Data Structures and Algorithm Analysis - Computer Science at ...

Sec. 8.5 External Sorting 289InputFileInput BufferRAMOutput BufferOutputRun FileFigure 8.7 Overview of replacement selection. Input records are processed sequentially.Initially RAM is filled with M records. As records are processed, theyare written to an output buffer. When this buffer becomes full, it is written to disk.Meanwhile, as replacement selection needs records, it reads them from the inputbuffer. Whenever this buffer becomes empty, the next block of records is readfrom disk.the 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.ii. Else replace the root with the record in array position LAST, andplace R at position LAST. Set LAST = LAST − 1.(c) Sift down the root to reorder the heap.When the test at step 3(b) is successful, a new record is added to the heap,eventually to be output as part of the run. As long as records coming from the inputfile have key values greater than the last key value output to the run, they can besafely added to the heap. Records with smaller key values cannot be output as partof the current run because they would not be in sorted order. Such values must be