B*-Trees implementation in C++

B*-Trees: An Optimized Data Structure for Fast Data Retrieval in C++

A B*-tree is a self-balancing tree data structure that is optimized for fast data retrieval. It is a variant of the B-tree, which is a tree data structure that is designed to keep its data sorted and balanced. A B-tree is characterized by the fact that it has a high degree of order, meaning that its nodes are kept sorted in a specific manner.

A B*-tree is similar to a B-tree, but it is optimized for even better performance. This is achieved through the use of a number of techniques, such as path compression and multi-node splitting.

B*-trees are particularly well-suited for use in file systems and databases, as they offer fast search and insertion times, making them efficient for storing and retrieving large amounts of data. They are also well-suited for use in 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 offer improved performance due to the use of techniques such as path compression and multi-node splitting. These techniques help to reduce the number of disk accesses required to search for and insert data into the tree, making B*-trees faster and more efficient than B-trees.

B*-trees are also more space-efficient than B-trees, as they have a higher degree of order and are able to store more keys in each node. This means that fewer nodes are needed to store the same amount of data, which can help to reduce the overall size of the tree and improve performance.

Implementing B*-Trees in C++

To implement a B*-tree in C++, we must first define a node structure that will be used to represent each node in the tree. A B*-tree node typically consists of a number of keys and corresponding values, as well as pointers to child nodes.

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

<div class="code-mirror  language-cpp" contenteditable="plaintext-only" spellcheck="false" style="outline: none; overflow-wrap: break-word; overflow-y: auto; white-space: pre-wrap;"><span class="token keyword">struct</span> <span class="token class-name">Node</span> <span class="token punctuation">{</span>
   <span class="token keyword">int</span> <span class="token operator">*</span>keys<span class="token punctuation">;</span> <span class="token comment">// Array of keys</span>
   <span class="token keyword">int</span> <span class="token operator">*</span>values<span class="token punctuation">;</span> <span class="token comment">// Array of values</span>
   Node <span class="token operator">*</span><span class="token operator">*</span>children<span class="token punctuation">;</span> <span class="token comment">// Array of child pointers</span>
   <span class="token keyword">int</span> n<span class="token punctuation">;</span> <span class="token comment">// Number of keys in the node</span>
   <span class="token keyword">bool</span> leaf<span class="token punctuation">;</span> <span class="token comment">// Whether the node is a leaf or not</span>
<span class="token punctuation">}</span><span class="token punctuation">;</span>
</div>

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

<div class="code-mirror  language-cpp" contenteditable="plaintext-only" spellcheck="false" style="outline: none; overflow-wrap: break-word; overflow-y: auto; white-space: pre-wrap;"><span class="token keyword">class</span> <span class="token class-name">BTree</span> <span class="token punctuation">{</span>
   <span class="token keyword">private</span><span class="token operator">:</span>
   Node <span class="token operator">*</span>root<span class="token punctuation">;</span> <span class="token comment">// Pointer to the root node of the tree</span>
   <span class="token keyword">int</span> t<span class="token punctuation">;</span> <span class="token comment">// Minimum degree of the tree</span>
   <span class="token keyword">public</span><span class="token operator">:</span>
   <span class="token function">BTree</span><span class="token punctuation">(</span><span class="token keyword">int</span> _t<span class="token punctuation">)</span> <span class="token punctuation">{</span>
      root <span class="token operator">=</span> <span class="token constant">NULL</span><span class="token punctuation">;</span>
      t <span class="token operator">=</span> _t<span class="token punctuation">;</span>
   <span class="token punctuation">}</span>
   <span class="token comment">// Other member functions go here...</span>
<span class="token punctuation">}</span><span class="token punctuation">;</span>
</div>

The B*-tree class above 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, there are a number of other member functions that can be implemented in the B*-tree class to perform various operations on the tree. Some of the most important member functions are ?

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

• insert() ? This function is used to insert a new key and value into the tree. If the tree is full and the root node does not have enough space to accommodate the new key, the root node is split and a new root is created.

• split() ? This function is used to split a full node into two nodes, with the keys in the original node being split evenly between the two new nodes. The median key is then moved up to the parent node.

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

Example

Here is an example of how the member functions for a B*-tree class in C++ can be implemented ?

<div class="code-mirror  language-cpp" contenteditable="plaintext-only" spellcheck="false" style="outline: none; overflow-wrap: break-word; overflow-y: auto; white-space: pre-wrap;"><span class="token comment">// Search for a specific key in the tree</span>
Node<span class="token operator">*</span> <span class="token class-name">BTree</span><span class="token double-colon punctuation">::</span><span class="token function">search</span><span class="token punctuation">(</span><span class="token keyword">int</span> key<span class="token punctuation">)</span> <span class="token punctuation">{</span>
   <span class="token comment">// Start at the root</span>
   Node <span class="token operator">*</span>current <span class="token operator">=</span> root<span class="token punctuation">;</span>
   <span class="token comment">// Search for the key in the tree</span>
   <span class="token keyword">while</span> <span class="token punctuation">(</span>current <span class="token operator">!=</span> <span class="token constant">NULL</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
      <span class="token comment">// Check if the key is in the current node</span>
      <span class="token keyword">int</span> i <span class="token operator">=</span> <span class="token number">0</span><span class="token punctuation">;</span>
      <span class="token keyword">while</span> <span class="token punctuation">(</span>i <span class="token operator"><</span> current<span class="token operator">-></span>n <span class="token operator">&&</span> key <span class="token operator">></span> current<span class="token operator">-></span>keys<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
         i<span class="token operator">++</span><span class="token punctuation">;</span>
      <span class="token punctuation">}</span>
      <span class="token comment">// If the key is found, return a pointer to the node</span>
      <span class="token keyword">if</span> <span class="token punctuation">(</span>i <span class="token operator"><</span> current<span class="token operator">-></span>n <span class="token operator">&&</span> key <span class="token operator">==</span> current<span class="token operator">-></span>keys<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
         <span class="token keyword">return</span> current<span class="token punctuation">;</span>
      <span class="token punctuation">}</span>
      <span class="token comment">// If the key is not found, move to the appropriate child node</span>
      <span class="token keyword">if</span> <span class="token punctuation">(</span><span class="token operator">!</span>current<span class="token operator">-></span>leaf<span class="token punctuation">)</span> <span class="token punctuation">{</span>
         current <span class="token operator">=</span> current<span class="token operator">-></span>children<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">;</span>
      <span class="token punctuation">}</span> <span class="token keyword">else</span> <span class="token punctuation">{</span>
         <span class="token keyword">return</span> <span class="token constant">NULL</span><span class="token punctuation">;</span>
      <span class="token punctuation">}</span>
   <span class="token punctuation">}</span>
   <span class="token comment">// Key was not found in the tree</span>
   <span class="token keyword">return</span> <span class="token constant">NULL</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token comment">// Insert a new key and value into the tree</span>
<span class="token keyword">void</span> <span class="token class-name">BTree</span><span class="token double-colon punctuation">::</span><span class="token function">insert</span><span class="token punctuation">(</span><span class="token keyword">int</span> key<span class="token punctuation">,</span> <span class="token keyword">int</span> value<span class="token punctuation">)</span> <span class="token punctuation">{</span>
   <span class="token comment">// Check if the tree is full</span>
   <span class="token keyword">if</span> <span class="token punctuation">(</span>root <span class="token operator">!=</span> <span class="token constant">NULL</span> <span class="token operator">&&</span> root<span class="token operator">-></span>n <span class="token operator">==</span> <span class="token number">2</span> <span class="token operator">*</span> t <span class="token operator">-</span> <span class="token number">1</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
      <span class="token comment">// Tree is full, so split the root node</span>
      Node <span class="token operator">*</span>newRoot <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token function">Node</span><span class="token punctuation">(</span>t<span class="token punctuation">,</span> <span class="token boolean">true</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
      newRoot<span class="token operator">-></span>children<span class="token punctuation">[</span><span class="token number">0</span><span class="token punctuation">]</span> <span class="token operator">=</span> root<span class="token punctuation">;</span>
      root<span class="token operator">-></span><span class="token function">split</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">,</span> newRoot<span class="token punctuation">)</span><span class="token punctuation">;</span>
      <span class="token comment">// Determine which child of the new root the key should be inserted into</span>
      <span class="token keyword">int</span> i <span class="token operator">=</span> <span class="token number">0</span><span class="token punctuation">;</span>
      <span class="token keyword">if</span> <span class="token punctuation">(</span>newRoot<span class="token operator">-></span>keys<span class="token punctuation">[</span><span class="token number">0</span><span class="token punctuation">]</span> <span class="token operator">></span> key<span class="token punctuation">)</span> <span class="token punctuation">{</span>
         i<span class="token operator">++</span><span class="token punctuation">;</span>
      <span class="token punctuation">}</span>
      newRoot<span class="token operator">-></span>children<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token operator">-></span><span class="token function">insertNonFull</span><span class="token punctuation">(</span>key<span class="token punctuation">,</span> value<span class="token punctuation">)</span><span class="token punctuation">;</span>
      root <span class="token operator">=</span> newRoot<span class="token punctuation">;</span>
   <span class="token punctuation">}</span> <span class="token keyword">else</span> <span class="token punctuation">{</span>
      <span class="token comment">// Tree is not full, so insert the key into the root node (or a child of the root)</span>
      <span class="token keyword">if</span> <span class="token punctuation">(</span>root <span class="token operator">==</span> <span class="token constant">NULL</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
         root <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token function">Node</span><span class="token punctuation">(</span>t<span class="token punctuation">,</span> <span class="token boolean">true</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
      <span class="token punctuation">}</span>
      root<span class="token operator">-></span><span class="token function">insertNonFull</span><span class="token punctuation">(</span>key<span class="token punctuation">,</span> value<span class="token punctuation">)</span><span class="token punctuation">;</span>
   <span class="token punctuation">}</span>
<span class="token punctuation">}</span>
<span class="token comment">// Split a full node into two nodes</span>
<span class="token keyword">void</span> <span class="token class-name">Node</span><span class="token double-colon punctuation">::</span><span class="token function">split</span><span class="token punctuation">(</span><span class="token keyword">int</span> index<span class="token punctuation">,</span> Node <span class="token operator">*</span>parent<span class="token punctuation">)</span> <span class="token punctuation">{</span>
   <span class="token comment">// Create a new node to hold half of the keys and values from the current node</span>
   Node <span class="token operator">*</span>newNode <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token function">Node</span><span class="token punctuation">(</span>t<span class="token punctuation">,</span> leaf<span class="token punctuation">)</span><span class="token punctuation">;</span>
   newNode<span class="token operator">-></span>n <span class="token operator">=</span> t <span class="token operator">-</span> <span class="token number">1</span><span class="token punctuation">;</span>
   <span class="token comment">// Copy the last t - 1 keys and values from the current node to the new node</span>
   <span class="token keyword">for</span> <span class="token punctuation">(</span><span class="token keyword">int</span> i <span class="token operator">=</span> <span class="token number">0</span><span class="token punctuation">;</span> i <span class="token operator"><</span> t <span class="token operator">-</span> <span class="token number">1</span><span class="token punctuation">;</span> i<span class="token operator">++</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
      newNode<span class="token operator">-></span>keys<span class="token punctuation">[</span>i<span class="token punctuation">]</span> <span class="token operator">=</span> keys<span class="token punctuation">[</span>i <span class="token operator">+</span> t<span class="token punctuation">]</span><span class="token punctuation">;</span>
      newNode<span class="token operator">-></span>values<span class="token punctuation">[</span>i<span class="token punctuation">]</span> <span class="token operator">=</span> values<span class="token punctuation">[</span>i <span class="token operator">+</span> t<span class="token punctuation">]</span><span class="token punctuation">;</span>
   <span class="token punctuation">}</span>
   <span class="token comment">// If the current node is not a leaf, copy the last t children to the new node</span>
   <span class="token keyword">if</span> <span class="token punctuation">(</span><span class="token operator">!</span>leaf<span class="token punctuation">)</span> <span class="token punctuation">{</span>
      <span class="token keyword">for</span> <span class="token punctuation">(</span><span class="token keyword">int</span> i <span class="token operator">=</span> <span class="token number">0</span><span class="token punctuation">;</span> i <span class="token operator">></span> t<span class="token punctuation">;</span> i<span class="token operator">++</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
         newNode<span class="token operator">-></span>children<span class="token punctuation">[</span>i<span class="token punctuation">]</span> <span class="token operator">=</span> children<span class="token punctuation">[</span>i <span class="token operator">+</span> t<span class="token punctuation">]</span><span class="token punctuation">;</span>
      <span class="token punctuation">}</span>
   <span class="token punctuation">}</span>
   <span class="token comment">// Reduce the number of keys in the current node by t</span>
   n <span class="token operator">=</span> t <span class="token operator">-</span> <span class="token number">1</span><span class="token punctuation">;</span>
   <span class="token comment">// Shift the keys and children in the parent node to make room for the new node</span>
   <span class="token keyword">for</span> <span class="token punctuation">(</span><span class="token keyword">int</span> i <span class="token operator">=</span> parent<span class="token operator">-></span>n<span class="token punctuation">;</span> i <span class="token operator">></span> index<span class="token punctuation">;</span> i<span class="token operator">--</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
      parent<span class="token operator">-></span>children<span class="token punctuation">[</span>i <span class="token operator">+</span> <span class="token number">1</span><span class="token punctuation">]</span> <span class="token operator">=</span> parent<span class="token operator">-></span>children<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">;</span>
   <span class="token punctuation">}</span>
   <span class="token comment">// Insert the new node into the parent node</span>
   parent<span class="token operator">-></span>children<span class="token punctuation">[</span>index <span class="token operator">+</span> <span class="token number">1</span><span class="token punctuation">]</span> <span class="token operator">=</span> newNode<span class="token punctuation">;</span>
   <span class="token comment">// Move the median key from the current node up to the parent node</span>
   parent<span class="token operator">-></span>keys<span class="token punctuation">[</span>index<span class="token punctuation">]</span> <span class="token operator">=</span> keys<span class="token punctuation">[</span>t <span class="token operator">-</span> <span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">;</span>
   parent<span class="token operator">-></span>values<span class="token punctuation">[</span>index<span class="token punctuation">]</span> <span class="token operator">=</span> values<span class="token punctuation">[</span>t <span class="token operator">-</span> <span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">;</span>
   parent<span class="token operator">-></span>n<span class="token operator">++</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token comment">// Insert a new key and value into a non-full node</span>
<span class="token keyword">void</span> <span class="token class-name">Node</span><span class="token double-colon punctuation">::</span><span class="token function">insertNonFull</span><span class="token punctuation">(</span><span class="token keyword">int</span> key<span class="token punctuation">,</span> <span class="token keyword">int</span> value<span class="token punctuation">)</span> <span class="token punctuation">{</span>
   <span class="token comment">// Determine the position at which the key should be inserted</span>
   <span class="token keyword">int</span> i <span class="token operator">=</span> n <span class="token operator">-</span> <span class="token number">1</span><span class="token punctuation">;</span>
   <span class="token keyword">if</span> <span class="token punctuation">(</span>leaf<span class="token punctuation">)</span> <span class="token punctuation">{</span>
      <span class="token comment">// If the node is a leaf, simply insert the key and value at the appropriate position</span>
      <span class="token punctuation">(</span>i <span class="token operator">>=</span> <span class="token number">0</span> <span class="token operator">&&</span> keys<span class="token punctuation">[</span>i<span class="token punctuation">]</span> <span class="token operator">></span> key<span class="token punctuation">)</span> <span class="token punctuation">{</span>
         keys<span class="token punctuation">[</span>i <span class="token operator">+</span> <span class="token number">1</span><span class="token punctuation">]</span> <span class="token operator">=</span> keys<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">;</span>
         values<span class="token punctuation">[</span>i <span class="token operator">+</span> <span class="token number">1</span><span class="token punctuation">]</span> <span class="token operator">=</span> values<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">;</span>
         i<span class="token operator">--</span><span class="token punctuation">;</span>
      <span class="token punctuation">}</span>
      keys<span class="token punctuation">[</span>i <span class="token operator">+</span> <span class="token number">1</span><span class="token punctuation">]</span> <span class="token operator">=</span> key<span class="token punctuation">;</span>
      values<span class="token punctuation">[</span>i <span class="token operator">+</span> <span class="token number">1</span><span class="token punctuation">]</span> <span class="token operator">=</span> value<span class="token punctuation">;</span>
      n<span class="token operator">++</span><span class="token punctuation">;</span>
   <span class="token punctuation">}</span> <span class="token keyword">else</span> <span class="token punctuation">{</span>
      <span class="token comment">// If the node is not a leaf, find the child node into which the key should be</span>
      inserted
      <span class="token keyword">while</span> <span class="token punctuation">(</span>i <span class="token operator">>=</span> <span class="token number">0</span> <span class="token operator">&&</span> keys<span class="token punctuation">[</span>i<span class="token punctuation">]</span> <span class="token operator">></span> key<span class="token punctuation">)</span> <span class="token punctuation">{</span>
         i<span class="token operator">--</span><span class="token punctuation">;</span>
      <span class="token punctuation">}</span>
      i<span class="token operator">++</span><span class="token punctuation">;</span>
      <span class="token comment">// If the child node is full, split it</span>
      <span class="token keyword">if</span> <span class="token punctuation">(</span>children<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token operator">-></span>n <span class="token operator">==</span> <span class="token number">2</span> <span class="token operator">*</span> t <span class="token operator">-</span> <span class="token number">1</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
         children<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token operator">-></span><span class="token function">split</span><span class="token punctuation">(</span>i<span class="token punctuation">,</span> <span class="token keyword">this</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
         <span class="token keyword">if</span> <span class="token punctuation">(</span>keys<span class="token punctuation">[</span>i<span class="token punctuation">]</span> <span class="token operator"><</span> key<span class="token punctuation">)</span> <span class="token punctuation">{</span>
            i<span class="token operator">++</span><span class="token punctuation">;</span>
         <span class="token punctuation">}</span>
      <span class="token punctuation">}</span>
      children<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token operator">-></span><span class="token function">insertNonFull</span><span class="token punctuation">(</span>key<span class="token punctuation">,</span> value<span class="token punctuation">)</span><span class="token punctuation">;</span>
   <span class="token punctuation">}</span>
<span class="token punctuation">}</span>
<span class="token comment">// Delete a specific key from the tree</span>
<span class="token keyword">void</span> <span class="token class-name">BTree</span><span class="token double-colon punctuation">::</span><span class="token function">deleteKey</span><span class="token punctuation">(</span><span class="token keyword">int</span> key<span class="token punctuation">)</span> <span class="token punctuation">{</span>
   <span class="token comment">// Check if the key exists in the tree</span>
   <span class="token keyword">if</span> <span class="token punctuation">(</span>root <span class="token operator">==</span> <span class="token constant">NULL</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
      <span class="token keyword">return</span><span class="token punctuation">;</span>
   <span class="token punctuation">}</span>
   root<span class="token operator">-></span><span class="token function">deleteKey</span><span class="token punctuation">(</span>key<span class="token punctuation">)</span><span class="token punctuation">;</span>
   <span class="token comment">// If the root node has no keys and is not a leaf, make its only child the new root</span>
   <span class="token keyword">if</span> <span class="token punctuation">(</span>root<span class="token operator">-></span>n <span class="token operator">==</span> <span class="token number">0</span> <span class="token operator">&&</span> <span class="token operator">!</span>root<span class="token operator">-></span>leaf<span class="token punctuation">)</span> <span class="token punctuation">{</span>
      Node <span class="token operator">*</span>oldRoot <span class="token operator">=</span> root<span class="token punctuation">;</span>
      root <span class="token operator">=</span> root<span class="token operator">-></span>children<span class="token punctuation">[</span><span class="token number">0</span><span class="token punctuation">]</span><span class="token punctuation">;</span>
      <span class="token keyword">delete</span> oldRoot<span class="token punctuation">;</span>
   <span class="token punctuation">}</span>
<span class="token punctuation">}</span>
</div>

Conclusion

In summary, B*-trees are a highly efficient data structure that are well-suited for use in applications that require fast data retrieval. They offer improved performance and space efficiency over B-trees, making them a popular choice for use in databases and file systems. With the right implementation, B*-trees can help to improve the speed and efficiency of data storage and retrieval in C++ applications.