Abstract:
The binary sort access method and apparatus makes use of a binary search to show where an item of data not found should be placed in sorted order within a list in a table in memory or in a file on a storage device. The method includes building the list structure when items of data are inserted in and maintained in sorted order in a table in memory or in a file on a storage device. When no blank table entry is available items of data are moved to make room for the next succeeding item of data. A partially filled or filled list of items may be rewritten again to provide one or more blank table entries between each item of data.

Description:
This is a continuation-in-part of application Ser. No. 507,967 filed Jul. 27, 1995 now abandoned. 
    
    
     TECHNICAL FIELD 
     The present invention relates to a method of and apparatus for accessing items of data in a sorted list. 
     BACKGROUND ART 
     A portion of the disclosure of this patent document contains material which is subject to copyright protection. The copyright owner has no objection to the facsimile reproduction by anyone of the patent document or the patent disclosure, as it appears in the Patent and Trademark Office patent files or records, but otherwise reserves all copyrights whatsoever. 
     In a binary search, the conventional method used is to determine the midpoint of a sorted list of items of data or a subset of a list by calculating the sum of the extreme pointers and then dividing by two. In a conventional binary search half of the remaining list is eliminated from the search by each comparison. When the searched item is not found, the pointers cross to indicate where that searched item would be inserted to be in sorted order. Given N items in a list, N/2 items on average must be physically moved to make room for a new item to be inserted in sorted order. 
     DISCLOSURE OF THE INVENTION 
     In accordance with the present invention there is the binary sort access method and apparatus wherein one or more blank table entries are interspersed between each item of data in a sorted list in a table in memory or in a file on a storage device, and a new item of data is added by insertion in the blank table entries to build the list. If a blank table entry is not available at the position desired, then the old items of data are searched until a blank entry is found, into which the next old item of data is moved respectively and consecutively until a blank table entry is available for the new item of data. The list is rewritten with one or more blank table entries interspersed between each item of data after a selected number of new insertions. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Details of this invention are described in connection with the accompanying drawings in which like parts bear similar reference numerals in which: 
     FIG. 1 is a block diagram showing parts of a general purpose computer and associated apparatus by which the method of the present invention is carried out. 
     FIG. 2 is a table representing a series of entries of data with a blank table entry between each item of data in a sorted list in the table in memory or in a file on a storage device. 
     FIG. 3 is a table of entries of data in which two additional items of data have been added to the sorted list in the table in memory or in a file on a storage device. 
     FIG. 4 is a table representing a series of entries of data in which one entry of data has been moved and replaced by a blank table entry. 
     FIG. 5 is a table of entries of data in which an additional item of data has been added to the sorted list. 
     FIG. 6 is the first portion of the program flow chart for carrying out the binary sort access method according to the present invention. 
     FIG. 7 is another portion of the program flow chart. 
     FIG. 8 is another portion of the program flow chart. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring now to FIG. 1, a general purpose computer 10 is shown having computer processor 12, a system bus 14, and a memory 16. The memory contains index tables 18 used in carrying out the binary sort access method according to the present invention. Auxiliary devices shown coupled to the bus 14 are a disc drive 20, monitor 22, keyboard 24 and printer 26. 
     The first step of the present invention involves physically placing or putting items of data in sorted order with one or more blank table entries interspersed between each item of data. This is represented in FIG. 2 wherein there is shown a table representing entries with items of data in a sorted list in locations in memory or in a file on a storage device identified by numerals 1, 21, 31, 41, 51, and 61 with a blank table entry &#34;B&#34; interspersed between each item of data. It is understood there may be a plurality of blank table entries instead of a single blank table entry between items of data. 
     The second step involves building the list of items by adding items of data in order in the space occupied by the blank table entries in memory or in a file on a storage device. A binary search is performed to locate the desired location for insertion of each new item of data. If the desired location is a blank table entry, the new item of data is inserted. This step is represented in FIG. 3 wherein there is shown the table of entries to which an item of data identified as numeral 25 has been added in order in the blank table entry B between items 21 and 31, and item of data represented by numeral 43 has been added in order in the blank table entry between items 41 and 51. 
     The third step involves attempting to insert a new item of data in order in the list and finding no space available. The fact there is no space available is detected by keeping a count of the items of data. When no space is available at the desired insertion location, the blank table entry nearest the desired insertion location is identified, the items of data between the nearest blank table entry and the desired insertion location are moved to make room for the new item of data, and the new item of data is inserted at the desired location. 
     In FIG. 4 there is shown the table of entries in which a blank table entry is added between item of data 25 and item of data 31, and item of data 31 is moved below to the next blank table entry so that item 27 subsequently may be inserted in the table, as is shown in the table in FIG. 5. At any time after the first item of data is added or when the table is filled, the table is rewritten to intersperse at least one blank table entry between each item of data as is shown in FIG. 2. 
     Referring now to FIGS. 6, 7 and 8 there is shown the flow chart for the program for carrying out the method. This chart shows that according to the present invention a list of items of data are placed in a sorted order in a table in memory or in a file on a storage device, and at least one and possibly more than one blank entry is interspersed between each item of data in memory 16 or in a file on a storage device such as disc drive 20. Items of data may be successively added in order in the space occupied by the blank table entries. When there is no blank table entry available in the list of items, the items of data are moved to form a blank table entry to make room for the next item of data. At any time after the first item is added until the blank entries become filled, the list of items may be rewritten providing one or more blank table entries between each item of data. This method shows that the step of moving the items of data to form the blank table entry includes the substep of finding the nearest blank table entry to a desired insertion location and moving all table entries between the nearest blank table entry and the desired insertion location to form the blank table entry resulting in opening up the blank table entry. As required, the method and apparatus of the present invention are able to rewrite all or part of the list structures. This is very rapid because while sequentially reading a sorted list once, the method and apparatus of the present invention also writes the same list with blank table entries inserted as necessary into memory or into a file on a storage device. 
     In the preferred embodiment of the present invention, the method includes the steps of counting the number of insertions made between pairs of successive initial items of data and rewriting the list when all blank entries between any pair of-successive initial items of data are filled. The method is optimized with initially placing items of data in the list with eleven blank entries between each pair of items of data, and rewriting the list as soon as eleven insertions are made between any pair of successive initial items of data. 
     In an alternative embodiment of the present invention, the method includes the steps of counting the number of insertions made after the list is initially written and rewriting the list after a selected number of insertions. For example, the method may count the insertions and rewrite the table when the number of insertions equals the number of remaining blank entries. 
     The method and apparatus of the present invention reduces the average number of items that must be physically moved to make room for a new item to be inserted in sorted order from the prior art average of N/2 to an average of less than one. The method and apparatus of the present invention is ideally suited as an index searching and sorting method for large, real-time applications such as those encountered in databases accessed by Structured Query language (SQL) which typically do not perform well with indexing schemes using structures known in the art as binary trees or B-trees. The present invention is a special case of such binary trees: it is a binary tree of a single depth or unitary level which is rewritten with blank node entries when the tree becomes full. 
     The program code lists are set forth in the attached Appendices consisting of six pages. 
     Although the present invention has been described with a certain degree of particularity, it is understood that the present disclosure has been made by way of example and that changes in details of structure may be made without departing from the spirit thereof. 
     
                       APPENDIX A______________________________________rem Source code for BSAM in TrueBASIC ™rem Copyright © 1992-1995., Colin James IIIrem All Rights Reservedbegin bsam.sub.-- routinerem set.sub.-- up.sub.-- beginlet sorted.sub.-- list.sub.-- minimum = 1let sorted.sub.-- list.sub.-- maximum = 100let blank.sub.-- pointer = 0dim sorted.sub.-- list( 100)for index = sorted.sub.-- list.sub.-- minimum tosorted.sub.-- list.sub.-- maximum    step 2    let sorted.sub.-- list( index) = index    let sorted.sub.-- list ( index + 1 ) = 0next indexrem set.sub.-- up.sub.-- endrem.sub.-- search.sub.-- beginset cursor 1,1input item.sub.-- searchedlet search.sub.-- item = item.sub.-- searchedlet lower.sub.-- index = sorted.sub.-- list.sub.-- minimumlet upper.sub.-- index = sorted.sub.-- list.sub.-- maximumlet test.sub.-- pointer = 0let item$ = &#34;To Insert&#34;do while lower.sub.-- index &lt;= upper.sub.-- index    let mid.sub.-- pointer = lower.sub.-- index + int(( upper.sub.--    index       lower.sub.-- index)/2)    if sorted.sub.-- list( mid.sub.-- pointer) = blank.sub.--    pointer then       let.sub.-- mid.sub.-- pointer = mid.sub.-- pointer - 1    end if    if test.sub.-- pointer = mid.sub.-- pointer then       let sorted.sub.-- list( lower.sub.-- index ) =       search.sub.-- item       let item$ = &#34;Inserted Ok&#34;       stop    end if    let test.sub.-- pointer = mid.sub.-- pointer    if sorted.sub.-- list( mid.sub.-- pointer) = search.sub.-- item    then       let item$ = &#34;Found ok - - No Insert&#34;       stop    elseif sorted.sub.-- list( mid.sub.-- pointer) = search.sub.--    item then       let upper.sub.-- index = mid.sub.-- pointer - 1    elseif sorted.sub.-- list{ mid.sub.-- pointer) &lt; search item    then       let lower.sub.-- index = mid.sub.-- pointer + 1    end iflooprem search.sub.-- endrem rotate.sub.-- and.sub.-- insert.sub.-- beginlet rotate.sub.-- left = upper.sub.-- indexlet rotate.sub.-- rght = lower.sub.-- indexwhile rotate.sub.-- left &gt; sorted.sub.-- list.sub.-- minimum and    rotate.sub.-- rght &lt; sorted.sub.-- list.sub.-- maximum    let rotate.sub.-- left = rotate.sub.-- left - 1    if sorted.sub.-- list( rotate.sub.-- left) = blank.sub.--    pointer then       let sorted.sub.-- list( rotate.sub.-- left) = search.sub.--       item       let item$ = &#34;Rotated and Inserted OK&#34;       stop    end if    let rotate.sub.-- rght = rotate.sub.-- rght + 1    if sorted.sub.-- list ( rotate.sub.-- rght) = blank.sub.--    pointer then       let sorted.sub.-- list( rotate.sub.-- rght) = search.sub.--       item       let item$ = &#34;Rotated.sub.-- and Inserted OK&#34;       stop.    end iflooprem rotate.sub.-- and.sub.-- insert.sub.-- endrem rewrite.sub.-- and.sub.-- insert.sub.-- beginlet.sub.-- new.sub.-- list.sub.-- maximum    = sorted.sub.-- list.sub.-- maximum + sorted.sub.-- list.sub.--    1    maximum + 2dim new.sub.-- list( sorted.sub.-- list.sub.-- maximum)let new.sub.-- indx = 0for old.sub.-- indx = sorted.sub.-- list.sub.-- minimum to upper.sub.--index    if sorted.sub.-- list( old.sub.-- indx) &lt;&gt; blank.sub.-- pointer    then       let new.sub.-- indx = new.sub.-- indx + 1       let new.sub.-- list( new.sub.-- indx)          = sorted.sub.-- list( oid.sub.-- indx)       let new.sub.-- indx = new.sub.-- indx + 1       let new.sub.-- list( new.sub.-- indx) = blank.sub.-- pointer    end ifnext old.sub.-- indxlet new.sub.-- indx = new indx + 1let new.sub.-- list( new.sub.-- indx) = search.sub.-- itemlet new.sub.-- indx = new.sub.-- indx + 1let new.sub.-- list( new.sub.-- indx) = blank.sub.-- pointerfor old.sub.-- indx = lower.sub.-- index to sorted.sub.-- list.sub.--maximum    if sorted.sub.-- list( old.sub.-- indx) &lt;&gt;blank.sub.-- pointer    then       let new.sub.-- indx = new.sub.-- indx + 1       let new.sub.-- list( new.sub.-- indx)          = sorted.sub.-- list( old.sub.-- indx)       let new.sub.-- indx = new.sub.-- indx + 1       let new.sub.-- list( new.sub.-- indx) = blank.sub.-- pointer    end ifnext old.sub.-- indxdim sorted.sub.-- list( old.sub.-- indx)for indx = 1 to old.sub.-- indx    let sorted.sub.-- list( indx) = new.sub.-- list( indx)next indxrem rewrite.sub.-- and.sub.-- insert.sub.-- endend bsam.sub.-- routine______________________________________ 
    
     
                       APPENDIX B______________________________________rem Source code for BSAM in TrueBASIC ™rem copyright © 1997, Colin James IIIrem All Rights Reservedrem set up sort parameterslibrary &#34;execlib.trc&#34;let n.sub.-- lim.sub.-- idx = 200000let increment.sub.-- step = 5000let num.sub.-- child = 11      rem number of empty nodeslet n.sub.-- lim = 1 + n.sub.-- lim.sub.-- idx          rem number of random keys to be testedlet n.sub.-- lim.sub.-- minus.sub.-- 1 = n.sub.-- lim - 1rem set up random permutation array of input valuesdim r1( 1: 1)dim keys$( 0)mat redim r1( 1: n.sub.-- lim.sub.-- idx)for i = 1 to n.sub.-- lim.sub.-- minus.sub.-- 1let r1.sub.-- ( i) = inext ifor i = n.sub.-- lim.sub.-- minus.sub.-- 1 to 2 step -1let idx = INT( RND * i) + 1let t = r1( i)let r1( i) = r1( idx)let r1( idx) = tnext irem set up sort file paramaterslet rec.sub.-- size = 8          rem 8-byte IEEE number formatlet file.sub.-- A$ = &#34;A.dat&#34;let file.sub.-- B$ = &#34;B.dat&#34;let file.sub.-- C$ = .sub.-- d.dat&#34;let zero$   = NUM$( 1) rem filler value is 1let minus.sub.-- one$ = NUM$( 0)          rem sentinel value is 0let z = 0let N1 = 1let left = 1let right = N1open #1: name file.sub.-- A$, org byte, create newold, access outin,recsize rec.sub.-- sizefor  j = to num.sub.-- child              rem first record is 0 1 1 1 1 1 1 1 1 1 1 1set  #1: record j * rec.sub.-- size + 1if j = 0 thenwrite #1: minus.sub.-- one$elsewrite #1: zero$end ifnext jclose #1let num.sub.-- items = n1let ix = 0rem main loop until ix = n.sub.-- lim.sub.-- minus 1dolet ix = ix + 1let v$ = num$( r1( ix))rem open filesopen #1: name file.sub.-- A$, org byte, create newold, access outin,recsize rec.sub.-- sizeopen #2: name file.sub.-- B$, org byte, create newold, access outin,recsize rec.sub.-- sizelet left = 1let right = N1let i = 0let j = 0rem.sub.-- binary.sub.-- search loopdolet i = IP( ( left + right) / 2)set     #1: record ( ( ( i - 1) * rec.sub.-- size *( num.sub.-- child + 1)) + ( 1))read #1: rec$if v$ &lt; rec$ thenlet right = i - 1elselet left = i + 1end ifloop until v$ = rec$ or left &gt; rightrem test search results loopdorem test if recS found at ( i, 0)if v$ = rec$ thenexit doend iflet bit.sub.-- limit = 0rem insert rec$ at first node ( right, 1 . . . num child) = 0for     j = 1 to num.sub.-- childset        #1: record ( ( right - 1) * rec.sub.-- size *    ( num.sub.-- child + 1)) + ( ( j * rec.sub.-- size) + 1)read #1: rec$if rec$ = zero$ then    set #1: record ( ( right - 1) * rec.sub.-- size *       ( num.sub.-- child + 1)) + ( ( j * rec.sub.-- size) + 1)    write #1: v$    let num.sub.-- items = num.sub.-- items + 1    let bit.sub.-- limit = j    exit forend ifnext    jif bit.sub.-- limit = 1 thenrem only one key in nodes of the record, so the noderem is already sortedexit doelserem more than one key, so sort the nodesrem ( i, 1 . . . num.sub.-- child)if bit.sub.-- limit &lt;= num.sub.-- child then    rem insertion sort of nodes using a    rem sentinel record    for   i = 2 to bit.sub.-- limit        set #1: record ( ( right -1) * rec.sub.-- size        * ( num.sub.-- child +1)) + ( ( i * rec.sub.--        size) + 1)        read #1: t.sub.-- rec$        let j = i        do           set  #1: record ( ( right - 1) *           rec.sub.-- size * ( num.sub.-- child + 1)) +           ( ( ( j - 1) * rec.sub.-- size) + 1)           read #1: rec$           if rec$ &gt; t.sub.-- rec$ then              set  #1: record ( ( right -              1) * rec.sub.-- size * ( num.sub.--              child +1)) + ( ( j * rec.sub.--              size) + 1)              write #1: rec$              let j = j - 1           else              exit do           end if       loop           set #1: record ( ( right - 1) *           rec.sub.-- size * ( num.sub.-- child + 1)) +            ( ( j           * rec.sub.-- size) + 1)           write #1: t.sub.-- rec$    next iend ifif bit.sub.-- limit &lt;&gt; num.sub.-- child then    exit doelse    rem empty nodes filled in this record, so    rem rewrite sorted file with empty nodes    rem in all records    let n2 = num.sub.-- items    let counter = 0    for  i = 1 to num.sub.-- items       for   j = 0 to num.sub.-- child           set #2: record ( ( i - 1) *           rec.sub.-- size * ( num.sub.-- child + 1)) +           ( ( j * rec.sub.-- size) + 1)           write #2: zero$       next  j    next i    for i = 1 to n1       for   j = 0 to num.sub.-- child           set  #1: record ( ( i - 1) *           rec.sub.-- size * ( num.sub.-- child +           1)) +( ( j * rec.sub.-- size) + 1)           read #1: rec$           if rec$ = zero$ THEN              exit for          else              let counter = counter + 1              set  #2: record              ( ( counter              - 1) * rec.sub.-- size *              ( num.sub.-- child              + 1)) + 1              write #2: rec$          end if       next j    next i    let n1 = n2    let num.sub.-- items = n1       rem close files       close #1       close #2       rem rename files       call Exec.sub.-- Rename( file.sub.-- A$, file.sub.-- C$)       call Exec.sub.-- Rename( file.sub.-- B$, file.sub.-- A$)       unsave file.sub.-- C$       exit do    end ifend iflooprem close.sub.-- filesclose   #1close   #2loop until ix = n.sub.-- lim.sub.-- minus.sub.-- 1end______________________________________