A Practical Introduction to Data Structures and Algorithm Analysis

304 Chap. 8 File Processing and External Sorting2. Merge the runs together to form a single sorted file.8.5.2 Replacement SelectionThis section treats the problem of creating initial runs as large as possible from adisk file, assuming a fixed amount of RAM is available for processing. As mentionedpreviously, a simple approach is to allocate as much RAM as possible to alarge array, fill this array from disk, and sort the array using Quicksort. Thus, ifthe size of memory available for the array is M records, then the input file can bebroken into initial runs of length M. A better approach is to use an algorithm calledreplacement selection that, on average, creates runs of 2M records in length. Replacementselection is actually a slight variation on the Heapsort algorithm. Thefact that Heapsort is slower than Quicksort is irrelevant in this context because I/Otime will dominate the total running time of any reasonable external sorting algorithm.Building longer initial runs will reduce the total I/O time required.Replacement selection views RAM as consisting of an array of size M in additionto an input buffer and an output buffer. (Additional I/O buffers might bedesirable if the operating system supports double buffering, because replacementselection does sequential processing on both its input and its output.) Imagine thatthe input and output files are streams of records. Replacement selection takes thenext record in sequential order from the input stream when needed, and outputsruns one record at a time to the output stream. Buffering is used so that disk I/O isperformed one block at a time. A block of records is initially read and held in theinput buffer. Replacement selection removes records from the input buffer one ata time until the buffer is empty. At this point the next block of records is read in.Output to a buffer is similar: Once the buffer fills up it is written to disk as a unit.This process is illustrated by Figure 8.7.Replacement selection works as follows. Assume that the main processing isdone in an array of size M records.1. Fill the array from disk. Set LAST = M − 1.2. Build a min-heap. (Recall that a min-heap is defined such that the record ateach node has a key value less than the key values of its children.)3. Repeat until the array is empty:(a) Send the record with the minimum key value (the root) to the outputbuffer.(b) Let R be the next record in the input buffer. If R’s key value is greaterthan the key value just output ...i. Then place R at the root.