Implementing B*-tree in C++

B*-Tree: Optimized data structure in C for fast data retrieval

B* Tree is a self-balancing tree data structure optimized for fast data retrieval. It is a variation of B-tree, a tree data structure designed to keep data ordered and balanced. The characteristic of a B-tree is that it is highly ordered, which means that its nodes remain ordered in a specific way.

B* tree is similar to B-tree, but it is optimized for better performance. This is achieved by using several techniques such as path compression and multi-node splitting.

B*-Trees are particularly suitable for file systems and databases because they provide fast search and insertion times, making them efficient when storing and retrieving large amounts of data. They are also ideal for applications that require fast data access, such as real-time systems and scientific simulations.

Advantages of B* trees over B trees

One of the main advantages of B*-trees over B-trees is that they are able to provide better performance due to the use of techniques such as path compression and multi-node splitting. These techniques help reduce the number of disk accesses required to search and insert data, making B*-trees faster and more efficient than B-trees.

B* trees are also more space-efficient than B-trees because they are more ordered and able to store more keys in each node. This means that fewer nodes are needed to store the same amount of data, which helps reduce the overall size of the tree and improves performance.

Implementing B*-tree in C

To implement B*-tree in C, we must first define a node structure to represent each node in the tree. A B*-tree node usually contains some keys and corresponding values, as well as pointers to child nodes.

This is an example of a node structure that can be used to implement a B* tree in C -

struct Node {
   int *keys; // Array of keys
   int *values; // Array of values
   Node **children; // Array of child pointers
   int n; // Number of keys in the node
   bool leaf; // Whether the node is a leaf or not
};

With the node structure defined, we can now implement the B* tree itself. Here is an example of how to implement a B* tree in C -

class BTree {
   private:
   Node *root; // Pointer to the root node of the tree
   int t; // Minimum degree of the tree
   public:
   BTree(int _t) {
      root = NULL;
      t = _t;
   }
   // Other member functions go here...
};

The above B*-tree class contains a private member variable root, which is a pointer to the root node of the tree, and a private member variable t, which is the minimum degree of the tree. The minimum degree of a B*-tree is the minimum number of keys that a node in the tree must contain.

In addition to the constructor, the B* tree class can also implement many other member functions to perform various operations on the tree. Some of the most important member functions include −

• search() − This function is used to search for a specific key in the tree. Returns a pointer to the node containing the key if the key is found, or NULL if not found.

• insert() - This function is used to insert new keys and values ​​into the tree. If the tree is full and the root node does not have enough space for the new key, the root node will be split and a new root created.

• split() − This function is used to split a complete node into two nodes, and the keys in the original node are evenly distributed between the two new nodes. The median key is then moved to the parent node.

• delete() - This function is used to delete a specific key from the tree. If the key is not found, this function does nothing. If the key is found and the node containing the key is not full, the node may be merged with one of its siblings to restore balance to the tree.

Example

The following is an example of implementing the member function of the B*-tree class in C:

// Search for a specific key in the tree
Node* BTree::search(int key) {
   // Start at the root
   Node *current = root;
   // Search for the key in the tree
   while (current != NULL) {
      // Check if the key is in the current node
      int i = 0;
      while (i < current->n && key > current->keys[i]) {
         i++;
      }
      // If the key is found, return a pointer to the node
      if (i < current->n && key == current->keys[i]) {
         return current;
      }
      // If the key is not found, move to the appropriate child node
      if (!current->leaf) {
         current = current->children[i];
      } else {
         return NULL;
      }
   }
   // Key was not found in the tree
   return NULL;
}
// Insert a new key and value into the tree
void BTree::insert(int key, int value) {
   // Check if the tree is full
   if (root != NULL && root->n == 2 * t - 1) {
      // Tree is full, so split the root node
      Node *newRoot = new Node(t, true);
      newRoot->children[0] = root;
      root->split(0, newRoot);
      // Determine which child of the new root the key should be inserted into
      int i = 0;
      if (newRoot->keys[0] > key) {
         i++;
      }
      newRoot->children[i]->insertNonFull(key, value);
      root = newRoot;
   } else {
      // Tree is not full, so insert the key into the root node (or a child of the root)
      if (root == NULL) {
         root = new Node(t, true);
      }
      root->insertNonFull(key, value);
   }
}
// Split a full node into two nodes
void Node::split(int index, Node *parent) {
   // Create a new node to hold half of the keys and values from the current node
   Node *newNode = new Node(t, leaf);
   newNode->n = t - 1;
   // Copy the last t - 1 keys and values from the current node to the new node
   for (int i = 0; i < t - 1; i++) {
      newNode->keys[i] = keys[i + t];
      newNode->values[i] = values[i + t];
   }
   // If the current node is not a leaf, copy the last t children to the new node
   if (!leaf) {
      for (int i = 0; i > t; i++) {
         newNode->children[i] = children[i + t];
      }
   }
   // Reduce the number of keys in the current node by t
   n = t - 1;
   // Shift the keys and children in the parent node to make room for the new node
   for (int i = parent->n; i > index; i--) {
      parent->children[i + 1] = parent->children[i];
   }
   // Insert the new node into the parent node
   parent->children[index + 1] = newNode;
   // Move the median key from the current node up to the parent node
   parent->keys[index] = keys[t - 1];
   parent->values[index] = values[t - 1];
   parent->n++;
}
// Insert a new key and value into a non-full node
void Node::insertNonFull(int key, int value) {
   // Determine the position at which the key should be inserted
   int i = n - 1;
   if (leaf) {
      // If the node is a leaf, simply insert the key and value at the appropriate position
      (i >= 0 && keys[i] > key) {
         keys[i + 1] = keys[i];
         values[i + 1] = values[i];
         i--;
      }
      keys[i + 1] = key;
      values[i + 1] = value;
      n++;
   } else {
      // If the node is not a leaf, find the child node into which the key should be
      inserted
      while (i >= 0 && keys[i] > key) {
         i--;
      }
      i++;
      // If the child node is full, split it
      if (children[i]->n == 2 * t - 1) {
         children[i]->split(i, this);
         if (keys[i] < key) {
            i++;
         }
      }
      children[i]->insertNonFull(key, value);
   }
}
// Delete a specific key from the tree
void BTree::deleteKey(int key) {
   // Check if the key exists in the tree
   if (root == NULL) {
      return;
   }
   root->deleteKey(key);
   // If the root node has no keys and is not a leaf, make its only child the new root
   if (root->n == 0 && !root->leaf) {
      Node *oldRoot = root;
      root = root->children[0];
      delete oldRoot;
   }
}

in conclusion

In summary, the B*-tree is an efficient data structure that is ideal for applications that require fast data retrieval. They have better performance and space efficiency than B-trees, so they are very popular in databases and file systems. With the right implementation, B*-trees can help improve the speed and efficiency of data storage and retrieval in C applications.

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