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SHell self-extracting ARchive  |  1991-03-29  |  54.9 KB

open in: MacOS 8.1     |     Win98     |     DOS

view JSON data     |     view as text

This file was processed as: SHell self-extracting ARchive (archive/shar).

You can browse this item here: 3147

ConfidenceProgramDetectionMatch TypeSupport
100% dexvert Newsgroup Content (archive/news) magic Supported
100% dexvert SHell self-extracting ARchive (archive/shar) magic Supported
100% dexvert Internet Message Format (text/imf) magic Supported
1% dexvert Text File (text/txt) fallback Supported
100% file news or mail, ASCII text default
100% TrID E-Mail message (Var. 2) default
100% perlTextCheck Likely Text (Perl) default
100% siegfried fmt/329 Shell Archive Format default
100% detectItEasy Format: plain text[LF] default (weak)
100% xdgMime message/rfc822 default



hex view
+--------+-------------------------+-------------------------+--------+--------+
|00000000| 46 72 6f 6d 3a 20 62 72 | 61 64 40 53 53 44 2e 43 |From: br|ad@SSD.C|
|00000010| 53 44 2e 48 41 52 52 49 | 53 2e 43 4f 4d 20 28 42 |SD.HARRI|S.COM (B|
|00000020| 72 61 64 20 41 70 70 6c | 65 74 6f 6e 29 0a 4e 65 |rad Appl|eton).Ne|
|00000030| 77 73 67 72 6f 75 70 73 | 3a 20 61 6c 74 2e 73 6f |wsgroups|: alt.so|
|00000040| 75 72 63 65 73 0a 53 75 | 62 6a 65 63 74 3a 20 41 |urces.Su|bject: A|
|00000050| 56 4c 20 74 72 65 65 20 | 6c 69 62 72 61 72 79 20 |VL tree |library |
|00000060| 28 70 61 72 74 20 31 20 | 6f 66 20 32 29 0a 4d 65 |(part 1 |of 2).Me|
|00000070| 73 73 61 67 65 2d 49 44 | 3a 20 3c 32 38 32 31 40 |ssage-ID|: <2821@|
|00000080| 74 72 61 76 69 73 2e 63 | 73 64 2e 68 61 72 72 69 |travis.c|sd.harri|
|00000090| 73 2e 63 6f 6d 3e 0a 44 | 61 74 65 3a 20 32 38 20 |s.com>.D|ate: 28 |
|000000a0| 4d 61 72 20 39 31 20 32 | 30 3a 33 38 3a 35 33 20 |Mar 91 2|0:38:53 |
|000000b0| 47 4d 54 0a 0a 54 68 69 | 73 20 69 73 20 61 20 42 |GMT..Thi|s is a B|
|000000c0| 65 74 61 20 72 65 6c 65 | 61 73 65 20 6f 66 20 70 |eta rele|ase of p|
|000000d0| 61 72 74 20 31 20 6f 66 | 20 61 6e 20 41 56 4c 20 |art 1 of| an AVL |
|000000e0| 74 72 65 65 20 6c 69 62 | 72 61 72 79 20 74 68 61 |tree lib|rary tha|
|000000f0| 74 20 49 20 68 61 76 65 | 20 62 65 65 6e 0a 75 73 |t I have| been.us|
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|00000120| 50 6c 65 61 73 65 20 72 | 65 70 6f 72 74 20 61 6e |Please r|eport an|
|00000130| 79 20 62 75 67 73 20 41 | 53 41 50 20 74 6f 20 6d |y bugs A|SAP to m|
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|00000150| 64 2e 68 61 72 72 69 73 | 2e 63 6f 6d 0a 0a 23 21 |d.harris|.com..#!|
|00000160| 20 2f 62 69 6e 2f 73 68 | 0a 23 20 54 68 69 73 20 | /bin/sh|.# This |
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|00000190| 68 69 6e 67 20 62 65 66 | 6f 72 65 20 74 68 69 73 |hing bef|ore this|
|000001a0| 20 6c 69 6e 65 2c 20 74 | 68 65 6e 20 75 6e 70 61 | line, t|hen unpa|
|000001b0| 63 6b 0a 23 20 69 74 20 | 62 79 20 73 61 76 69 6e |ck.# it |by savin|
|000001c0| 67 20 69 74 20 69 6e 74 | 6f 20 61 20 66 69 6c 65 |g it int|o a file|
|000001d0| 20 61 6e 64 20 74 79 70 | 69 6e 67 20 22 73 68 20 | and typ|ing "sh |
|000001e0| 66 69 6c 65 22 2e 20 20 | 54 6f 20 6f 76 65 72 77 |file". |To overw|
|000001f0| 72 69 74 65 20 65 78 69 | 73 74 69 6e 67 0a 23 20 |rite exi|sting.# |
|00000200| 66 69 6c 65 73 2c 20 74 | 79 70 65 20 22 73 68 20 |files, t|ype "sh |
|00000210| 66 69 6c 65 20 2d 63 22 | 2e 20 20 59 6f 75 20 63 |file -c"|. You c|
|00000220| 61 6e 20 61 6c 73 6f 20 | 66 65 65 64 20 74 68 69 |an also |feed thi|
|00000230| 73 20 61 73 20 73 74 61 | 6e 64 61 72 64 20 69 6e |s as sta|ndard in|
|00000240| 70 75 74 20 76 69 61 0a | 23 20 75 6e 73 68 61 72 |put via.|# unshar|
|00000250| 2c 20 6f 72 20 62 79 20 | 74 79 70 69 6e 67 20 22 |, or by |typing "|
|00000260| 73 68 20 3c 66 69 6c 65 | 22 2c 20 65 2e 67 2e 2e |sh <file|", e.g..|
|00000270| 20 20 49 66 20 74 68 69 | 73 20 61 72 63 68 69 76 | If thi|s archiv|
|00000280| 65 20 69 73 20 63 6f 6d | 70 6c 65 74 65 2c 20 79 |e is com|plete, y|
|00000290| 6f 75 0a 23 20 77 69 6c | 6c 20 73 65 65 20 74 68 |ou.# wil|l see th|
|000002a0| 65 20 66 6f 6c 6c 6f 77 | 69 6e 67 20 6d 65 73 73 |e follow|ing mess|
|000002b0| 61 67 65 20 61 74 20 74 | 68 65 20 65 6e 64 3a 0a |age at t|he end:.|
|000002c0| 23 09 09 22 45 6e 64 20 | 6f 66 20 61 72 63 68 69 |#.."End |of archi|
|000002d0| 76 65 20 31 20 28 6f 66 | 20 32 29 2e 22 0a 23 20 |ve 1 (of| 2).".# |
|000002e0| 43 6f 6e 74 65 6e 74 73 | 3a 20 20 4d 41 4e 49 46 |Contents|: MANIF|
|000002f0| 45 53 54 20 4d 61 6b 65 | 66 69 6c 65 20 52 45 41 |EST Make|file REA|
|00000300| 44 4d 45 20 61 76 6c 2e | 68 20 61 76 6c 5f 74 65 |DME avl.|h avl_te|
|00000310| 73 74 2e 63 20 61 76 6c | 5f 74 79 70 73 2e 68 0a |st.c avl|_typs.h.|
|00000320| 23 20 20 20 6b 65 79 5f | 67 65 6e 2e 63 20 72 6f |# key_|gen.c ro|
|00000330| 74 61 74 65 2e 6f 6c 64 | 20 74 65 73 74 76 61 6c |tate.old| testval|
|00000340| 73 2e 68 0a 23 20 57 72 | 61 70 70 65 64 20 62 79 |s.h.# Wr|apped by|
|00000350| 20 62 72 61 64 40 68 63 | 78 32 20 6f 6e 20 54 68 | brad@hc|x2 on Th|
|00000360| 75 20 4d 61 72 20 32 38 | 20 31 35 3a 33 32 3a 35 |u Mar 28| 15:32:5|
|00000370| 34 20 31 39 39 31 0a 50 | 41 54 48 3d 2f 62 69 6e |4 1991.P|ATH=/bin|
|00000380| 3a 2f 75 73 72 2f 62 69 | 6e 3a 2f 75 73 72 2f 75 |:/usr/bi|n:/usr/u|
|00000390| 63 62 20 3b 20 65 78 70 | 6f 72 74 20 50 41 54 48 |cb ; exp|ort PATH|
|000003a0| 0a 69 66 20 74 65 73 74 | 20 2d 66 20 27 4d 41 4e |.if test| -f 'MAN|
|000003b0| 49 46 45 53 54 27 20 2d | 61 20 22 24 7b 31 7d 22 |IFEST' -|a "${1}"|
|000003c0| 20 21 3d 20 22 2d 63 22 | 20 3b 20 74 68 65 6e 20 | != "-c"| ; then |
|000003d0| 0a 20 20 65 63 68 6f 20 | 73 68 61 72 3a 20 57 69 |. echo |shar: Wi|
|000003e0| 6c 6c 20 6e 6f 74 20 63 | 6c 6f 62 62 65 72 20 65 |ll not c|lobber e|
|000003f0| 78 69 73 74 69 6e 67 20 | 66 69 6c 65 20 5c 22 27 |xisting |file \"'|
|00000400| 4d 41 4e 49 46 45 53 54 | 27 5c 22 0a 65 6c 73 65 |MANIFEST|'\".else|
|00000410| 0a 65 63 68 6f 20 73 68 | 61 72 3a 20 45 78 74 72 |.echo sh|ar: Extr|
|00000420| 61 63 74 69 6e 67 20 5c | 22 27 4d 41 4e 49 46 45 |acting \|"'MANIFE|
|00000430| 53 54 27 5c 22 20 5c 28 | 38 39 32 20 63 68 61 72 |ST'\" \(|892 char|
|00000440| 61 63 74 65 72 73 5c 29 | 0a 73 65 64 20 22 73 2f |acters\)|.sed "s/|
|00000450| 5e 58 2f 2f 22 20 3e 27 | 4d 41 4e 49 46 45 53 54 |^X//" >'|MANIFEST|
|00000460| 27 20 3c 3c 27 45 4e 44 | 5f 4f 46 5f 46 49 4c 45 |' <<'END|_OF_FILE|
|00000470| 27 0a 58 20 20 20 46 69 | 6c 65 20 4e 61 6d 65 09 |'.X Fi|le Name.|
|00000480| 09 41 72 63 68 69 76 65 | 20 23 09 44 65 73 63 72 |.Archive| #.Descr|
|00000490| 69 70 74 69 6f 6e 0a 58 | 2d 2d 2d 2d 2d 2d 2d 2d |iption.X|--------|
|000004a0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|000004b0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|000004c0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|000004d0| 2d 2d 2d 0a 58 20 4c 49 | 43 45 4e 53 45 20 20 20 |---.X LI|CENSE |
|000004e0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000004f0| 20 32 09 50 65 72 6d 69 | 73 73 69 6f 6e 20 74 6f | 2.Permi|ssion to|
|00000500| 20 75 73 65 2f 63 6f 70 | 79 20 74 68 69 73 20 70 | use/cop|y this p|
|00000510| 61 63 6b 61 67 65 0a 58 | 20 4d 41 4e 49 46 45 53 |ackage.X| MANIFES|
|00000520| 54 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |T | |
|00000530| 20 20 20 20 31 09 54 68 | 69 73 20 66 69 6c 65 0a | 1.Th|is file.|
|00000540| 58 20 4d 61 6b 65 66 69 | 6c 65 20 20 20 20 20 20 |X Makefi|le |
|00000550| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 31 09 4d | | 1.M|
|00000560| 61 6b 65 66 69 6c 65 20 | 66 6f 72 20 74 68 65 20 |akefile |for the |
|00000570| 6c 69 62 72 61 72 79 0a | 58 20 52 45 41 44 4d 45 |library.|X README|
|00000580| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000590| 20 20 20 20 20 31 09 44 | 69 73 63 75 73 73 69 6f | 1.D|iscussio|
|000005a0| 6e 20 6f 66 20 61 6c 67 | 6f 72 69 74 68 6d 28 73 |n of alg|orithm(s|
|000005b0| 29 20 66 6f 72 20 41 56 | 4c 20 74 72 65 65 73 0a |) for AV|L trees.|
|000005c0| 58 20 61 76 6c 2e 33 20 | 20 20 20 20 20 20 20 20 |X avl.3 | |
|000005d0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 32 09 44 | | 2.D|
|000005e0| 6f 63 75 6d 65 6e 74 61 | 74 69 6f 6e 20 66 6f 72 |ocumenta|tion for|
|000005f0| 20 74 68 65 20 41 56 4c | 20 74 72 65 65 20 6c 69 | the AVL| tree li|
|00000600| 62 72 61 72 79 0a 58 20 | 61 76 6c 2e 63 20 20 20 |brary.X |avl.c |
|00000610| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000620| 20 20 20 32 09 53 6f 75 | 72 63 65 20 66 6f 72 20 | 2.Sou|rce for |
|00000630| 74 68 65 20 65 6e 74 69 | 72 65 20 41 56 4c 20 6c |the enti|re AVL l|
|00000640| 69 62 72 61 72 79 0a 58 | 20 61 76 6c 2e 68 20 20 |ibrary.X| avl.h |
|00000650| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000660| 20 20 20 20 31 09 49 6e | 63 6c 75 64 65 20 66 69 | 1.In|clude fi|
|00000670| 6c 65 20 66 6f 72 20 74 | 68 65 20 41 56 4c 20 74 |le for t|he AVL t|
|00000680| 72 65 65 20 6c 69 62 72 | 61 72 79 0a 58 20 61 76 |ree libr|ary.X av|
|00000690| 6c 5f 74 65 73 74 2e 63 | 20 20 20 20 20 20 20 20 |l_test.c| |
|000006a0| 20 20 20 20 20 20 20 20 | 20 31 09 54 68 65 20 74 | | 1.The t|
|000006b0| 65 73 74 20 70 72 6f 67 | 72 61 6d 0a 58 20 61 76 |est prog|ram.X av|
|000006c0| 6c 5f 74 79 70 73 2e 68 | 20 20 20 20 20 20 20 20 |l_typs.h| |
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|000007b0| 74 20 76 61 6c 75 65 73 | 20 66 6f 72 20 74 68 65 |t values| for the|
|000007c0| 20 74 65 73 74 20 70 72 | 6f 67 72 61 6d 0a 58 20 | test pr|ogram.X |
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|000007e0| 20 20 20 20 20 20 20 20 | 20 20 20 32 09 4f 6c 64 | | 2.Old|
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|00000800| 5f 4f 46 5f 46 49 4c 45 | 0a 69 66 20 74 65 73 74 |_OF_FILE|.if test|
|00000810| 20 38 39 32 20 2d 6e 65 | 20 60 77 63 20 2d 63 20 | 892 -ne| `wc -c |
|00000820| 3c 27 4d 41 4e 49 46 45 | 53 54 27 60 3b 20 74 68 |<'MANIFE|ST'`; th|
|00000830| 65 6e 0a 20 20 20 20 65 | 63 68 6f 20 73 68 61 72 |en. e|cho shar|
|00000840| 3a 20 5c 22 27 4d 41 4e | 49 46 45 53 54 27 5c 22 |: \"'MAN|IFEST'\"|
|00000850| 20 75 6e 70 61 63 6b 65 | 64 20 77 69 74 68 20 77 | unpacke|d with w|
|00000860| 72 6f 6e 67 20 73 69 7a | 65 21 0a 66 69 0a 23 20 |rong siz|e!.fi.# |
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|00000880| 27 0a 66 69 0a 69 66 20 | 74 65 73 74 20 2d 66 20 |'.fi.if |test -f |
|00000890| 27 4d 61 6b 65 66 69 6c | 65 27 20 2d 61 20 22 24 |'Makefil|e' -a "$|
|000008a0| 7b 31 7d 22 20 21 3d 20 | 22 2d 63 22 20 3b 20 74 |{1}" != |"-c" ; t|
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|000008c0| 3a 20 57 69 6c 6c 20 6e | 6f 74 20 63 6c 6f 62 62 |: Will n|ot clobb|
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|000008e0| 20 5c 22 27 4d 61 6b 65 | 66 69 6c 65 27 5c 22 0a | \"'Make|file'\".|
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|000009d0| 54 3d 09 2d 4f 0a 58 50 | 52 49 4e 54 3d 09 70 72 |T=.-O.XP|RINT=.pr|
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|00000a20| 24 28 4f 50 54 29 20 24 | 28 44 45 46 53 29 0a 58 |$(OPT) $|(DEFS).X|
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|00000a80| 0a 58 09 61 72 20 63 72 | 75 20 24 28 4c 49 42 52 |.X.ar cr|u $(LIBR|
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|00000aa0| 6c 69 62 20 24 28 4c 49 | 42 52 41 52 59 29 0a 58 |lib $(LI|BRARY).X|
|00000ab0| 0a 58 24 28 54 45 53 54 | 29 3a 20 24 28 4f 42 4a |.X$(TEST|): $(OBJ|
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|00000ad0| 41 47 53 29 20 2d 6f 20 | 24 28 54 45 53 54 29 20 |AGS) -o |$(TEST) |
|00000ae0| 24 28 4f 42 4a 53 29 0a | 58 0a 58 63 6c 65 61 6e |$(OBJS).|X.Xclean|
|00000af0| 3a 0a 58 09 24 28 44 45 | 4c 29 20 24 28 4f 42 4a |:.X.$(DE|L) $(OBJ|
|00000b00| 53 29 0a 58 0a 58 63 6c | 6f 62 62 65 72 3a 20 63 |S).X.Xcl|obber: c|
|00000b10| 6c 65 61 6e 0a 58 09 24 | 28 44 45 4c 29 20 24 28 |lean.X.$|(DEL) $(|
|00000b20| 4c 49 42 52 41 52 59 29 | 20 24 28 54 45 53 54 29 |LIBRARY)| $(TEST)|
|00000b30| 0a 58 09 0a 58 69 6e 64 | 65 78 3a 0a 58 09 63 74 |.X..Xind|ex:.X.ct|
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|00000b50| 24 28 53 52 43 53 29 0a | 58 0a 58 70 72 69 6e 74 |$(SRCS).|X.Xprint|
|00000b60| 3a 0a 58 09 24 28 50 52 | 49 4e 54 29 20 24 28 48 |:.X.$(PR|INT) $(H|
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|00000b80| 74 61 67 73 3a 20 24 28 | 48 44 52 53 29 20 24 28 |tags: $(|HDRS) $(|
|00000b90| 53 52 43 53 29 0a 58 09 | 20 63 74 61 67 73 20 24 |SRCS).X.| ctags $|
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|00000bb0| 0a 58 23 23 23 0a 58 61 | 76 6c 2e 6f 3a 20 61 76 |.X###.Xa|vl.o: av|
|00000bc0| 6c 2e 68 20 61 76 6c 5f | 74 79 70 73 2e 68 0a 58 |l.h avl_|typs.h.X|
|00000bd0| 61 76 6c 5f 74 65 73 74 | 2e 6f 3a 20 61 76 6c 2e |avl_test|.o: avl.|
|00000be0| 68 20 74 65 73 74 76 61 | 6c 73 2e 68 0a 45 4e 44 |h testva|ls.h.END|
|00000bf0| 5f 4f 46 5f 46 49 4c 45 | 0a 69 66 20 74 65 73 74 |_OF_FILE|.if test|
|00000c00| 20 36 31 38 20 2d 6e 65 | 20 60 77 63 20 2d 63 20 | 618 -ne| `wc -c |
|00000c10| 3c 27 4d 61 6b 65 66 69 | 6c 65 27 60 3b 20 74 68 |<'Makefi|le'`; th|
|00000c20| 65 6e 0a 20 20 20 20 65 | 63 68 6f 20 73 68 61 72 |en. e|cho shar|
|00000c30| 3a 20 5c 22 27 4d 61 6b | 65 66 69 6c 65 27 5c 22 |: \"'Mak|efile'\"|
|00000c40| 20 75 6e 70 61 63 6b 65 | 64 20 77 69 74 68 20 77 | unpacke|d with w|
|00000c50| 72 6f 6e 67 20 73 69 7a | 65 21 0a 66 69 0a 23 20 |rong siz|e!.fi.# |
|00000c60| 65 6e 64 20 6f 66 20 27 | 4d 61 6b 65 66 69 6c 65 |end of '|Makefile|
|00000c70| 27 0a 66 69 0a 69 66 20 | 74 65 73 74 20 2d 66 20 |'.fi.if |test -f |
|00000c80| 27 52 45 41 44 4d 45 27 | 20 2d 61 20 22 24 7b 31 |'README'| -a "${1|
|00000c90| 7d 22 20 21 3d 20 22 2d | 63 22 20 3b 20 74 68 65 |}" != "-|c" ; the|
|00000ca0| 6e 20 0a 20 20 65 63 68 | 6f 20 73 68 61 72 3a 20 |n . ech|o shar: |
|00000cb0| 57 69 6c 6c 20 6e 6f 74 | 20 63 6c 6f 62 62 65 72 |Will not| clobber|
|00000cc0| 20 65 78 69 73 74 69 6e | 67 20 66 69 6c 65 20 5c | existin|g file \|
|00000cd0| 22 27 52 45 41 44 4d 45 | 27 5c 22 0a 65 6c 73 65 |"'README|'\".else|
|00000ce0| 0a 65 63 68 6f 20 73 68 | 61 72 3a 20 45 78 74 72 |.echo sh|ar: Extr|
|00000cf0| 61 63 74 69 6e 67 20 5c | 22 27 52 45 41 44 4d 45 |acting \|"'README|
|00000d00| 27 5c 22 20 5c 28 33 37 | 37 37 32 20 63 68 61 72 |'\" \(37|772 char|
|00000d10| 61 63 74 65 72 73 5c 29 | 0a 73 65 64 20 22 73 2f |acters\)|.sed "s/|
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|00001b30| 20 20 20 20 20 4e 65 77 | 42 61 6c 28 42 29 20 3d | New|Bal(B) =|
|00001b40| 20 68 74 28 63 29 20 2d | 20 68 74 28 41 29 0a 58 | ht(c) -| ht(A).X|
|00001b50| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001b60| 20 20 3d 20 68 74 28 63 | 29 20 2d 20 28 31 20 2b | = ht(c|) - (1 +|
|00001b70| 20 6d 61 78 28 68 74 28 | 61 29 2c 20 68 74 28 62 | max(ht(|a), ht(b|
|00001b80| 29 29 20 29 0a 58 0a 58 | 20 20 20 20 20 20 20 20 |)) ).X.X| |
|00001b90| 4f 6c 64 42 61 6c 28 42 | 29 20 3d 20 68 74 28 63 |OldBal(B|) = ht(c|
|00001ba0| 29 20 2d 20 68 74 28 62 | 29 0a 58 0a 58 0a 58 73 |) - ht(b|).X.X.Xs|
|00001bb0| 75 62 74 72 61 63 74 69 | 6e 67 20 74 68 65 20 73 |ubtracti|ng the s|
|00001bc0| 65 63 6f 6e 64 20 65 71 | 75 61 74 69 6f 6e 20 66 |econd eq|uation f|
|00001bd0| 72 6f 6d 20 74 68 65 20 | 66 69 72 73 74 20 79 69 |rom the |first yi|
|00001be0| 65 6c 64 73 3a 0a 58 0a | 58 0a 58 20 20 20 20 20 |elds:.X.|X.X |
|00001bf0| 20 20 20 4e 65 77 42 61 | 6c 28 42 29 20 2d 20 4f | NewBa|l(B) - O|
|00001c00| 6c 64 42 61 6c 28 42 29 | 20 3d 20 68 74 28 63 29 |ldBal(B)| = ht(c)|
|00001c10| 20 2d 20 68 74 28 63 29 | 0a 58 20 20 20 20 20 20 | - ht(c)|.X |
|00001c20| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001c30| 20 20 20 20 20 20 20 20 | 20 20 2b 20 68 74 28 62 | | + ht(b|
|00001c40| 29 20 2d 20 28 31 20 2b | 20 6d 61 78 28 68 74 28 |) - (1 +| max(ht(|
|00001c50| 61 29 2c 20 68 74 28 62 | 29 29 20 29 0a 58 0a 58 |a), ht(b|)) ).X.X|
|00001c60| 0a 58 63 61 6e 63 65 6c | 69 6e 67 2c 20 61 6e 64 |.Xcancel|ing, and|
|00001c70| 20 61 64 64 69 6e 67 20 | 4f 6c 64 42 61 6c 28 42 | adding |OldBal(B|
|00001c80| 29 20 74 6f 20 62 6f 74 | 68 20 73 69 64 65 73 20 |) to bot|h sides |
|00001c90| 67 69 76 65 73 3a 0a 58 | 0a 58 0a 58 20 20 20 20 |gives:.X|.X.X |
|00001ca0| 20 20 20 20 4e 65 77 42 | 61 6c 28 42 29 20 3d 20 | NewB|al(B) = |
|00001cb0| 4f 6c 64 42 61 6c 28 42 | 29 20 2d 20 31 20 2d 20 |OldBal(B|) - 1 - |
|00001cc0| 28 6d 61 78 28 68 74 28 | 61 29 2c 20 68 74 28 62 |(max(ht(|a), ht(b|
|00001cd0| 29 29 20 2d 20 68 74 28 | 62 29 29 0a 58 20 20 20 |)) - ht(|b)).X |
|00001ce0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 3d | | =|
|00001cf0| 20 4f 6c 64 42 61 6c 28 | 42 29 20 2d 20 31 20 2d | OldBal(|B) - 1 -|
|00001d00| 20 28 6d 61 78 28 68 74 | 28 61 29 20 2d 20 68 74 | (max(ht|(a) - ht|
|00001d10| 28 62 29 2c 20 68 74 28 | 62 29 20 2d 20 68 74 28 |(b), ht(|b) - ht(|
|00001d20| 62 29 29 0a 58 0a 58 0a | 58 42 75 74 20 20 68 74 |b)).X.X.|XBut ht|
|00001d30| 28 61 29 20 2d 20 68 74 | 28 62 29 20 20 69 73 20 |(a) - ht|(b) is |
|00001d40| 20 2d 20 28 68 74 28 62 | 29 20 2d 20 68 74 28 61 | - (ht(b|) - ht(a|
|00001d50| 29 29 20 20 3d 20 20 2d | 4e 65 77 42 61 6c 28 41 |)) = -|NewBal(A|
|00001d60| 29 2c 20 73 6f 20 2e 2e | 2e 0a 58 0a 58 0a 58 20 |), so ..|..X.X.X |
|00001d70| 20 20 20 20 20 20 20 4e | 65 77 42 61 6c 28 42 29 | N|ewBal(B)|
|00001d80| 20 3d 20 4f 6c 64 42 61 | 6c 28 42 29 20 2d 20 31 | = OldBa|l(B) - 1|
|00001d90| 20 2d 20 6d 61 78 28 20 | 2d 4e 65 77 42 61 6c 28 | - max( |-NewBal(|
|00001da0| 41 29 2c 20 30 29 0a 58 | 0a 58 0a 58 55 73 69 6e |A), 0).X|.X.XUsin|
|00001db0| 67 20 74 68 65 20 66 61 | 63 74 20 74 68 61 74 20 |g the fa|ct that |
|00001dc0| 20 6d 69 6e 28 78 2c 79 | 29 20 3d 20 2d 6d 61 78 | min(x,y|) = -max|
|00001dd0| 28 2d 78 2c 20 2d 79 29 | 20 77 65 20 67 65 74 3a |(-x, -y)| we get:|
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|00001df0| 77 42 61 6c 28 42 29 20 | 3d 20 4f 6c 64 42 61 6c |wBal(B) |= OldBal|
|00001e00| 28 42 29 20 2d 20 31 20 | 2b 20 6d 69 6e 28 20 4e |(B) - 1 |+ min( N|
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|00001e20| 0a 58 53 6f 2c 20 66 6f | 72 20 61 20 73 69 6e 67 |.XSo, fo|r a sing|
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|00001e40| 20 77 65 20 68 61 76 65 | 20 73 68 6f 77 6e 20 74 | we have| shown t|
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|00001e70| 65 73 20 41 20 61 6e 64 | 20 42 20 61 72 65 20 67 |es A and| B are g|
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|00001e90| 6f 77 69 6e 67 20 65 71 | 75 61 74 69 6f 6e 73 3a |owing eq|uations:|
|00001ea0| 0a 58 0a 58 20 20 20 20 | 20 20 20 20 4e 65 77 42 |.X.X | NewB|
|00001eb0| 61 6c 28 41 29 20 3d 20 | 4f 6c 64 42 61 6c 28 41 |al(A) = |OldBal(A|
|00001ec0| 29 20 2d 20 31 20 2d 20 | 6d 61 78 28 4f 6c 64 42 |) - 1 - |max(OldB|
|00001ed0| 61 6c 28 42 29 2c 20 30 | 29 0a 58 20 20 20 20 20 |al(B), 0|).X |
|00001ee0| 20 20 20 4e 65 77 42 61 | 6c 28 42 29 20 3d 20 4f | NewBa|l(B) = O|
|00001ef0| 6c 64 42 61 6c 28 42 29 | 20 2d 20 31 20 2b 20 6d |ldBal(B)| - 1 + m|
|00001f00| 69 6e 28 4e 65 77 42 61 | 6c 28 41 29 2c 20 30 29 |in(NewBa|l(A), 0)|
|00001f10| 0a 58 0a 58 4e 6f 77 20 | 6c 65 74 20 75 73 20 6c |.X.XNow |let us l|
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|00002020| 0a 58 0a 58 20 20 20 20 | 20 20 20 20 20 20 20 20 |.X.X | |
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|00002040| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002050| 20 20 20 20 20 20 20 20 | 20 20 20 20 42 0a 58 20 | | B.X |
|00002060| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002070| 2f 20 5c 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |/ \ | |
|00002080| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002090| 20 20 20 20 20 20 2f 20 | 5c 0a 58 20 20 20 20 20 | / |\.X |
|000020a0| 20 20 20 20 20 20 20 20 | 20 20 20 2f 20 20 20 5c | | / \|
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|00002160| 20 20 2f 20 20 20 5c 20 | 20 20 20 20 20 20 20 20 | / \ | |
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|00002190| 20 20 5c 0a 58 20 20 20 | 20 20 20 20 20 20 20 20 | \.X | |
|000021a0| 20 63 20 20 20 20 20 62 | 20 20 20 20 20 20 20 20 | c b| |
|000021b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
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|000044c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 62 20 20 | | b |
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|00004510| 3d 3d 3d 3d 3d 3d 3d 3d | 3d 3d 3d 3d 3d 3d 3d 3d |========|========|
|00004520| 3d 3d 3d 3d 3d 3d 3d 3d | 3d 3d 3d 3d 3d 3d 3d 3d |========|========|
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|000045d0| 20 20 20 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d | -----|--------|
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|00004680| 3d 3d 3d 3d 3d 3d 3d 3d | 3d 3d 3d 3d 3d 3d 3d 3d |========|========|
|00004690| 3d 3d 3d 3d 3d 3d 3d 3d | 3d 3d 3d 3d 3d 3d 3d 3d |========|========|
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|000047c0| 3d 3d 3d 3d 3d 3d 3d 3d | 3d 3d 3d 3d 3d 3d 3d 3d |========|========|
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|00005280| 3d 3d 3d 3d 3d 3d 3d 3d | 3d 3d 3d 3d 3d 3d 3d 3d |========|========|
|00005290| 3d 3d 3d 3d 3d 3d 3d 3d | 3d 3d 3d 3d 3d 3d 3d 3d |========|========|
|000052a0| 3d 3d 3d 3d 3d 3d 3d 3d | 3d 3d 3d 3d 3d 3d 3d 0a |========|=======.|
|000052b0| 58 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |X | |
|000052c0| 20 20 20 20 20 20 20 20 | 20 20 42 41 4c 41 4e 43 | | BALANC|
|000052d0| 45 20 46 41 43 54 4f 52 | 53 0a 58 20 20 20 20 42 |E FACTOR|S.X B|
|000052e0| 45 46 4f 52 45 20 52 4f | 54 41 54 49 4f 4e 20 20 |EFORE RO|TATION |
|000052f0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00005300| 20 20 20 20 20 20 20 20 | 20 20 20 20 41 46 54 45 | | AFTE|
|00005310| 52 20 52 4f 54 41 54 49 | 4f 4e 0a 58 2d 2d 2d 2d |R ROTATI|ON.X----|
|00005320| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00005330| 2d 2d 2d 2d 20 20 20 20 | 20 20 20 20 20 20 20 20 |---- | |
|00005340| 20 20 20 20 20 20 20 20 | 2d 2d 2d 2d 2d 2d 2d 2d | |--------|
|00005350| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 0a |--------|-------.|
|00005360| 58 41 20 3d 20 2b 32 20 | 3b 20 43 20 3d 20 2d 31 |XA = +2 |; C = -1|
|00005370| 20 3b 20 42 20 3d 20 2b | 31 20 20 20 20 20 20 20 | ; B = +|1 |
|00005380| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 41 20 3d | | A =|
|00005390| 20 2d 31 20 3b 20 42 20 | 3d 20 30 20 3b 20 43 20 | -1 ; B |= 0 ; C |
|000053a0| 3d 20 30 0a 58 41 20 3d | 20 2b 32 20 3b 20 43 20 |= 0.XA =| +2 ; C |
|000053b0| 3d 20 2d 31 20 3b 20 42 | 20 3d 20 20 30 20 20 20 |= -1 ; B| = 0 |
|000053c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000053d0| 20 41 20 3d 20 20 30 20 | 3b 20 42 20 3d 20 30 20 | A = 0 |; B = 0 |
|000053e0| 3b 20 43 20 3d 20 30 0a | 58 41 20 3d 20 2b 32 20 |; C = 0.|XA = +2 |
|000053f0| 3b 20 43 20 3d 20 2d 31 | 20 3b 20 42 20 3d 20 2d |; C = -1| ; B = -|
|00005400| 31 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |1 | |
|00005410| 20 20 20 20 20 41 20 3d | 20 20 30 20 3b 20 42 20 | A =| 0 ; B |
|00005420| 3d 20 30 20 3b 20 43 20 | 3d 2b 31 0a 58 3d 3d 3d |= 0 ; C |=+1.X===|
|00005430| 3d 3d 3d 3d 3d 3d 3d 3d | 3d 3d 3d 3d 3d 3d 3d 3d |========|========|
|00005440| 3d 3d 3d 3d 3d 3d 3d 3d | 3d 3d 3d 3d 3d 3d 3d 3d |========|========|
|00005450| 3d 3d 3d 3d 3d 3d 3d 3d | 3d 3d 3d 3d 3d 3d 3d 3d |========|========|
|00005460| 3d 3d 3d 3d 3d 3d 3d 3d | 3d 3d 3d 0a 58 0a 58 53 |========|===.X.XS|
|00005470| 6f 20 77 65 20 67 65 74 | 2c 20 69 6e 20 61 6c 6c |o we get|, in all|
|00005480| 20 74 68 72 65 65 20 63 | 61 73 65 73 3a 0a 58 0a | three c|ases:.X.|
|00005490| 58 20 20 20 20 20 20 20 | 20 20 20 6e 65 77 41 20 |X | newA |
|000054a0| 3d 20 2d 6d 61 78 28 20 | 6f 6c 64 42 2c 20 30 20 |= -max( |oldB, 0 |
|000054b0| 29 0a 58 20 20 20 20 20 | 20 20 20 20 20 6e 65 77 |).X | new|
|000054c0| 43 20 3d 20 2d 6d 69 6e | 28 20 6f 6c 64 42 2c 20 |C = -min|( oldB, |
|000054d0| 30 20 29 0a 58 20 20 20 | 20 20 20 20 20 20 20 6e |0 ).X | n|
|000054e0| 65 77 42 20 3d 20 30 0a | 58 0a 58 4e 6f 77 20 66 |ewB = 0.|X.XNow f|
|000054f0| 6f 72 20 61 20 64 6f 75 | 62 6c 65 20 52 4c 20 72 |or a dou|ble RL r|
|00005500| 6f 74 61 74 69 6f 6e 20 | 77 65 20 68 61 76 65 20 |otation |we have |
|00005510| 74 68 65 20 66 6f 6c 6c | 6f 77 69 6e 67 20 70 6f |the foll|owing po|
|00005520| 73 73 69 62 69 6c 69 74 | 69 65 73 20 28 61 67 61 |ssibilit|ies (aga|
|00005530| 69 6e 2c 20 74 68 65 0a | 58 70 69 63 74 75 72 65 |in, the.|Xpicture|
|00005540| 20 69 73 20 74 68 65 20 | 6d 69 72 72 6f 72 20 69 | is the |mirror i|
|00005550| 6d 61 67 65 20 6f 66 20 | 74 68 65 20 4c 52 20 63 |mage of |the LR c|
|00005560| 61 73 65 29 3a 0a 58 0a | 58 3d 3d 3d 3d 3d 3d 3d |ase):.X.|X=======|
|00005570| 3d 3d 3d 3d 3d 3d 3d 3d | 3d 3d 3d 3d 3d 3d 3d 3d |========|========|
|00005580| 3d 3d 3d 3d 3d 3d 3d 3d | 3d 3d 3d 3d 3d 3d 3d 3d |========|========|
|00005590| 3d 3d 3d 3d 3d 3d 3d 3d | 3d 3d 3d 3d 3d 3d 3d 3d |========|========|
|000055a0| 3d 3d 3d 3d 3d 3d 3d 0a | 58 20 20 20 20 20 20 20 |=======.|X |
|000055b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000055c0| 20 20 42 41 4c 41 4e 43 | 45 20 46 41 43 54 4f 52 | BALANC|E FACTOR|
|000055d0| 53 0a 58 20 20 20 20 42 | 45 46 4f 52 45 20 52 4f |S.X B|EFORE RO|
|000055e0| 54 41 54 49 4f 4e 20 20 | 20 20 20 20 20 20 20 20 |TATION | |
|000055f0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00005600| 20 20 20 20 41 46 54 45 | 52 20 52 4f 54 41 54 49 | AFTE|R ROTATI|
|00005610| 4f 4e 0a 58 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |ON.X----|--------|
|00005620| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 20 20 20 20 |--------|---- |
|00005630| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00005640| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00005650| 2d 2d 2d 2d 2d 2d 2d 0a | 58 41 20 3d 20 2d 32 20 |-------.|XA = -2 |
|00005660| 3b 20 43 20 3d 20 2b 31 | 20 3b 20 42 20 3d 20 2b |; C = +1| ; B = +|
|00005670| 31 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |1 | |
|00005680| 20 20 20 20 20 41 20 3d | 20 2d 31 20 3b 20 42 20 | A =| -1 ; B |
|00005690| 3d 20 30 20 3b 20 43 20 | 3d 20 30 0a 58 41 20 3d |= 0 ; C |= 0.XA =|
|000056a0| 20 2d 32 20 3b 20 43 20 | 3d 20 2b 31 20 3b 20 42 | -2 ; C |= +1 ; B|
|000056b0| 20 3d 20 20 30 20 20 20 | 20 20 20 20 20 20 20 20 | = 0 | |
|000056c0| 20 20 20 20 20 20 20 20 | 20 41 20 3d 20 20 30 20 | | A = 0 |
|000056d0| 3b 20 42 20 3d 20 30 20 | 3b 20 43 20 3d 20 30 0a |; B = 0 |; C = 0.|
|000056e0| 58 41 20 3d 20 2d 32 20 | 3b 20 43 20 3d 20 2b 31 |XA = -2 |; C = +1|
|000056f0| 20 3b 20 42 20 3d 20 2d | 31 20 20 20 20 20 20 20 | ; B = -|1 |
|00005700| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 41 20 3d | | A =|
|00005710| 20 20 30 20 3b 20 42 20 | 3d 20 30 20 3b 20 43 20 | 0 ; B |= 0 ; C |
|00005720| 3d 2b 31 0a 58 3d 3d 3d | 3d 3d 3d 3d 3d 3d 3d 3d |=+1.X===|========|
|00005730| 3d 3d 3d 3d 3d 3d 3d 3d | 3d 3d 3d 3d 3d 3d 3d 3d |========|========|
|00005740| 3d 3d 3d 3d 3d 3d 3d 3d | 3d 3d 3d 3d 3d 3d 3d 3d |========|========|
|00005750| 3d 3d 3d 3d 3d 3d 3d 3d | 3d 3d 3d 3d 3d 3d 3d 3d |========|========|
|00005760| 3d 3d 3d 0a 58 0a 58 53 | 6f 20 77 65 20 67 65 74 |===.X.XS|o we get|
|00005770| 2c 20 69 6e 20 61 6c 6c | 20 74 68 72 65 65 20 63 |, in all| three c|
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|000057b0| 20 20 20 20 20 6e 65 77 | 43 20 3d 20 2d 6d 69 6e | new|C = -min|
|000057c0| 28 20 6f 6c 64 42 2c 20 | 30 20 29 0a 58 20 20 20 |( oldB, |0 ).X |
|000057d0| 20 20 20 20 20 20 20 6e | 65 77 42 20 3d 20 30 0a | n|ewB = 0.|
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|00006280| 20 2a 2f 0a 58 20 20 20 | 20 20 20 20 20 20 20 20 | */.X | |
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|000062c0| 20 20 7d 2f 2a 20 69 66 | 20 2a 2f 0a 58 20 20 0a | }/* if| */.X .|
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|00006390| 20 64 6f 75 62 6c 65 20 | 4c 52 20 72 6f 74 61 74 | double |LR rotat|
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|000063b0| 58 20 20 20 20 20 20 20 | 20 65 6c 73 65 09 2f 2a |X | else./*|
|000063c0| 20 73 69 6e 67 6c 65 20 | 4c 4c 20 72 6f 74 61 74 | single |LL rotat|
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|000063e0| 20 20 20 20 20 20 20 20 | 20 20 20 73 70 65 63 69 | | speci|
|000063f0| 61 6c 5f 63 61 73 65 20 | 3d 20 72 6f 74 61 74 65 |al_case |= rotate|
+--------+-------------------------+-------------------------+--------+--------+
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