Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Statement 1: When a node is split during inse...
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Statement 1: When a node is split during insertion, the middle key is promoted to the parent as well as retained in right half-node.
Statement 2: When a key is deleted from the leaf, it is also deleted from the non-leaf nodes of the tree.
Statement 2: When a key is deleted from the leaf, it is also deleted from the non-leaf nodes of the tree.
- a)Statement 1 is true but statement 2 is false
- b)Statement 2 is true but statement 1 is false
- c)Both the statements are true
- d)Both the statements are false
Correct answer is option 'A'. Can you explain this answer?
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Statement 1: When a node is split during insertion, the middle key is ...
During the split, the middle key is retained in the right half node and also promoted to parent node. When a key is deleted from the leaf, it is retained in non-leaves, because it can be still a valid separator between keys in nodes below.
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Statement 1: When a node is split during insertion, the middle key is ...
Statement 1: When a node is split during insertion, the middle key is promoted to the parent as well as retained in the right half-node.
Statement 2: When a key is deleted from the leaf, it is also deleted from the non-leaf nodes of the tree.
Explanation:
Statement 1: When a node is split during insertion, the middle key is promoted to the parent as well as retained in the right half-node.
When a B-tree is full and a new key needs to be inserted, the node is split into two halves. The middle key is then promoted to the parent node. This process continues recursively until the root node is reached.
For example, let's say we have a B-tree with the following structure:
5
/ \
2,4 7,8
If we need to insert the key 6, we split the node containing 7,8 into two nodes:
5
/ \
2,4 7,8
\
6
In this case, the middle key 7 is promoted to the parent node, resulting in the following structure:
5,7
/ \
2,4 6,8
So, statement 1 is true.
Statement 2: When a key is deleted from the leaf, it is also deleted from the non-leaf nodes of the tree.
When a key is deleted from a leaf node in a B-tree, it may create an imbalance in the tree. In order to maintain the B-tree properties, the key must also be deleted from the non-leaf nodes until the root node is reached.
For example, let's consider the same B-tree structure as before:
5,7
/ \
2,4 6,8
If we delete the key 6 from the leaf node, the tree becomes unbalanced:
5,7
/ \
2,4 8
In order to maintain the B-tree properties, the key 6 must also be deleted from the non-leaf node:
5
/ \
2,4 8
So, statement 2 is false.
Therefore, the correct answer is option A: Statement 1 is true but statement 2 is false.
Statement 2: When a key is deleted from the leaf, it is also deleted from the non-leaf nodes of the tree.
Explanation:
Statement 1: When a node is split during insertion, the middle key is promoted to the parent as well as retained in the right half-node.
When a B-tree is full and a new key needs to be inserted, the node is split into two halves. The middle key is then promoted to the parent node. This process continues recursively until the root node is reached.
For example, let's say we have a B-tree with the following structure:
5
/ \
2,4 7,8
If we need to insert the key 6, we split the node containing 7,8 into two nodes:
5
/ \
2,4 7,8
\
6
In this case, the middle key 7 is promoted to the parent node, resulting in the following structure:
5,7
/ \
2,4 6,8
So, statement 1 is true.
Statement 2: When a key is deleted from the leaf, it is also deleted from the non-leaf nodes of the tree.
When a key is deleted from a leaf node in a B-tree, it may create an imbalance in the tree. In order to maintain the B-tree properties, the key must also be deleted from the non-leaf nodes until the root node is reached.
For example, let's consider the same B-tree structure as before:
5,7
/ \
2,4 6,8
If we delete the key 6 from the leaf node, the tree becomes unbalanced:
5,7
/ \
2,4 8
In order to maintain the B-tree properties, the key 6 must also be deleted from the non-leaf node:
5
/ \
2,4 8
So, statement 2 is false.
Therefore, the correct answer is option A: Statement 1 is true but statement 2 is false.
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Statement 1: When a node is split during insertion, the middle key is promoted to the parent as well as retained in right half-node.Statement 2: When a key is deleted from the leaf, it is also deleted from the non-leaf nodes of the tree.a)Statement 1 is true but statement 2 is falseb)Statement 2 is true but statement 1 is falsec)Both the statements are trued)Both the statements are falseCorrect answer is option 'A'. Can you explain this answer?
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