Data Processing Techniques - All about the IBM 1130 Computing ...

Section Subsections Page75 30 10 03Input and Pass 113 \___„ 1369 i - 613\ 5613561356135656 56 )--'.6 \ 02 02 0202 02 02 )---)' 69 08 08---4.--08 08 08 08 1 6 \ , 2121 21 21 21 21 )—'.69Pass 213 13 13 13 1356 56 02 02 0202 02 56 \ 08 0808 08 08 56 \ 2121 21 21 21 5669 69 69 69 69Pass 3Output13 02 02 02 0202 )-- 13 08 08 0808 08 T1 13 1321 21 21 )-- 21 2156 56 56 56 5669 69 69 69 69The size of the file is of great importance, sincethe total number of comparisons and interchangesincreases roughly with the square of the number ofrecords in the file.MergingMerging is the process of combining severalsequences of records to form a single specifiedsequence. The same rules by which sequences arecombined may also be used to form sequences (oftwo or more items). Thus, the merging processhas, essentially, a dual nature: it can be used forcreating sequences (usually in an internal sort),and it is also capable of reducing previously createdsequences to one (usually in an external sort). Thisdual capability contrasts with the selection andexchange techniques described thus far, which areuseful primarily for internal sorting of relativelyshort files of records. The versatility, speed, andsimplicity of merging make it one of the most widelyused sorting techniques.There are two basic methods of merge sorting:(1) straight or standard merging, with fixed-lengthsequences, and (2) natural merging, with variablelengthsequences, or strings. (The words "sequence"and "string" are often used interchangeably inmerging terminology.)In straight merging, the input file is distributedinitially into two or more work areas, dependingupon the number of sequences to be combined duringeach merge (that is, the order of merge). Forexample, in a method of two-way straight merging,the first merge pass alternates between two storageareas to form strings of two records, one fromeach area. Subsequent passes double the lengthof the strings each time (for example, 4, 8, 16,etc.), until the last pass produces a single sequenceof all the records. The length of the strings duringeach pass and the number of passes are fixed.The natural merge sort takes advantage of"natural" sequences in the original file, whichoccur with a certain "probable" frequency. Thelength of the strings on each pass is no longer fixed,but depends upon the existing sequences. The totalnumber of passes required to sort a given file, then,also depends on the number of natural sequences inthe original file. For a file that is in correctsequence, only a single pass is required -- to verifythat sequence. In the worst case, the number ofpasses is the same as for straight merging.