Applications of B-Tree

Representation of B-Tree in C

A B-tree is organized as a balanced tree with the following properties-...

Basic Operations on B-Tree in C

Basic Operations:...

C Program to Implement B-Tree in C

C #include #include #include #define M 4 // Maximum degree of the B-tree struct BTreeNode { int num_keys; // Number of keys currently in the node int keys[M-1]; // Array of keys struct BTreeNode *children[M]; // Array of child pointers bool is_leaf; // True if node is a leaf }; // Function to create a new node struct BTreeNode *createNode(bool is_leaf) { struct BTreeNode *newNode = (struct BTreeNode *)malloc(sizeof(struct BTreeNode)); if (newNode == NULL) { perror("Memory allocation failed"); exit(EXIT_FAILURE); } newNode->num_keys = 0; newNode->is_leaf = is_leaf; for (int i = 0; i < M; i++) { newNode->children[i] = NULL; } return newNode; } // Function to split a full child node void splitChild(struct BTreeNode *parent, int index) { struct BTreeNode *child = parent->children[index]; struct BTreeNode *newNode = createNode(child->is_leaf); newNode->num_keys = M/2 - 1; // Move keys and children to the new node for (int i = 0; i < M/2 - 1; i++) { newNode->keys[i] = child->keys[i + M/2]; } if (!child->is_leaf) { for (int i = 0; i < M/2; i++) { newNode->children[i] = child->children[i + M/2]; } } child->num_keys = M/2 - 1; // Shift parent's children to make space for the new node for (int i = parent->num_keys; i > index; i--) { parent->children[i + 1] = parent->children[i]; } parent->children[index + 1] = newNode; // Shift parent's keys to insert the middle key from the child for (int i = parent->num_keys - 1; i >= index; i--) { parent->keys[i + 1] = parent->keys[i]; } parent->keys[index] = child->keys[M/2 - 1]; parent->num_keys++; } // Function to insert a key into a non-full node void insertNonFull(struct BTreeNode *node, int key) { int i = node->num_keys - 1; if (node->is_leaf) { // Insert key into the sorted order while (i >= 0 && node->keys[i] > key) { node->keys[i + 1] = node->keys[i]; i--; } node->keys[i + 1] = key; node->num_keys++; } else { // Find the child to insert the key while (i >= 0 && node->keys[i] > key) { i--; } i++; if (node->children[i]->num_keys == M - 1) { // Split child if it's full splitChild(node, i); // Determine which of the two children is the new one if (node->keys[i] < key) { i++; } } insertNonFull(node->children[i], key); } } // Function to insert a key into the B-tree void insert(struct BTreeNode **root, int key) { struct BTreeNode *node = *root; if (node == NULL) { // Create a new root node *root = createNode(true); (*root)->keys[0] = key; (*root)->num_keys = 1; } else { if (node->num_keys == M - 1) { // Split the root if it's full struct BTreeNode *new_root = createNode(false); new_root->children[0] = node; splitChild(new_root, 0); *root = new_root; } insertNonFull(*root, key); } } // Function to traverse and print the B-tree in-order void traverse(struct BTreeNode *root) { if (root != NULL) { int i; for (i = 0; i < root->num_keys; i++) { traverse(root->children[i]); printf("%d ", root->keys[i]); } traverse(root->children[i]); } } // Main function to test B-tree implementation int main() { struct BTreeNode *root = NULL; insert(&root, 10); insert(&root, 20); insert(&root, 5); insert(&root, 6); insert(&root, 12); insert(&root, 30); printf("In-order traversal of the B-tree: "); traverse(root); printf("\n"); return 0; }...

Applications of B-Tree

Here are some applications of B-Tree-...

Conclusion

B-trees being the fundamental data structure frequently used in databases, file systems, key-value stores, and cache systems all boil down to the balanced nature and the efficient operations it provides. They provide the three basic functions of stores the data, processes it and thus are crucial in the designing of large scale and high performing systems in the world of applications. The knowledge about B-tree applications plays a critical part in the software development of this technology for the real world use....