The maximum number of node-splitting operations in a B-tree of order 4 during 10 successive insertions can be calculated as follows:

1. For the first 4 insertions, no splitting is required because a B-tree of order 4 can hold up to 3 keys and 4 pointers.

2. On the 5th insertion, the root node is full and needs to be split. This results in 1 split operation.

3. For the next 3 insertions (6th, 7th, and 8th), no additional splitting is required because the new root after the first split can hold up to 3 keys and 4 pointers.

4. On the 9th insertion, one of the child nodes is full and needs to be split. This results in another split operation.

5. On the 10th insertion, if the key is inserted into the node that was just split, another split operation will be required.

So, the maximum number of node-splitting operations that may take place during 10 successive insertions into a B-tree of order 4 is 3.

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The maximum number of node-splitting operations in a B-tree of order 4 during 10 successive insertions can be calculated as follows:

1. For the first 4 insertions, no splitting is required because a B-tree of order 4 can hold up to 3 keys and 4 pointers.

2. On the 5th insertion, the root node is full and needs to be split. This results in 1 split operation.

3. For the next 3 insertions (6th, 7th, and 8th), no additional splitting is required because the new root after the first split can hold up to 3 keys and 4 pointers.

4. On the 9th insertion, one of the child nodes is full and needs to be split. This results in another split operation.

5. On the 10th insertion, if the key is inserted into the node that was just split, another split operation will be required.

So, the maximum number of node-splitting operations that may take place during 10 successive insertions into a B-tree of order 4 is 3.

Knowee AI · Accepted Answer

The maximum number of node-splitting operations in a B-tree of order 4 during 10 successive insertions can be calculated as follows:

1. For the first 4 insertions, no splitting is required because a B-tree of order 4 can hold up to 3 keys and 4 pointers.

2. On the 5th insertion, the root node is full and needs to be split. This results in 1 split operation.

3. For the next 3 insertions (6th, 7th, and 8th), no additional splitting is required because the new root after the first split can hold up to 3 keys and 4 pointers.

4. On the 9th insertion, one of the child nodes is full and needs to be split. This results in another split operation.

5. On the 10th insertion, if the key is inserted into the node that was just split, another split operation will be required.

So, the maximum number of node-splitting operations that may take place during 10 successive insertions into a B-tree of order 4 is 3.

A B-tree of order 4 is built from scratch by 10 successive insertions. What is the maximum number of node-splitting operations that may take place?

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