- Consider that a secondary-level index with 10,400 blocks needs to be represented using multi-level linear indexing. The blocking factor is 52 entries per block, which is also the fan-out factor for multi-level indexing:
- How many levels are required for indexing?
- How many blocks are required at the second level?
- What would be the minimum blocking factor to fit the dataset using a second-level linear index?
- Write the code for deletion of an element from a 2-3 tree. Also, prove that the number of leaf nodes in a 2-3 tree with height h will be between 2h-1 and 3h-1.
- Assume a computer system with disk blocks of 8,192, and that you want to store records with 16-byte keys and 64-byte fields. What will be the greatest number of records that can be stored in a file if a linear index of size 4 MB is used?Assume the records are sorted and packaged sequentially into the disk file.
- In the balanced binary tree given in the figure that follows, how many nodes will become unbalanced when inserted as a child of the node g?
Figure 7.22: Balanced binary tree
- Illustrate what the insertion of 1, 3, 6, 2, 7, 9, 10 (in same order) into a B+ tree will look like.
- Suppose N is an interior node whose capacity is m keys and m+1 leaves. Let m be assigned the m+2 leaf because of leaf splitting below which leads to the creation of a new node m which will be siblings to immediately to its right of m.
- Write a program to create and manage a B+ tree. The program should implement the following operations: creation, insertion, deletion, and tree display.
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