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

Section Subsections Page75 30 10 05Address CalculationWhen the approximate distribution of the key valuesis known, it becomes possible to sort a file internallyby estimating the eventual (sorted) positionof each key. This method is called "address calculation"or "pigeonhole sorting".Briefly, it consists of calculating the correctrecord number of each item within the file by apredetermined linear formula of the form y= a +bx.If the location at that record number is empty, theitem (record or key) is placed there; if it is full,a search is made to find the closest empty space inthe vicinity of the calculated record number. Theitem at the calculated record number and the adjacentitems are then moved so that the new item canbe inserted in its proper place in the sequence.Address calculation is similar to the insertionmethod in that each item is placed directly in itsproper relative position within the file, and theentire file is in order just after the last item hasbeen inserted. The method differs from insertion,however, in that some foreknowledge of the rangeand distribution of the keys is required to estimatethe relative location for each item. When this isavailable, address calculation is a relatively simpleand rapid method for sorting a medium-size file(several hundred to a few thousand items) of smallto medium-length records. The major disadvantageof the method is the need for a fairly large storagearea -- about two or three times the size of the areaneeded for the original file. If only a relativelysmall working storage area is available, or if thedistribution within the file is not as forecast, a greatdeal of processing time will be spent in redistributingthe records.To illustrate this method, let us consider ahypothetical case: Many years ago, the ABC Companyset up a man-number system based on a threedigitnumber. Since they had about 150 employees,each man was assigned, in alphabetic order, a numberevenly divisible by 5 (005, 010, 015, 020, 025,, 995). However, there are now about 240 employees,and the system is not quite as neat as itonce was.Some of the men (50 of them) have been assignednumbers out of the normal pattern (for example,862 in between 860 and 865). They are still in alphabeticorder, though.The address calculation sort could be used toplace this employee file onto the disk in alphabetic(man-number) sequence in the following way:1. Set up a file containing 500 records.2. As each man-number is encountered, divideit by 2.5, and convert the result to an integer (callit N).3. Check record number N to see whether thereis already an employee there.4. If there isn't, put the man just processed intothat record.5. If there is someone there already, move theadjacent records up (or down) until there is roomto insert the new man.This will be quite fast, provided the "moving around"(step 5) is not required too frequently. If it is, thefile could be increased to 600 records, and the mannumberdivided by 2. This, however, would wastea considerable amount of space on the disk.