In a B+- tree where each node can hold at most four key values, a root to leaf path consists of the following nodes:
\( A = (49, 77, 83, -) \)
\( B = (7, 19, 33, 44) \)
\( C = (20^*, 22^*, 25^*, 26^*) \)
The *-marked keys signify that these are data entries in a leaf. Assume that a pointer between keys \( k_1 \) and \( k_2 \) points to a subtree containing keys in \([ k_1, k_2 )\), and that when a leaf is created, the smallest key in it is copied up into its parent. A record with key value 23 is inserted into the B+- tree. The smallest key value in the parent of the leaf that contains 25* is ___________ . (Answer in integer)
\( B = (7, 19, 33, 44) \)
\( C = (20^*, 22^*, 25^*, 26^*) \)
The *-marked keys signify that these are data entries in a leaf. Assume that a pointer between keys \( k_1 \) and \( k_2 \) points to a subtree containing keys in \([ k_1, k_2 )\), and that when a leaf is created, the smallest key in it is copied up into its parent. A record with key value 23 is inserted into the B+- tree. The smallest key value in the parent of the leaf that contains 25* is ___________ . (Answer in integer)
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Correct Answer: 33
Solution and Explanation
To restore validity, the keys are redistributed into two adjacent leaves. The left leaf keeps the smaller keys, while the right leaf keeps the larger ones. The boundary key separating these two leaves is passed upward.
This boundary value becomes a new entry in the parent node. As a result, the parent now holds more keys than permitted.
The parent node is therefore divided into two parts, and the separating key between these two parts is promoted further upward. This promoted key is the one that determines the final change at the root level.
The key that ultimately moves upward after all required adjustments is:
\(\boxed{33}\)
Top Questions on Trees
- Consider the following algorithm tt{someAlgo that takes an undirected graph \( G \) as input.} tt{someAlgo(G)} Let \( v \) be any vertex in \( G \). Run BFS on \( G \) starting at \( v \). Let \( u \) be a vertex in \( G \) at maximum distance from \( v \) as given by the BFS. Run BFS on \( G \) again with \( u \) as the starting vertex. Let \( z \) be the vertex at maximum distance from \( u \) as given by the BFS. Output the distance between \( u \) and \( z \) in \( G \). The output of tt{someAlgo(T)} for the tree shown in the given figure is ___________ . (Answer in integer) \begin{center} \includegraphics{q59_fig.png} \end{center}
- Suppose the values 10, β4, 15, 30, 20, 5, 60, 19 are inserted in that order into an initially empty binary search tree. Let \( T \) be the resulting binary search tree. The number of edges in the path from the node containing 19 to the root node of \( T \) is \underline{{1cm}}. {(Answer in integer)}
- A binary search tree \( T \) contains \( n \) distinct elements. What is the time complexity of picking an element in \( T \) that is smaller than the maximum element in \( T \)?
Let π be an odd number greater than 100. Consider a binary minheap with
π elements stored in an array π whose index starts from 1.
Which of the following indices of π do/does NOT correspond to any leaf node of
the minheap?- Want to practice more? Try solving extra ecology questions todayView All Questions
Questions Asked in GATE CS exam
A database has 25,000 fixed-length records of 100 bytes (primary key 15 bytes). The data file is block-aligned so each record is fully contained within a block. The file is indexed by a primary index file, also block-aligned and ordered. Block size is 1024 bytes and a block pointer is 5 bytes. Each index entry stores the blockβs anchor key (15 bytes) and a pointer (5 bytes). Binary search on an index file of \(b\) blocks needs \(\lceil \log_2 b \rceil\) block accesses in the worst case. Given a key, the number of block accesses required to identify the data file block that may contain the record, in the worst case, is ____________.
- GATE CS - 2023
- Database Management Systems