prime); node * delete_entry(node * root, node * n, int key, void * pointer); node * delete(node * root, int key); // FUNCTION DEFINITIONS. // OUTPUT AND UTILITIES /* Copyright and license notice to user at startup. */ void license_notice(void) { printf("bpt version %s -- Copyright (c) 2018 Amittai Aviram " "http://www.amittai.com\n", Version); printf("This program comes with ABSOLUTELY NO WARRANTY.\n" "This is free software, and you are welcome to redistribute it\n" "under certain conditions.\n" "Please see the headnote in the source code for details.\n"); } /* First message to the user. */ void usage_1(void) { printf("B+ Tree of Order %d.\n", order); printf("Following Silberschatz, Korth, Sidarshan, Database Concepts, " "5th ed.\n\n" "To build a B+ tree of a different order, start again and enter " "the order\n" "as an integer argument: bpt "); printf("(%d <= order <= %d).\n", MIN_ORDER, MAX_ORDER); printf("To start with input from a file of newline-delimited integers, \n" "start again and enter the order followed by the filename:\n" "bpt .\n"); } /* Second message to the user. */ void usage_2(void) { printf("Enter any of the following commands after the prompt > :\n" "\ti -- Insert (an integer) as both key and value).\n" "\ti -- Insert the value (an integer) as the value of key (an integer).\n" "\tf -- Find the value under key .\n" "\tp -- Print the path from the root to key k and its associated " "value.\n" "\tr -- Print the keys and values found in the range " "[, \n" "\td -- Delete key and its associated value.\n" "\tx -- Destroy the whole tree. Start again with an empty tree of the " "same order.\n" "\tt -- Print the B+ tree.\n" "\tl -- Print the keys of the leaves (bottom row of the tree).\n" "\tv -- Toggle output of pointer addresses (\"verbose\") in tree and " "leaves.\n" "\tq -- Quit. (Or use Ctl-D or Ctl-C.)\n" "\t? -- Print this help message.\n"); } /* Brief usage note. */ void usage_3(void) { printf("Usage: ./bpt []\n"); printf("\twhere %d <= order <= %d .\n", MIN_ORDER, MAX_ORDER); } /* Helper function for printing the * tree out. See print_tree. */ void enqueue(node * new_node) { node * c; if (queue == NULL) { queue = new_node; queue->next = NULL; } else { c = queue; while(c->next != NULL) { c = c->next; } c->next = new_node; new_node->next = NULL; } } /* Helper function for printing the * tree out. See print_tree. */ node * dequeue(void) { node * n = queue; queue = queue->next; n->next = NULL; return n; } /* Prints the bottom row of keys * of the tree (with their respective * pointers, if the verbose_output flag is set. */ void print_leaves(node * const root) { if (root == NULL) { printf("Empty tree.\n"); return; } int i; node * c = root; while (!c->is_leaf) c = c->pointers[0]; while (true) { for (i = 0; i < c->num_keys; i++) { if (verbose_output) printf("%p ", c->pointers[i]); printf("%d ", c->keys[i]); } if (verbose_output) printf("%p ", c->pointers[order - 1]); if (c->pointers[order - 1] != NULL) { printf(" | "); c = c->pointers[order - 1]; } else break; } printf("\n"); } /* Utility function to give the height * of the tree, which length in number of edges * of the path from the root to any leaf. */ int height(node * const root) { int h = 0; node * c = root; while (!c->is_leaf) { c = c->pointers[0]; h++; } return h; } /* Utility function to give the length in edges * of the path from any node to the root. */ int path_to_root(node * const root, node * child) { int length = 0; node * c = child; while (c != root) { c = c->parent; length++; } return length; } /* Prints the B+ tree in the command * line in level (rank) order, with the * keys in each node and the '|' symbol * to separate nodes. * With the verbose_output flag set. * the values of the pointers corresponding * to the keys also appear next to their respective * keys, in hexadecimal notation. */ void print_tree(node * const root) { node * n = NULL; int i = 0; int rank = 0; int new_rank = 0; if (root == NULL) { printf("Empty tree.\n"); return; } queue = NULL; enqueue(root); while(queue != NULL) { n = dequeue(); if (n->parent != NULL && n == n->parent->pointers[0]) { new_rank = path_to_root(root, n); if (new_rank != rank) { rank = new_rank; printf("\n"); } } if (verbose_output) printf("(%p)", n); for (i = 0; i < n->num_keys; i++) { if (verbose_output) printf("%p ", n->pointers[i]); printf("%d ", n->keys[i]); } if (!n->is_leaf) for (i = 0; i <= n->num_keys; i++) enqueue(n->pointers[i]); if (verbose_output) { if (n->is_leaf) printf("%p ", n->pointers[order - 1]); else printf("%p ", n->pointers[n->num_keys]); } printf("| "); } printf("\n"); } /* Finds the record under a given key and prints an * appropriate message to stdout. */ void find_and_print(node * const root, int key, bool verbose) { node * leaf = NULL; record * r = find(root, key, verbose, NULL); if (r == NULL) printf("Record not found under key %d.\n", key); else printf("Record at %p -- key %d, value %d.\n", r, key, r->value); } /* Finds and prints the keys, pointers, and values within a range * of keys between key_start and key_end, including both bounds. */ void find_and_print_range(node * const root, int key_start, int key_end, bool verbose) { int i; int array_size = key_end - key_start + 1; int returned_keys[array_size]; void * returned_pointers[array_size]; int num_found = find_range(root, key_start, key_end, verbose, returned_keys, returned_pointers); if (!num_found) printf("None found.\n"); else { for (i = 0; i < num_found; i++) printf("Key: %d Location: %p Value: %d\n", returned_keys[i], returned_pointers[i], ((record *) returned_pointers[i])->value); } } /* Finds keys and their pointers, if present, in the range specified * by key_start and key_end, inclusive. Places these in the arrays * returned_keys and returned_pointers, and returns the number of * entries found. */ int find_range(node * const root, int key_start, int key_end, bool verbose, int returned_keys[], void * returned_pointers[]) { int i, num_found; num_found = 0; node * n = find_leaf(root, key_start, verbose); if (n == NULL) return 0; for (i = 0; i < n->num_keys && n->keys[i] < key_start; i++) ; if (i == n->num_keys) return 0; while (n != NULL) { for (; i < n->num_keys && n->keys[i] <= key_end; i++) { returned_keys[num_found] = n->keys[i]; returned_pointers[num_found] = n->pointers[i]; num_found++; } n = n->pointers[order - 1]; i = 0; } return num_found; } /* Traces the path from the root to a leaf, searching * by key. Displays information about the path * if the verbose flag is set. * Returns the leaf containing the given key. */ node * find_leaf(node * const root, int key, bool verbose) { if (root == NULL) { if (verbose) printf("Empty tree.\n"); return root; } int i = 0; node * c = root; while (!c->is_leaf) { if (verbose) { printf("["); for (i = 0; i < c->num_keys - 1; i++) printf("%d ", c->keys[i]); printf("%d] ", c->keys[i]); } i = 0; while (i < c->num_keys) { if (key >= c->keys[i]) i++; else break; } if (verbose) printf("%d ->\n", i); c = (node *)c->pointers[i]; } if (verbose) { printf("Leaf ["); for (i = 0; i < c->num_keys - 1; i++) printf("%d ", c->keys[i]); printf("%d] ->\n", c->keys[i]); } return c; } /* Finds and returns the record to which * a key refers. */ record * find(node * root, int key, bool verbose, node ** leaf_out) { if (root == NULL) { if (leaf_out != NULL) { *leaf_out = NULL; } return NULL; } int i = 0; node * leaf = NULL; leaf = find_leaf(root, key, verbose); /* If root != NULL, leaf must have a value, even * if it does not contain the desired key. * (The leaf holds the range of keys that would * include the desired key.) */ for (i = 0; i < leaf->num_keys; i++) if (leaf->keys[i] == key) break; if (leaf_out != NULL) { *leaf_out = leaf; } if (i == leaf->num_keys) return NULL; else return (record *)leaf->pointers[i]; } /* Finds the appropriate place to * split a node that is too big into two. */ int cut(int length) { if (length % 2 == 0) return length/2; else return length/2 + 1; } // INSERTION /* Creates a new record to hold the value * to which a key refers. */ record * make_record(int value) { record * new_record = (record *)malloc(sizeof(record)); if (new_record == NULL) { perror("Record creation."); exit(EXIT_FAILURE); } else { new_record->value = value; } return new_record; } /* Creates a new general node, which can be adapted * to serve as either a leaf or an internal node. */ node * make_node(void) { node * new_node; new_node = malloc(sizeof(node)); if (new_node == NULL) { perror("Node creation."); exit(EXIT_FAILURE); } new_node->keys = malloc((order - 1) * sizeof(int)); if (new_node->keys == NULL) { perror("New node keys array."); exit(EXIT_FAILURE); } new_node->pointers = malloc(order * sizeof(void *)); if (new_node->pointers == NULL) { perror("New node pointers array."); exit(EXIT_FAILURE); } new_node->is_leaf = false; new_node->num_keys = 0; new_node->parent = NULL; new_node->next = NULL; return new_node; } /* Creates a new leaf by creating a node * and then adapting it appropriately. */ node * make_leaf(void) { node * leaf = make_node(); leaf->is_leaf = true; return leaf; } /* Helper function used in insert_into_parent * to find the index of the parent's pointer to * the node to the left of the key to be inserted. */ int get_left_index(node * parent, node * left) { int left_index = 0; while (left_index <= parent->num_keys && parent->pointers[left_index] != left) left_index++; return left_index; } /* Inserts a new pointer to a record and its corresponding * key into a leaf. * Returns the altered leaf. */ node * insert_into_leaf(node * leaf, int key, record * pointer) { int i, insertion_point; insertion_point = 0; while (insertion_point < leaf->num_keys && leaf->keys[insertion_point] < key) insertion_point++; for (i = leaf->num_keys; i > insertion_point; i--) { leaf->keys[i] = leaf->keys[i - 1]; leaf->pointers[i] = leaf->pointers[i - 1]; } leaf->keys[insertion_point] = key; leaf->pointers[insertion_point] = pointer; leaf->num_keys++; return leaf; } /* Inserts a new key and pointer * to a new record into a leaf so as to exceed * the tree's order, causing the leaf to be split * in half. */ node * insert_into_leaf_after_splitting(node * root, node * leaf, int key, record * pointer) { node * new_leaf; int * temp_keys; void ** temp_pointers; int insertion_index, split, new_key, i, j; new_leaf = make_leaf(); temp_keys = malloc(order * sizeof(int)); if (temp_keys == NULL) { perror("Temporary keys array."); exit(EXIT_FAILURE); } temp_pointers = malloc(order * sizeof(void *)); if (temp_pointers == NULL) { perror("Temporary pointers array."); exit(EXIT_FAILURE); } insertion_index = 0; while (insertion_index < order - 1 && leaf->keys[insertion_index] < key) insertion_index++; for (i = 0, j = 0; i < leaf->num_keys; i++, j++) { if (j == insertion_index) j++; temp_keys[j] = leaf->keys[i]; temp_pointers[j] = leaf->pointers[i]; } temp_keys[insertion_index] = key; temp_pointers[insertion_index] = pointer; leaf->num_keys = 0; split = cut(order - 1); for (i = 0; i < split; i++) { leaf->pointers[i] = temp_pointers[i]; leaf->keys[i] = temp_keys[i]; leaf->num_keys++; } for (i = split, j = 0; i < order; i++, j++) { new_leaf->pointers[j] = temp_pointers[i]; new_leaf->keys[j] = temp_keys[i]; new_leaf->num_keys++; } free(temp_pointers); free(temp_keys); new_leaf->pointers[order - 1] = leaf->pointers[order - 1]; leaf->pointers[order - 1] = new_leaf; for (i = leaf->num_keys; i < order - 1; i++) leaf->pointers[i] = NULL; for (i = new_leaf->num_keys; i < order - 1; i++) new_leaf->pointers[i] = NULL; new_leaf->parent = leaf->parent; new_key = new_leaf->keys[0]; return insert_into_parent(root, leaf, new_key, new_leaf); } /* Inserts a new key and pointer to a node * into a node into which these can fit * without violating the B+ tree properties. */ node * insert_into_node(node * root, node * n, int left_index, int key, node * right) { int i; for (i = n->num_keys; i > left_index; i--) { n->pointers[i + 1] = n->pointers[i]; n->keys[i] = n->keys[i - 1]; } n->pointers[left_index + 1] = right; n->keys[left_index] = key; n->num_keys++; return root; } /* Inserts a new key and pointer to a node * into a node, causing the node's size to exceed * the order, and causing the node to split into two. */ node * insert_into_node_after_splitting(node * root, node * old_node, int left_index, int key, node * right) { int i, j, split, k_prime; node * new_node, * child; int * temp_keys; node ** temp_pointers; /* First create a temporary set of keys and pointers * to hold everything in order, including * the new key and pointer, inserted in their * correct places. * Then create a new node and copy half of the * keys and pointers to the old node and * the other half to the new. */ temp_pointers = malloc((order + 1) * sizeof(node *)); if (temp_pointers == NULL) { perror("Temporary pointers array for splitting nodes."); exit(EXIT_FAILURE); } temp_keys = malloc(order * sizeof(int)); if (temp_keys == NULL) { perror("Temporary keys array for splitting nodes."); exit(EXIT_FAILURE); } for (i = 0, j = 0; i < old_node->num_keys + 1; i++, j++) { if (j == left_index + 1) j++; temp_pointers[j] = old_node->pointers[i]; } for (i = 0, j = 0; i < old_node->num_keys; i++, j++) { if (j == left_index) j++; temp_keys[j] = old_node->keys[i]; } temp_pointers[left_index + 1] = right; temp_keys[left_index] = key; /* Create the new node and copy * half the keys and pointers to the * old and half to the new. */ split = cut(order); new_node = make_node(); old_node->num_keys = 0; for (i = 0; i < split - 1; i++) { old_node->pointers[i] = temp_pointers[i]; old_node->keys[i] = temp_keys[i]; old_node->num_keys++; } old_node->pointers[i] = temp_pointers[i]; k_prime = temp_keys[split - 1]; for (++i, j = 0; i < order; i++, j++) { new_node->pointers[j] = temp_pointers[i]; new_node->keys[j] = temp_keys[i]; new_node->num_keys++; } new_node->pointers[j] = temp_pointers[i]; free(temp_pointers); free(temp_keys); new_node->parent = old_node->parent; for (i = 0; i <= new_node->num_keys; i++) { child = new_node->pointers[i]; child->parent = new_node; } /* Insert a new key into the parent of the two * nodes resulting from the split, with * the old node to the left and the new to the right. */ return insert_into_parent(root, old_node, k_prime, new_node); } /* Inserts a new node (leaf or internal node) into the B+ tree. * Returns the root of the tree after insertion. */ node * insert_into_parent(node * root, node * left, int key, node * right) { int left_index; node * parent; parent = left->parent; /* Case: new root. */ if (parent == NULL) return insert_into_new_root(left, key, right); /* Case: leaf or node. (Remainder of * function body.) */ /* Find the parent's pointer to the left * node. */ left_index = get_left_index(parent, left); /* Simple case: the new key fits into the node. */ if (parent->num_keys < order - 1) return insert_into_node(root, parent, left_index, key, right); /* Harder case: split a node in order * to preserve the B+ tree properties. */ return insert_into_node_after_splitting(root, parent, left_index, key, right); } /* Creates a new root for two subtrees * and inserts the appropriate key into * the new root. */ node * insert_into_new_root(node * left, int key, node * right) { node * root = make_node(); root->keys[0] = key; root->pointers[0] = left; root->pointers[1] = right; root->num_keys++; root->parent = NULL; left->parent = root; right->parent = root; return root; } /* First insertion: * start a new tree. */ node * start_new_tree(int key, record * pointer) { node * root = make_leaf(); root->keys[0] = key; root->pointers[0] = pointer; root->pointers[order - 1] = NULL; root->parent = NULL; root->num_keys++; return root; } /* Master insertion function. * Inserts a key and an associated value into * the B+ tree, causing the tree to be adjusted * however necessary to maintain the B+ tree * properties. */ node * insert(node * root, int key, int value) { record * record_pointer = NULL; node * leaf = NULL; /* The current implementation ignores * duplicates. */ record_pointer = find(root, key, false, NULL); if (record_pointer != NULL) { /* If the key already exists in this tree, update * the value and return the tree. */ record_pointer->value = value; return root; } /* Create a new record for the * value. */ record_pointer = make_record(value); /* Case: the tree does not exist yet. * Start a new tree. */ if (root == NULL) return start_new_tree(key, record_pointer); /* Case: the tree already exists. * (Rest of function body.) */ leaf = find_leaf(root, key, false); /* Case: leaf has room for key and record_pointer. */ if (leaf->num_keys < order - 1) { leaf = insert_into_leaf(leaf, key, record_pointer); return root; } /* Case: leaf must be split. */ return insert_into_leaf_after_splitting(root, leaf, key, record_pointer); } // DELETION. /* Utility function for deletion. Retrieves * the index of a node's nearest neighbor (sibling) * to the left if one exists. If not (the node * is the leftmost child), returns -1 to signify * this special case. */ int get_neighbor_index(node * n) { int i; /* Return the index of the key to the left * of the pointer in the parent pointing * to n. * If n is the leftmost child, this means * return -1. */ for (i = 0; i <= n->parent->num_keys; i++) if (n->parent->pointers[i] == n) return i - 1; // Error state. printf("Search for nonexistent pointer to node in parent.\n"); printf("Node: %#lx\n", (unsigned long)n); exit(EXIT_FAILURE); } node * remove_entry_from_node(node * n, int key, node * pointer) { int i, num_pointers; // Remove the key and shift other keys accordingly. i = 0; while (n->keys[i] != key) i++; for (++i; i < n->num_keys; i++) n->keys[i - 1] = n->keys[i]; // Remove the pointer and shift other pointers accordingly. // First determine number of pointers. num_pointers = n->is_leaf ? n->num_keys : n->num_keys + 1; i = 0; while (n->pointers[i] != pointer) i++; for (++i; i < num_pointers; i++) n->pointers[i - 1] = n->pointers[i]; // One key fewer. n->num_keys--; // Set the other pointers to NULL for tidiness. // A leaf uses the last pointer to point to the next leaf. if (n->is_leaf) for (i = n->num_keys; i < order - 1; i++) n->pointers[i] = NULL; else for (i = n->num_keys + 1; i < order; i++) n->pointers[i] = NULL; return n; } node * adjust_root(node * root) { node * new_root; /* Case: nonempty root. * Key and pointer have already been deleted, * so nothing to be done. */ if (root->num_keys > 0) return root; /* Case: empty root. */ // If it has a child, promote // the first (only) child // as the new root. if (!root->is_leaf) { new_root = root->pointers[0]; new_root->parent = NULL; } // If it is a leaf (has no children), // then the whole tree is empty. else new_root = NULL; free(root->keys); free(root->pointers); free(root); return new_root; } /* Coalesces a node that has become * too small after deletion * with a neighboring node that * can accept the additional entries * without exceeding the maximum. */ node * coalesce_nodes(node * root, node * n, node * neighbor, int neighbor_index, int k_prime) { int i, j, neighbor_insertion_index, n_end; node * tmp; /* Swap neighbor with node if node is on the * extreme left and neighbor is to its right. */ if (neighbor_index == -1) { tmp = n; n = neighbor; neighbor = tmp; } /* Starting point in the neighbor for copying * keys and pointers from n. * Recall that n and neighbor have swapped places * in the special case of n being a leftmost child. */ neighbor_insertion_index = neighbor->num_keys; /* Case: nonleaf node. * Append k_prime and the following pointer. * Append all pointers and keys from the neighbor. */ if (!n->is_leaf) { /* Append k_prime. */ neighbor->keys[neighbor_insertion_index] = k_prime; neighbor->num_keys++; n_end = n->num_keys; for (i = neighbor_insertion_index + 1, j = 0; j < n_end; i++, j++) { neighbor->keys[i] = n->keys[j]; neighbor->pointers[i] = n->pointers[j]; neighbor->num_keys++; n->num_keys--; } /* The number of pointers is always * one more than the number of keys. */ neighbor->pointers[i] = n->pointers[j]; /* All children must now point up to the same parent. */ for (i = 0; i < neighbor->num_keys + 1; i++) { tmp = (node *)neighbor->pointers[i]; tmp->parent = neighbor; } } /* In a leaf, append the keys and pointers of * n to the neighbor. * Set the neighbor's last pointer to point to * what had been n's right neighbor. */ else { for (i = neighbor_insertion_index, j = 0; j < n->num_keys; i++, j++) { neighbor->keys[i] = n->keys[j]; neighbor->pointers[i] = n->pointers[j]; neighbor->num_keys++; } neighbor->pointers[order - 1] = n->pointers[order - 1]; } root = delete_entry(root, n->parent, k_prime, n); free(n->keys); free(n->pointers); free(n); return root; } /* Redistributes entries between two nodes when * one has become too small after deletion * but its neighbor is too big to append the * small node's entries without exceeding the * maximum */ node * redistribute_nodes(node * root, node * n, node * neighbor, int neighbor_index, int k_prime_index, int k_prime) { int i; node * tmp; /* Case: n has a neighbor to the left. * Pull the neighbor's last key-pointer pair over * from the neighbor's right end to n's left end. */ if (neighbor_index != -1) { if (!n->is_leaf) n->pointers[n->num_keys + 1] = n->pointers[n->num_keys]; for (i = n->num_keys; i > 0; i--) { n->keys[i] = n->keys[i - 1]; n->pointers[i] = n->pointers[i - 1]; } if (!n->is_leaf) { n->pointers[0] = neighbor->pointers[neighbor->num_keys]; tmp = (node *)n->pointers[0]; tmp->parent = n; neighbor->pointers[neighbor->num_keys] = NULL; n->keys[0] = k_prime; n->parent->keys[k_prime_index] = neighbor->keys[neighbor->num_keys - 1]; } else { n->pointers[0] = neighbor->pointers[neighbor->num_keys - 1]; neighbor->pointers[neighbor->num_keys - 1] = NULL; n->keys[0] = neighbor->keys[neighbor->num_keys - 1]; n->parent->keys[k_prime_index] = n->keys[0]; } } /* Case: n is the leftmost child. * Take a key-pointer pair from the neighbor to the right. * Move the neighbor's leftmost key-pointer pair * to n's rightmost position. */ else { if (n->is_leaf) { n->keys[n->num_keys] = neighbor->keys[0]; n->pointers[n->num_keys] = neighbor->pointers[0]; n->parent->keys[k_prime_index] = neighbor->keys[1]; } else { n->keys[n->num_keys] = k_prime; n->pointers[n->num_keys + 1] = neighbor->pointers[0]; tmp = (node *)n->pointers[n->num_keys + 1]; tmp->parent = n; n->parent->keys[k_prime_index] = neighbor->keys[0]; } for (i = 0; i < neighbor->num_keys - 1; i++) { neighbor->keys[i] = neighbor->keys[i + 1]; neighbor->pointers[i] = neighbor->pointers[i + 1]; } if (!n->is_leaf) neighbor->pointers[i] = neighbor->pointers[i + 1]; } /* n now has one more key and one more pointer; * the neighbor has one fewer of each. */ n->num_keys++; neighbor->num_keys--; return root; } /* Deletes an entry from the B+ tree. * Removes the record and its key and pointer * from the leaf, and then makes all appropriate * changes to preserve the B+ tree properties. */ node * delete_entry(node * root, node * n, int key, void * pointer) { int min_keys; node * neighbor; int neighbor_index; int k_prime_index, k_prime; int capacity; // Remove key and pointer from node. n = remove_entry_from_node(n, key, pointer); /* Case: deletion from the root. */ if (n == root) return adjust_root(root); /* Case: deletion from a node below the root. * (Rest of function body.) */ /* Determine minimum allowable size of node, * to be preserved after deletion. */ min_keys = n->is_leaf ? cut(order - 1) : cut(order) - 1; /* Case: node stays at or above minimum. * (The simple case.) */ if (n->num_keys >= min_keys) return root; /* Case: node falls below minimum. * Either coalescence or redistribution * is needed. */ /* Find the appropriate neighbor node with which * to coalesce. * Also find the key (k_prime) in the parent * between the pointer to node n and the pointer * to the neighbor. */ neighbor_index = get_neighbor_index(n); k_prime_index = neighbor_index == -1 ? 0 : neighbor_index; k_prime = n->parent->keys[k_prime_index]; neighbor = neighbor_index == -1 ? n->parent->pointers[1] : n->parent->pointers[neighbor_index]; capacity = n->is_leaf ? order : order - 1; /* Coalescence. */ if (neighbor->num_keys + n->num_keys < capacity) return coalesce_nodes(root, n, neighbor, neighbor_index, k_prime); /* Redistribution. */ else return redistribute_nodes(root, n, neighbor, neighbor_index, k_prime_index, k_prime); } /* Master deletion function. */ node * delete(node * root, int key) { node * key_leaf = NULL; record * key_record = NULL; key_record = find(root, key, false, &key_leaf); /* CHANGE */ if (key_record != NULL && key_leaf != NULL) { root = delete_entry(root, key_leaf, key, key_record); free(key_record); } return root; } void destroy_tree_nodes(node * root) { int i; if (root->is_leaf) for (i = 0; i < root->num_keys; i++) free(root->pointers[i]); else for (i = 0; i < root->num_keys + 1; i++) destroy_tree_nodes(root->pointers[i]); free(root->pointers); free(root->keys); free(root); } node * destroy_tree(node * root) { destroy_tree_nodes(root); return NULL; } // MAIN int main(int argc, char ** argv) { char * input_file; FILE * fp; node * root; int input_key, input_key_2; char instruction; root = NULL; verbose_output = false; if (argc > 1) { order = atoi(argv[1]); if (order < MIN_ORDER || order > MAX_ORDER) { fprintf(stderr, "Invalid order: %d .\n\n", order); usage_3(); exit(EXIT_FAILURE); } } if (argc < 3) { license_notice(); usage_1(); usage_2(); } if (argc > 2) { input_file = argv[2]; fp = fopen(input_file, "r"); if (fp == NULL) { perror("Failure to open input file."); exit(EXIT_FAILURE); } while (!feof(fp)) { fscanf(fp, "%d\n", &input_key); root = insert(root, input_key, input_key); } fclose(fp); print_tree(root); return EXIT_SUCCESS; } printf("> "); char buffer[BUFFER_SIZE]; int count = 0; bool line_consumed = false; while (scanf("%c", &instruction) != EOF) { line_consumed = false; switch (instruction) { case 'd': scanf("%d", &input_key); root = delete(root, input_key); print_tree(root); break; case 'i': fgets(buffer, BUFFER_SIZE, stdin); line_consumed = true; count = sscanf(buffer, "%d %d", &input_key, &input_key_2); if (count == 1) input_key_2 = input_key; root = insert(root, input_key, input_key_2); print_tree(root); break; case 'f': case 'p': scanf("%d", &input_key); find_and_print(root, input_key, instruction == 'p'); break; case 'r': scanf("%d %d", &input_key, &input_key_2); if (input_key > input_key_2) { int tmp = input_key_2; input_key_2 = input_key; input_key = tmp; } find_and_print_range(root, input_key, input_key_2, instruction == 'p'); break; case 'l': print_leaves(root); break; case 'q': while (getchar() != (int)'\n'); return EXIT_SUCCESS; break; case 't': print_tree(root); break; case 'v': verbose_output = !verbose_output; break; case 'x': if (root) root = destroy_tree(root); print_tree(root); break; default: usage_2(); break; } if (!line_consumed) while (getchar() != (int)'\n'); printf("> "); } printf("\n"); return EXIT_SUCCESS; }