Assume that a file contains one million records sorted by key value. A query to the file returns a single record containing the requested key value. Files are stored on disk in sectors each containing 100 records. Assume that the average time to read a sector selected at random is 10.0 ms. In contrast, it takes only 2.0 ms to read the sector adjacent to the current position of the I/O head. The “batch” algorithm for processing queries is to first sort the queries by order of appearance in the file, and then read the entire file sequentially, processing all queries in sequential order as the file is read. This algorithm implies that the queries must all be available before processing begins. The “interactive” algorithm is to process each query in order of its arrival, searching for the requested sector each time (unless by chance two queries in a row are to the same sector). Carefully define under what conditions the batch method is more efficient than the interactive method.