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 ...
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 being modified through an insertion operation and a node becomes full, it needs to be split into two nodes. During this split, the keys in the full node are divided into two halves. The middle key is then promoted to the parent node, and the remaining keys are split between the left and right half-nodes.
For example, let's say we have a node with keys [1, 3, 5, 7, 9] and we want to insert the key 6. Since the node is already full, it needs to be split. The middle key in this case is 5, so it will be promoted to the parent node. The left half-node will contain the keys [1, 3] and the right half-node will contain the keys [7, 9]. The key 6 will be inserted into the right half-node.
This process ensures that the B-tree maintains its properties, such as the keys being sorted within each node and the height of the tree remaining balanced.
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 also need to be deleted from the non-leaf nodes of the tree in order to maintain the integrity of the tree structure.
If the deleted key is not present in any non-leaf node, then the deletion process is complete and no further action is required. However, if the deleted key is present in a non-leaf node, it needs to be removed as well.
To delete a key from a non-leaf node, we have to find the key in the node and remove it. This may cause the node to become underflowed, meaning it has too few keys to satisfy the minimum requirements of the B-tree. In this case, we need to perform some additional operations, such as borrowing a key from a neighboring node or merging nodes, to ensure that the B-tree remains balanced and all the properties are maintained.
Overall, both statements are true. Statement 1 describes the process of key promotion during node split in insertion, while statement 2 highlights the need to delete a key from non-leaf nodes during deletion from a leaf node.
When a B-tree is being modified through an insertion operation and a node becomes full, it needs to be split into two nodes. During this split, the keys in the full node are divided into two halves. The middle key is then promoted to the parent node, and the remaining keys are split between the left and right half-nodes.
For example, let's say we have a node with keys [1, 3, 5, 7, 9] and we want to insert the key 6. Since the node is already full, it needs to be split. The middle key in this case is 5, so it will be promoted to the parent node. The left half-node will contain the keys [1, 3] and the right half-node will contain the keys [7, 9]. The key 6 will be inserted into the right half-node.
This process ensures that the B-tree maintains its properties, such as the keys being sorted within each node and the height of the tree remaining balanced.
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 also need to be deleted from the non-leaf nodes of the tree in order to maintain the integrity of the tree structure.
If the deleted key is not present in any non-leaf node, then the deletion process is complete and no further action is required. However, if the deleted key is present in a non-leaf node, it needs to be removed as well.
To delete a key from a non-leaf node, we have to find the key in the node and remove it. This may cause the node to become underflowed, meaning it has too few keys to satisfy the minimum requirements of the B-tree. In this case, we need to perform some additional operations, such as borrowing a key from a neighboring node or merging nodes, to ensure that the B-tree remains balanced and all the properties are maintained.
Overall, both statements are true. Statement 1 describes the process of key promotion during node split in insertion, while statement 2 highlights the need to delete a key from non-leaf nodes during deletion from a leaf node.
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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 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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