Given a fixed-length record file that is ordered on the key field. The file needs B disk blocks to store R number of records. Find the average access time needed to access any record of the given file using binary search.

Correct option is D

The given problem involves finding the average access time needed to access any record in a fixed-length record file ordered on the key field using binary search.
Step-by-step Explanation:
1. Binary Search Overview: Binary search reduces the search space by half at every step. The time complexity is proportional to the number of steps required to divide the search space until the desired record is found.
2. Key Parameters:
· B: The number of disk blocks needed to store R records.
· Each division reduces the search space to half, and the number of steps required is equal to the base-2 logarithm of B.
3. Average Access Time: The number of divisions required to access the desired block is log2 B. Binary search ensures that this logarithmic time provides efficient access.
4. Conclusion: The average access time required for binary search is log2 B.
Information Booster:
1. Binary Search Mechanism: It works efficiently for sorted data structures. The search space is reduced by half in each step, ensuring logarithmic performance.
2. Application of Binary Search in Files: In ordered files, binary search minimizes disk I/O operations by logarithmically narrowing down the number of blocks to be accessed.
3. Logarithmic Access Times: In computer science, logarithmic access times are considered optimal for large datasets as the growth of log2 B is much slower compared to linear or polynomial growth.
Additional Knowledge:
Option (a) : Incorrect as it implies a linear relationship between access time and the number of blocks.
Option (b) B + R: Incorrect as it adds a constant overhead that is not justified in the context of binary search.
Option (b) B: Incorrect as it assumes a linear access time for each block, which contradicts the logarithmic nature of binary search.