Final answer:
Using a merge-sort with a 3-block buffer and 2 records per block, the given records 10, 11, 1, 5, 90, 1, 2, 101 are sorted into 3 runs: initial sorted runs, an intermediate merge, and the final sorted run resulting in (1, 1, 2, 5, 10, 11, 90, 101).
Step-by-step explanation:
The student is asking about sorting records using merge-sort in the context of databases or data structures, specifically when constrained by memory buffers. With a buffer that can hold up to 3 blocks, and each block holding two records, the merge-sort algorithm will begin by dividing the input array into runs that can fit within the buffer. The records given are 10, 11, 1, 5, 90, 1, 2, and 101.
- First, divide the list into parts that can fit into the buffers:
Each block can hold two records, and our buffer can hold 3 blocks, so we will divide our records into halves that fit this capacity (although, in this case, we are only sorting 8 records which can be held in 2 blocks). - Next, sort each sub-list:
Each sub-list is sorted individually, resulting in the initial sorted runs. - Then, perform merging:
Combine the sorted runs into larger sorted runs until the whole list is sorted.
For the given records, the steps would be as follows:
- Initial Runs (each block contains 2 records, hence we will have 4 runs):
(10, 11), (1, 5), (1, 90), (2, 101) - Merge (since buffer holds 3 blocks, we merge 3 runs at a time when possible):
(1, 5, 10, 11), (1, 2, 90, 101) - Final Merge:
(1, 1, 2, 5, 10, 11, 90, 101)
Throughout this process, we have produced 3 runs: two initial runs and one final run after merging.