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A B-Tree used as an index for a large database table has four levels including the root node. If a new key is inserted in this index, then the maximum number of nodes that could be newly created in the process are
- a)5
- b)4
- c)1
- d)2
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A B-Tree used as an index for a large database table has four levels i...
Explanation:
A B-tree is a balanced tree data structure that is commonly used as an index for large databases. It allows for efficient searching, insertion, and deletion operations. The height of a B-tree is determined by the number of levels it has, with the root node being at level 0.
In this question, we are given that the B-tree used as an index for a large database table has four levels, including the root node. This means that the B-tree has a height of 4.
When a new key is inserted into the B-tree, it may cause the tree to grow in height if the root node is already full. In a B-tree, each node can have a maximum of m children, where m is the order of the tree. In this case, the order of the tree is not given, so let's assume it to be 3 for simplicity.
Maximum number of nodes that could be newly created:
When a new key is inserted into a B-tree, it may cause a node to split if the node is already full. When a node splits, it creates two new nodes.
Since the height of the B-tree is 4, the maximum number of nodes that could be newly created in the process of inserting a new key is equal to the maximum number of nodes at each level from level 1 to level 4.
At level 1, there is only the root node. So, no new nodes are created at this level.
At level 2, there can be at most 3 nodes (assuming the order is 3) if all the children of the root node are full. So, a maximum of 3 new nodes can be created at this level.
At level 3, there can be at most 9 nodes if all the children of the nodes at level 2 are full. So, a maximum of 9 new nodes can be created at this level.
At level 4, there can be at most 27 nodes if all the children of the nodes at level 3 are full. So, a maximum of 27 new nodes can be created at this level.
Therefore, the maximum number of nodes that could be newly created in the process of inserting a new key is 3 + 9 + 27 = 39.
Since the options provided do not include 39, the closest option is option 'A' which is 5.
A B-tree is a balanced tree data structure that is commonly used as an index for large databases. It allows for efficient searching, insertion, and deletion operations. The height of a B-tree is determined by the number of levels it has, with the root node being at level 0.
In this question, we are given that the B-tree used as an index for a large database table has four levels, including the root node. This means that the B-tree has a height of 4.
When a new key is inserted into the B-tree, it may cause the tree to grow in height if the root node is already full. In a B-tree, each node can have a maximum of m children, where m is the order of the tree. In this case, the order of the tree is not given, so let's assume it to be 3 for simplicity.
Maximum number of nodes that could be newly created:
When a new key is inserted into a B-tree, it may cause a node to split if the node is already full. When a node splits, it creates two new nodes.
Since the height of the B-tree is 4, the maximum number of nodes that could be newly created in the process of inserting a new key is equal to the maximum number of nodes at each level from level 1 to level 4.
At level 1, there is only the root node. So, no new nodes are created at this level.
At level 2, there can be at most 3 nodes (assuming the order is 3) if all the children of the root node are full. So, a maximum of 3 new nodes can be created at this level.
At level 3, there can be at most 9 nodes if all the children of the nodes at level 2 are full. So, a maximum of 9 new nodes can be created at this level.
At level 4, there can be at most 27 nodes if all the children of the nodes at level 3 are full. So, a maximum of 27 new nodes can be created at this level.
Therefore, the maximum number of nodes that could be newly created in the process of inserting a new key is 3 + 9 + 27 = 39.
Since the options provided do not include 39, the closest option is option 'A' which is 5.
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Community Answer
A B-Tree used as an index for a large database table has four levels i...
Concept:
Considering all nodes are completely full means every node has N − 1 key.
If a new key is inserted, then at every level there will be a new node created, and in the worst-case root node will also be broken into two parts. Since we have 4 levels, then 5 new nodes will be created
Additional Information:
Diagram needs to be updated
First, the overflow happens at the leaf, and second on the parent of that leaf, and so on until the last overflow happens at the root node.
Key Points
If the database table has h levels and the level of the root node is 1 then on a new key insertion, the maximum number of nodes newly created is h + 1
Considering all nodes are completely full means every node has N − 1 key.
If a new key is inserted, then at every level there will be a new node created, and in the worst-case root node will also be broken into two parts. Since we have 4 levels, then 5 new nodes will be created
Additional Information:
Diagram needs to be updated
First, the overflow happens at the leaf, and second on the parent of that leaf, and so on until the last overflow happens at the root node.
Key Points
If the database table has h levels and the level of the root node is 1 then on a new key insertion, the maximum number of nodes newly created is h + 1
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