Question

In a record embedded b tree containing a particular record set, leaf blocks holds 10 records when full, 5 records when half full and internal node blocks holds 100 subtree pointers when full and 50 when half full. What is the maximum number of records that this structure can contain if it has 3 levels of internal nodes plus 1 leaf node level?

Answer 1

The structure being described is a B-tree, and with 3 levels of internal nodes where each node can point to 100 subtrees and each leaf node can hold 10 records when full, the B-tree can hold a maximum of 1,000,000 records.

Step-by-step explanation:

The question is asking about the capacity of a specific type of data structure called a B-tree. A B-tree is a balanced tree data structure that maintains sorted data in a way that allows for efficient insertion, deletion, and searching operations. The question specifies that the B-tree in question has 4 levels – 3 internal node levels and 1 leaf node level – and provides details on the capacity of each type of node.

Let's calculate the maximum number of records this B-tree could contain:

1. At the leaf level, each block can contain 10 records when full.
2. At each of the internal node levels, each block can point to 100 subtrees when full.

Because there are three levels of internal nodes, the total number of leaf nodes can be calculated by taking the number of subtree pointers at the highest internal level and multiplying it by the number of pointers per node at each subsequent level:

Number of leaves = 100 (level 1) * 100 (level 2) * 100 (level 3)

Finally, the total capacity for records in the B-tree is the number of leaf blocks multiplied by the number of records each can hold when full:

Total capacity = Number of leaves * 10 records per leaf

Total capacity = 100 * 100 * 100 * 10 records

Total capacity = 1,000,000 records