Question

Which one of the following statements is NOT correct about the B$^+$ tree data structure used for creating an index of a relational database table?

• A. B$^+$ tree is a height-balanced tree
• B. Non-leaf nodes have pointers to data records
• C. Key values in each node are kept in sorted order
• D. Each leaf node has a pointer to the next leaf node

Hint:

Key difference to remember: {B-tree} may store data pointers in internal nodes, but {B$^+$ tree} stores all data pointers {only at leaf nodes}.

Answer 1

The Correct Option is B

To correctly identify which statement is NOT accurate regarding the B$^+$ tree data structure utilized in indexing relational database tables, we must examine each option based on the characteristics of B$^+$ trees.

1. Option 1: B$^+$ tree is a height-balanced tree
   • This statement is correct. B$^+$ trees are indeed height-balanced. The balancing ensures that all leaf nodes are at the same depth, which facilitates efficient searching, insertion, and deletion operations, typically in logarithmic time.
2. Option 2: Non-leaf nodes have pointers to data records
   • This statement is incorrect and thus the right answer. In a B$^+$ tree, only leaf nodes directly have pointers to data records. Non-leaf nodes merely contain keys and pointers to other child nodes, thus maintaining the tree's structure and helping in efficient data searching.
3. Option 3: Key values in each node are kept in sorted order
   • This statement is correct. In a B$^+$ tree, the keys within each node (leaf or non-leaf) are stored in sorted order. This ordering accelerates the process of searching within nodes and contributes to the tree’s efficiency.
4. Option 4: Each leaf node has a pointer to the next leaf node
   • This statement is correct. In B$^+$ trees, leaf nodes are linked via pointers, creating a linked list among the leaves. This linkage provides an efficient means to perform range queries and traversals over the data records.

Thus, the statement that is NOT correct about the B$^+$ tree data structure is: Non-leaf nodes have pointers to data records.

Answer 2

Step 1: Recall the structure of a B$^+$ tree.
A B$^+$ tree is a balanced search tree widely used for indexing in databases. It stores keys in internal nodes and actual data record pointers only at the leaf nodes.
Step 2: Analyze each statement.
(A) B$^+$ tree is a height-balanced tree
This statement is correct. All root-to-leaf paths in a B$^+$ tree have the same length, ensuring balanced height.
(B) Non-leaf nodes have pointers to data records
This statement is incorrect. In a B$^+$ tree, non-leaf (internal) nodes contain only keys and pointers to child nodes, not pointers to actual data records. Data record pointers exist only in the leaf nodes.
(C) Key values in each node are kept in sorted order
This statement is correct. Sorted keys enable efficient searching and range queries.
(D) Each leaf node has a pointer to the next leaf node
This statement is correct. Leaf nodes are linked together to support efficient sequential and range access.
Step 3: Conclusion.
The statement that is NOT correct about a B$^+$ tree is: \[ \boxed{\text{Non-leaf nodes have pointers to data records}} \]