The question asks for the minimum number of keys in a non-root node of a B+ tree, given that the maximum number of keys in a node is 5.
Understanding B+ Tree Properties
In a B+ tree, the structure is balanced, and nodes have specific rules regarding the number of keys and children:
- Let $m$ be the maximum number of children a node can have (order of the tree).
- The maximum number of keys a node can hold is $m - 1$.
- The minimum number of keys in a non-root node is $ceil(m / 2) - 1$.
- The minimum number of keys in the root node is 1 (unless it's the only node).
Calculating Minimum Keys
We are given that the maximum number of keys in a node is 5.
Using the property $Maximum keys = m - 1$:
$5 = m - 1$
Solving for $m$, we get:
$m = 5 + 1 = 6$
So, the maximum number of children a node can have is 6.
Now, we calculate the minimum number of keys required in any non-root node using the formula $Minimum keys = ceil(m / 2) - 1$:
$ \text{Minimum keys} = \lceil \frac{6}{2} \rceil - 1 $
$ \text{Minimum keys} = \lceil 3 \rceil - 1 $
$ \text{Minimum keys} = 3 - 1 = 2 $
Therefore, the minimum number of keys in any non-root node is 2.
Important Questions from Indexing
- In a relational database, a B+ Tree Index is to be constructed for a relation on a key field. In a B+ Tree, a Node Pointer points to a sub-tree and a Data Record Pointer points to a block of database records.
Let, Node size = 4096 bytes, Node Pointer size = 10 bytes, Search Key Field size = 11 bytes and Data Record Pointer size = 12 bytes.
The maximum number of Node Pointers that can be present in a non-leaf node of the B+ Tree is ________ . (Answer in integer) Consider a B+ Tree where the maximum number of key values in each leaf node is 2 and the maximum number of pointers in each non-leaf node is 3. Let the content of the B+ Tree be as shown in the figure.
Which of the following options denotes the key value(s) stored in the root node after inserting a key value 3 in the given B+ Tree?
An OTT company is maintaining a large disk-based relational database of different movies with the following schema:
Movie(ID, CustomerRating)
Genre(ID, Name)
Movie_Genre(MovieID, GenreID)
Consider the following SQL query on the relation database above:
SELECT *
FROM Movie, Genre, Movie_Genre
WHERE
Movie.CustomerRating > 3.4 AND
Genre.Name = “Comedy” AND
Movie_Genre.MovieID = Movie.ID AND
Movie_Genre.GenreID = Genre.ID;
This SQL query can be sped up using which of the following indexing options?
Primary index in sequential order file organisation is also known as ______.
The total cost of retrieving records in sorted order using an unclustered B+ tree is
(P-Average number of records per data page
N-Data pages
F-Ratio of the size of a data entry to the size of a data record)
