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1160 24 e8 52 05 00 00 83 fe 01 74 15 8b 43 0c 31 d2 8b 28 89 38 89 d8 e8 f5 fd ff ff 83 f8 ff 74 10 $.R......t..C.1..(.8..........t.
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11e0 04 24 e8 f9 04 00 00 eb 97 8d b4 26 00 00 00 00 55 57 56 53 83 ec 2c 8d 44 24 18 c7 44 24 04 d8 .$.........&....UWVS..,.D$..D$..
1200 60 30 70 89 44 24 0c 8d 44 24 1c 89 44 24 08 8b 44 24 44 89 04 24 e8 dd 04 00 00 85 c0 0f 84 dd `0p.D$..D$..D$..D$D..$..........
1220 00 00 00 8b 44 24 18 89 04 24 e8 71 04 00 00 85 c0 89 c5 0f 84 c7 00 00 00 c7 04 24 00 00 00 00 ....D$...$.q...............$....
1240 e8 83 04 00 00 85 c0 89 c7 0f 84 a1 00 00 00 8b 44 24 1c 85 c0 7e 5a 31 f6 eb 10 90 8d 74 26 00 ................D$...~Z1.....t&.
1260 8b 44 24 1c 83 c6 01 39 f0 7e 46 89 2c 24 e8 65 04 00 00 85 c0 89 c3 0f 84 93 00 00 00 89 44 24 .D$....9.~F.,$.e..............D$
1280 04 89 3c 24 e8 47 04 00 00 83 f8 ff 8b 03 0f 84 a1 00 00 00 83 e8 01 85 c0 89 03 75 c3 8b 43 04 ..<$.G.....................u..C.
12a0 89 1c 24 83 c6 01 ff 50 18 8b 44 24 1c 39 f0 7f ba 8b 57 08 85 d2 0f 85 94 00 00 00 89 3c 24 e8 ..$....P..D$.9....W..........<$.
12c0 ec 03 00 00 83 f8 ff 74 50 89 3c 24 e8 ef 03 00 00 83 f8 ff 74 43 83 6d 00 01 75 26 8b 45 04 89 .......tP.<$........tC.m..u&.E..
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1300 31 ff 83 c4 2c 89 f8 5b 5e 5f 5d c3 8d 74 26 00 e8 d3 03 00 00 85 c0 74 a3 83 6d 00 01 0f 84 cd 1...,..[^_]..t&........t..m.....
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1360 89 da 89 f8 e8 07 fc ff ff 83 f8 ff 74 ab 83 eb 01 83 fb ff 75 ea 8d 76 00 8d bc 27 00 00 00 00 ............t.......u..v...'....
1380 8b 47 0c 8b 30 89 2c 24 e8 4b 03 00 00 85 c0 89 c3 0f 84 79 ff ff ff 89 c2 89 f0 e8 d0 f5 ff ff .G..0.,$.K.........y............
13a0 83 f8 ff 74 8e 85 c0 75 17 83 2b 01 75 d7 8b 43 04 89 1c 24 ff 50 18 eb cc 8d b4 26 00 00 00 00 ...t...u..+.u..C...$.P.....&....
13c0 8b 47 0c 8b 10 89 18 83 2a 01 74 14 31 d2 89 f8 e8 9b fb ff ff 83 f8 ff 75 a6 e9 3a ff ff ff 90 .G......*.t.1...........u..:....
13e0 8b 42 04 89 14 24 ff 50 18 eb e1 90 8d 74 26 00 8b 45 04 89 2c 24 ff 50 18 e9 25 ff ff ff 66 90 .B...$.P.....t&..E..,$.P..%...f.
1400 53 83 ec 38 8d 44 24 2c c7 44 24 0c 02 00 00 00 c7 44 24 08 02 00 00 00 c7 44 24 04 e4 60 30 70 S..8.D$,.D$......D$......D$..`0p
1420 89 44 24 14 8d 44 24 28 89 44 24 10 8b 44 24 44 89 04 24 e8 b8 02 00 00 85 c0 74 68 8b 44 24 28 .D$..D$(.D$..D$D..$.......th.D$(
1440 8b 50 04 f6 42 57 02 0f 84 83 00 00 00 8b 48 08 85 c9 7e 5c 8b 40 0c 8b 54 24 2c 8b 00 e8 0e f5 .P..BW........H...~\.@..T$,.....
1460 ff ff 83 f8 ff 74 3d 85 c0 74 45 8b 44 24 28 8b 50 08 85 d2 74 7a 8b 40 0c 8b 18 8b 44 24 2c 83 .....t=..tE.D$(.P...tz.@....D$,.
1480 00 01 8b 44 24 28 8b 54 24 2c 8b 40 0c 89 10 8b 44 24 28 31 d2 e8 d6 fa ff ff 83 f8 ff 75 1c 83 ...D$(.T$,.@....D$(1.........u..
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14e0 04 24 e8 f9 01 00 00 eb d2 8d b4 26 00 00 00 00 a1 70 a1 30 70 c7 44 24 04 6b 60 30 70 31 db 89 .$.........&.....p.0p.D$.k`0p1..
1500 04 24 e8 d9 01 00 00 eb b2 8d b4 26 00 00 00 00 56 53 83 ec 14 8b 74 24 24 8b 46 04 f6 40 57 02 .$.........&....VS....t$$.F..@W.
1520 74 43 8b 46 08 89 c3 c1 eb 1f 01 c3 d1 fb 83 eb 01 79 0a eb 1e 83 eb 01 83 fb ff 74 16 89 da 89 tC.F.............y.........t....
1540 f0 e8 2a fa ff ff 83 f8 ff 75 ea 31 c0 83 c4 14 5b 5e c3 83 05 ac a1 30 70 01 83 c4 14 b8 ac a1 ..*......u.1....[^.....0p.......
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15a0 44 24 14 8d 44 24 28 89 44 24 10 8b 44 24 44 89 04 24 e8 39 01 00 00 85 c0 74 5d 8b 44 24 28 8b D$..D$(.D$..D$D..$.9.....t].D$(.
15c0 50 04 f6 42 57 02 74 3b 8b 54 24 2c 89 04 24 89 54 24 04 e8 f8 00 00 00 83 f8 ff 74 3b 8b 44 24 P..BW.t;.T$,..$.T$.........t;.D$
15e0 28 31 d2 8b 48 08 83 e9 01 e8 b2 f8 ff ff 83 f8 ff 74 25 83 05 ac a1 30 70 01 b8 ac a1 30 70 83 (1..H............t%....0p....0p.
1600 c4 3c c3 a1 78 a1 30 70 c7 44 24 04 bb 60 30 70 89 04 24 e8 c8 00 00 00 31 c0 83 c4 3c c3 66 90 .<..x.0p.D$..`0p..$.....1...<.f.
1620 53 83 ec 28 c7 44 24 10 f5 03 00 00 c7 44 24 0c 00 00 00 00 c7 44 24 08 a0 52 30 70 c7 44 24 04 S..(.D$......D$......D$..R0p.D$.
1640 a0 57 30 70 c7 04 24 f9 60 30 70 e8 30 00 00 00 85 c0 74 22 89 c3 c7 04 24 20 40 30 70 e8 26 00 .W0p..$.`0p.0.....t"....$.@0p.&.
1660 00 00 c7 44 24 04 00 61 30 70 89 44 24 08 89 1c 24 e8 32 00 00 00 83 c4 28 5b c3 90 90 90 90 90 ...D$..a0p.D$...$.2.....([......
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16a0 ff 25 98 a1 30 70 90 90 ff 25 94 a1 30 70 90 90 ff 25 90 a1 30 70 90 90 ff 25 8c a1 30 70 90 90 .%..0p...%..0p...%..0p...%..0p..
16c0 ff 25 88 a1 30 70 90 90 ff 25 84 a1 30 70 90 90 ff 25 80 a1 30 70 90 90 ff 25 7c a1 30 70 90 90 .%..0p...%..0p...%..0p...%|.0p..
16e0 ff 25 6c a1 30 70 90 90 ff 25 68 a1 30 70 90 90 ff 25 64 a1 30 70 90 90 ff 25 60 a1 30 70 90 90 .%l.0p...%h.0p...%d.0p...%`.0p..
1700 53 83 ec 28 a1 cc 83 30 70 89 04 24 e8 8f 03 00 00 83 f8 ff 89 44 24 18 0f 84 82 00 00 00 c7 04 S..(...0p..$.........D$.........
1720 24 08 00 00 00 e8 be 0e 00 00 a1 cc 83 30 70 89 04 24 e8 69 03 00 00 89 44 24 18 a1 c8 83 30 70 $............0p..$.i....D$....0p
1740 89 04 24 e8 58 03 00 00 89 44 24 1c 8d 44 24 1c 89 44 24 08 8d 44 24 18 89 44 24 04 8b 44 24 30 ..$.X....D$..D$..D$..D$..D$..D$0
1760 89 04 24 e8 98 0e 00 00 89 c3 8b 44 24 18 89 04 24 e8 3a 03 00 00 a3 cc 83 30 70 8b 44 24 1c 89 ..$........D$...$.:......0p.D$..
1780 04 24 e8 29 03 00 00 c7 04 24 08 00 00 00 a3 c8 83 30 70 e8 48 0e 00 00 83 c4 28 89 d8 5b c3 90 .$.).....$.......0p.H.....(..[..
17a0 8b 44 24 30 89 04 24 ff 15 24 a2 30 70 83 c4 28 89 c3 89 d8 5b c3 8d 76 00 8d bc 27 00 00 00 00 .D$0..$..$.0p..(....[..v...'....
17c0 83 ec 1c 8b 44 24 20 89 04 24 e8 31 ff ff ff 85 c0 0f 94 c0 83 c4 1c 0f b6 c0 f7 d8 c3 90 90 90 ....D$...$.1....................
17e0 a1 80 5c 30 70 8b 00 85 c0 74 1f 83 ec 0c 66 90 ff d0 a1 80 5c 30 70 8d 50 04 8b 40 04 89 15 80 ..\0p....t....f.....\0p.P..@....
1800 5c 30 70 85 c0 75 e9 83 c4 0c f3 c3 8d 74 26 00 53 83 ec 18 8b 1d 20 32 30 70 83 fb ff 74 21 85 \0p..u.......t&.S......20p...t!.
1820 db 74 0c ff 14 9d 20 32 30 70 83 eb 01 75 f4 c7 04 24 e0 23 30 70 e8 85 ff ff ff 83 c4 18 5b c3 .t.....20p...u...$.#0p........[.
1840 31 db eb 02 89 c3 8d 43 01 8b 14 85 20 32 30 70 85 d2 75 f0 eb c9 8d 76 00 8d bc 27 00 00 00 00 1......C.....20p..u....v...'....
1860 a1 20 80 30 70 85 c0 74 07 f3 c3 90 8d 74 26 00 c7 05 20 80 30 70 01 00 00 00 eb 94 90 90 90 90 ...0p..t.....t&.....0p..........
1880 55 57 56 53 83 ec 2c a1 90 5c 30 70 c7 44 24 10 00 00 00 00 c7 44 24 14 00 00 00 00 3d 4e e6 40 UWVS..,..\0p.D$......D$.....=N.@
18a0 bb 74 0f f7 d0 a3 94 5c 30 70 83 c4 2c 5b 5e 5f 5d c3 8d 44 24 10 89 04 24 ff 15 d8 a1 30 70 83 .t.....\0p..,[^_]..D$...$....0p.
18c0 ec 04 8b 5c 24 10 33 5c 24 14 ff 15 c4 a1 30 70 89 c5 ff 15 c8 a1 30 70 89 c7 ff 15 dc a1 30 70 ...\$.3\$.....0p......0p......0p
18e0 89 c6 8d 44 24 18 89 04 24 ff 15 ec a1 30 70 83 ec 04 8b 44 24 18 31 d8 33 44 24 1c 31 e8 31 f8 ...D$...$....0p....D$.1.3D$.1.1.
1900 31 f0 3d 4e e6 40 bb 74 17 89 c2 f7 d2 a3 90 5c 30 70 89 15 94 5c 30 70 83 c4 2c 5b 5e 5f 5d c3 1.=N.@.t.......\0p...\0p..,[^_].
1920 ba b0 19 bf 44 b8 4f e6 40 bb eb e1 8d 74 26 00 55 89 e5 83 ec 28 c7 05 20 83 30 70 09 04 00 c0 ....D.O.@....t&.U....(....0p....
1940 8b 45 04 8d 55 04 c7 05 24 83 30 70 01 00 00 00 c7 04 24 00 00 00 00 89 15 04 81 30 70 a3 f8 80 .E..U...$.0p......$........0p...
1960 30 70 a3 2c 83 30 70 8b 45 08 a3 ec 80 30 70 a1 90 5c 30 70 89 45 f0 a1 94 5c 30 70 89 45 f4 ff 0p.,.0p.E....0p..\0p.E...\0p.E..
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19a0 24 04 09 04 00 c0 89 04 24 ff 15 f8 a1 30 70 83 ec 08 e8 21 0c 00 00 90 90 90 90 90 90 90 90 90 $.......$....0p....!............
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19e0 8b 54 24 28 89 44 24 04 8b 44 24 20 89 54 24 08 89 04 24 e8 d8 06 00 00 b8 01 00 00 00 83 c4 1c .T$(.D$..D$..T$...$.............
1a00 c2 0c 00 8d b6 00 00 00 00 8d bc 27 00 00 00 00 56 53 83 ec 14 83 3d 8c 5c 30 70 02 8b 44 24 24 ...........'....VS....=.\0p..D$$
1a20 74 0a c7 05 8c 5c 30 70 02 00 00 00 83 f8 02 74 12 83 f8 01 74 3a 83 c4 14 b8 01 00 00 00 5b 5e t....\0p.......t....t:........[^
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1d40 0f 84 19 01 00 00 83 fa 20 0f 84 88 01 00 00 83 fa 08 0f 84 58 01 00 00 89 54 24 04 c7 04 24 08 ....................X....T$...$.
1d60 62 30 70 e8 58 fd ff ff be a8 65 30 70 81 fe 80 66 30 70 0f 83 fa fe ff ff 89 5d c4 8d 74 26 00 b0p.X.....e0p...f0p.......]..t&.
1d80 8b 7e 04 8b 16 83 c6 08 03 97 00 00 30 70 8d 87 00 00 30 70 89 d3 e8 85 fd ff ff 81 fe 80 66 30 .~..........0p....0p..........f0
1da0 70 89 9f 00 00 30 70 72 d7 8b 5d c4 a1 98 83 30 70 85 c0 7f 1a e9 b9 fe ff ff 8d b6 00 00 00 00 p....0pr..]....0p...............
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1e00 70 83 ec 0c 85 c0 0f 84 e2 00 00 00 8d 45 c8 89 44 24 0c a1 9c 83 30 70 8b 04 b8 89 44 24 08 8b p............E..D$....0p....D$..
1e20 45 d8 89 44 24 04 8b 45 cc 89 04 24 ff 15 04 a2 30 70 83 ec 10 eb 89 89 f6 8d bc 27 00 00 00 00 E..D$..E...$....0p.........'....
1e40 be a8 65 30 70 8b 3e 85 ff 0f 85 1e ff ff ff 8b 4e 04 85 c9 0f 84 a7 fe ff ff e9 0e ff ff ff 0f ..e0p.>.........N...............
1e60 b7 97 00 00 30 70 89 d0 0d 00 00 ff ff 66 83 bf 00 00 30 70 00 0f 48 d0 8b 45 c4 29 ca 01 d0 89 ....0p.......f....0p..H..E.)....
1e80 45 cc 89 d8 e8 97 fc ff ff 0f b7 45 cc 66 89 87 00 00 30 70 83 c6 0c 81 fe 80 66 30 70 0f 82 7c E..........E.f....0p......f0p..|
1ea0 fe ff ff 8b 5d c0 a1 98 83 30 70 e9 01 ff ff ff 0f b6 13 89 d7 81 cf 00 ff ff ff 80 3b 00 0f 48 ....]....0p.................;..H
1ec0 d7 29 ca 01 d0 89 45 cc 89 d8 e8 51 fc ff ff 0f b6 45 cc 88 03 eb bd 8b 45 c4 29 c8 03 03 89 c7 .)....E....Q.....E......E.).....
1ee0 89 45 cc 89 d8 e8 36 fc ff ff 89 3b eb a6 8b 0d 9c 83 30 70 01 f1 8b 41 04 89 44 24 08 8b 41 08 .E....6....;......0p...A..D$..A.
1f00 8b 40 08 c7 04 24 78 61 30 70 89 44 24 04 e8 ad fb ff ff 89 44 24 04 c7 04 24 d4 61 30 70 e8 9d .@...$xa0p.D$.......D$...$.a0p..
1f20 fb ff ff 90 90 90 90 90 90 90 90 90 90 90 90 90 55 57 56 53 83 ec 1c c7 04 24 a8 83 30 70 ff 15 ................UWVS.....$..0p..
1f40 b8 a1 30 70 8b 1d a0 83 30 70 83 ec 04 8b 2d fc a1 30 70 8b 3d cc a1 30 70 85 db 74 28 8d 76 00 ..0p....0p....-..0p.=..0p..t(.v.
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1f80 08 85 db 75 db c7 04 24 a8 83 30 70 ff 15 e4 a1 30 70 83 ec 04 83 c4 1c 5b 5e 5f 5d c3 8d 76 00 ...u...$..0p....0p......[^_]..v.
1fa0 56 53 31 f6 83 ec 14 a1 a4 83 30 70 85 c0 75 10 83 c4 14 89 f0 5b 5e c3 90 8d b4 26 00 00 00 00 VS1.......0p..u......[^....&....
1fc0 c7 44 24 04 0c 00 00 00 c7 04 24 01 00 00 00 e8 fc 05 00 00 85 c0 89 c3 74 43 8b 44 24 20 c7 04 .D$.......$.............tC.D$...
1fe0 24 a8 83 30 70 89 03 8b 44 24 24 89 43 04 ff 15 b8 a1 30 70 a1 a0 83 30 70 83 ec 04 89 1d a0 83 $..0p...D$$.C.....0p...0p.......
2000 30 70 c7 04 24 a8 83 30 70 89 43 08 ff 15 e4 a1 30 70 83 ec 04 89 f0 83 c4 14 5b 5e c3 be ff ff 0p..$..0p.C.....0p........[^....
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2040 0f 83 c4 18 31 c0 5b c3 90 8d b4 26 00 00 00 00 c7 04 24 a8 83 30 70 ff 15 b8 a1 30 70 8b 15 a0 ....1.[....&......$..0p....0p...
2060 83 30 70 83 ec 04 85 d2 74 17 8b 02 39 c3 75 0a eb 4e 8b 08 39 d9 74 28 89 c2 8b 42 08 85 c0 75 .0p.....t...9.u..N..9.t(...B...u
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20a0 8b 48 08 89 4a 08 89 04 24 e8 1a 05 00 00 c7 04 24 a8 83 30 70 ff 15 e4 a1 30 70 83 ec 04 eb d1 .H..J...$.......$..0p....0p.....
20c0 8b 42 08 a3 a0 83 30 70 89 d0 eb da 8d 74 26 00 53 83 ec 18 8b 44 24 24 83 f8 01 0f 84 8f 00 00 .B....0p.....t&.S....D$$........
20e0 00 72 2d 83 f8 02 74 18 83 f8 03 75 18 a1 a4 83 30 70 85 c0 74 0f e8 35 fe ff ff eb 08 8d 76 00 .r-...t....u....0p..t..5......v.
2100 e8 2b 04 00 00 83 c4 18 b8 01 00 00 00 5b c3 90 a1 a4 83 30 70 85 c0 0f 85 85 00 00 00 a1 a4 83 .+...........[.....0p...........
2120 30 70 83 f8 01 75 de a1 a0 83 30 70 85 c0 74 11 8b 58 08 89 04 24 e8 8d 04 00 00 85 db 89 d8 75 0p...u....0p..t..X...$.........u
2140 ef c7 05 a0 83 30 70 00 00 00 00 c7 05 a4 83 30 70 00 00 00 00 c7 04 24 a8 83 30 70 ff 15 b4 a1 .....0p........0p......$..0p....
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2480 57 56 31 f6 66 81 3d 00 00 30 70 4d 5a 53 8b 5c 24 10 74 0c 89 f0 5b 5e 5f c3 8d b6 00 00 00 00 WV1.f.=..0pMZS.\$.t...[^_.......
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2500 83 eb 01 83 c0 14 8b 48 04 85 c9 75 07 8b 50 0c 85 d2 74 d7 85 db 7f e8 8b 70 0c 5b 81 c6 00 00 .......H...u..P...t......p.[....
2520 30 70 89 f0 5e 5f c3 90 90 90 90 90 90 90 90 90 db e3 c3 90 90 90 90 90 90 90 90 90 90 90 90 90 0p..^_..........................
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25e0 ff 25 28 a2 30 70 90 90 ff 25 20 a2 30 70 90 90 ff 25 18 a2 30 70 90 90 ff 25 14 a2 30 70 90 90 .%(.0p...%..0p...%..0p...%..0p..
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26e0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................................
2700 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................................
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27e0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................................
2800 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................................
2820 48 65 61 70 20 71 75 65 75 65 73 0a 0a 5b 65 78 70 6c 61 6e 61 74 69 6f 6e 20 62 79 20 46 72 61 Heap.queues..[explanation.by.Fra
2840 6e e7 6f 69 73 20 50 69 6e 61 72 64 5d 0a 0a 48 65 61 70 73 20 61 72 65 20 61 72 72 61 79 73 20 n.ois.Pinard]..Heaps.are.arrays.
2860 66 6f 72 20 77 68 69 63 68 20 61 5b 6b 5d 20 3c 3d 20 61 5b 32 2a 6b 2b 31 5d 20 61 6e 64 20 61 for.which.a[k].<=.a[2*k+1].and.a
2880 5b 6b 5d 20 3c 3d 20 61 5b 32 2a 6b 2b 32 5d 20 66 6f 72 0a 61 6c 6c 20 6b 2c 20 63 6f 75 6e 74 [k].<=.a[2*k+2].for.all.k,.count
28a0 69 6e 67 20 65 6c 65 6d 65 6e 74 73 20 66 72 6f 6d 20 30 2e 20 20 46 6f 72 20 74 68 65 20 73 61 ing.elements.from.0...For.the.sa
28c0 6b 65 20 6f 66 20 63 6f 6d 70 61 72 69 73 6f 6e 2c 0a 6e 6f 6e 2d 65 78 69 73 74 69 6e 67 20 65 ke.of.comparison,.non-existing.e
28e0 6c 65 6d 65 6e 74 73 20 61 72 65 20 63 6f 6e 73 69 64 65 72 65 64 20 74 6f 20 62 65 20 69 6e 66 lements.are.considered.to.be.inf
2900 69 6e 69 74 65 2e 20 20 54 68 65 20 69 6e 74 65 72 65 73 74 69 6e 67 0a 70 72 6f 70 65 72 74 79 inite...The.interesting.property
2920 20 6f 66 20 61 20 68 65 61 70 20 69 73 20 74 68 61 74 20 61 5b 30 5d 20 69 73 20 61 6c 77 61 79 .of.a.heap.is.that.a[0].is.alway
2940 73 20 69 74 73 20 73 6d 61 6c 6c 65 73 74 20 65 6c 65 6d 65 6e 74 2e 0a 0a 54 68 65 20 73 74 72 s.its.smallest.element...The.str
2960 61 6e 67 65 20 69 6e 76 61 72 69 61 6e 74 20 61 62 6f 76 65 20 69 73 20 6d 65 61 6e 74 20 74 6f ange.invariant.above.is.meant.to
2980 20 62 65 20 61 6e 20 65 66 66 69 63 69 65 6e 74 20 6d 65 6d 6f 72 79 0a 72 65 70 72 65 73 65 6e .be.an.efficient.memory.represen
29a0 74 61 74 69 6f 6e 20 66 6f 72 20 61 20 74 6f 75 72 6e 61 6d 65 6e 74 2e 20 20 54 68 65 20 6e 75 tation.for.a.tournament...The.nu
29c0 6d 62 65 72 73 20 62 65 6c 6f 77 20 61 72 65 20 60 6b 27 2c 20 6e 6f 74 20 61 5b 6b 5d 3a 0a 0a mbers.below.are.`k',.not.a[k]:..
29e0 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 ................................
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2a20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 32 0a 0a 20 20 20 ..........................2.....
2a40 20 20 20 20 20 20 20 33 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 34 20 20 20 20 20 20 20 20 .......3...............4........
2a60 20 20 20 20 20 20 20 20 35 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 36 0a 0a 20 20 20 20 20 ........5...............6.......
2a80 20 37 20 20 20 20 20 20 20 38 20 20 20 20 20 20 20 39 20 20 20 20 20 20 20 31 30 20 20 20 20 20 .7.......8.......9.......10.....
2aa0 20 31 31 20 20 20 20 20 20 31 32 20 20 20 20 20 20 31 33 20 20 20 20 20 20 31 34 0a 0a 20 20 20 .11......12......13......14.....
2ac0 20 31 35 20 31 36 20 20 20 31 37 20 31 38 20 20 20 31 39 20 32 30 20 20 20 32 31 20 32 32 20 20 .15.16...17.18...19.20...21.22..
2ae0 20 32 33 20 32 34 20 20 20 32 35 20 32 36 20 20 20 32 37 20 32 38 20 20 20 32 39 20 33 30 0a 0a .23.24...25.26...27.28...29.30..
2b00 0a 49 6e 20 74 68 65 20 74 72 65 65 20 61 62 6f 76 65 2c 20 65 61 63 68 20 63 65 6c 6c 20 60 6b .In.the.tree.above,.each.cell.`k
2b20 27 20 69 73 20 74 6f 70 70 69 6e 67 20 60 32 2a 6b 2b 31 27 20 61 6e 64 20 60 32 2a 6b 2b 32 27 '.is.topping.`2*k+1'.and.`2*k+2'
2b40 2e 20 20 49 6e 0a 61 20 75 73 75 61 6c 20 62 69 6e 61 72 79 20 74 6f 75 72 6e 61 6d 65 6e 74 20 ...In.a.usual.binary.tournament.
2b60 77 65 20 73 65 65 20 69 6e 20 73 70 6f 72 74 73 2c 20 65 61 63 68 20 63 65 6c 6c 20 69 73 20 74 we.see.in.sports,.each.cell.is.t
2b80 68 65 20 77 69 6e 6e 65 72 0a 6f 76 65 72 20 74 68 65 20 74 77 6f 20 63 65 6c 6c 73 20 69 74 20 he.winner.over.the.two.cells.it.
2ba0 74 6f 70 73 2c 20 61 6e 64 20 77 65 20 63 61 6e 20 74 72 61 63 65 20 74 68 65 20 77 69 6e 6e 65 tops,.and.we.can.trace.the.winne
2bc0 72 20 64 6f 77 6e 20 74 68 65 20 74 72 65 65 0a 74 6f 20 73 65 65 20 61 6c 6c 20 6f 70 70 6f 6e r.down.the.tree.to.see.all.oppon
2be0 65 6e 74 73 20 73 2f 68 65 20 68 61 64 2e 20 20 48 6f 77 65 76 65 72 2c 20 69 6e 20 6d 61 6e 79 ents.s/he.had...However,.in.many
2c00 20 63 6f 6d 70 75 74 65 72 20 61 70 70 6c 69 63 61 74 69 6f 6e 73 0a 6f 66 20 73 75 63 68 20 74 .computer.applications.of.such.t
2c20 6f 75 72 6e 61 6d 65 6e 74 73 2c 20 77 65 20 64 6f 20 6e 6f 74 20 6e 65 65 64 20 74 6f 20 74 72 ournaments,.we.do.not.need.to.tr
2c40 61 63 65 20 74 68 65 20 68 69 73 74 6f 72 79 20 6f 66 20 61 20 77 69 6e 6e 65 72 2e 0a 54 6f 20 ace.the.history.of.a.winner..To.
2c60 62 65 20 6d 6f 72 65 20 6d 65 6d 6f 72 79 20 65 66 66 69 63 69 65 6e 74 2c 20 77 68 65 6e 20 61 be.more.memory.efficient,.when.a
2c80 20 77 69 6e 6e 65 72 20 69 73 20 70 72 6f 6d 6f 74 65 64 2c 20 77 65 20 74 72 79 20 74 6f 0a 72 .winner.is.promoted,.we.try.to.r
2ca0 65 70 6c 61 63 65 20 69 74 20 62 79 20 73 6f 6d 65 74 68 69 6e 67 20 65 6c 73 65 20 61 74 20 61 eplace.it.by.something.else.at.a
2cc0 20 6c 6f 77 65 72 20 6c 65 76 65 6c 2c 20 61 6e 64 20 74 68 65 20 72 75 6c 65 20 62 65 63 6f 6d .lower.level,.and.the.rule.becom
2ce0 65 73 0a 74 68 61 74 20 61 20 63 65 6c 6c 20 61 6e 64 20 74 68 65 20 74 77 6f 20 63 65 6c 6c 73 es.that.a.cell.and.the.two.cells
2d00 20 69 74 20 74 6f 70 73 20 63 6f 6e 74 61 69 6e 20 74 68 72 65 65 20 64 69 66 66 65 72 65 6e 74 .it.tops.contain.three.different
2d20 20 69 74 65 6d 73 2c 0a 62 75 74 20 74 68 65 20 74 6f 70 20 63 65 6c 6c 20 22 77 69 6e 73 22 20 .items,.but.the.top.cell."wins".
2d40 6f 76 65 72 20 74 68 65 20 74 77 6f 20 74 6f 70 70 65 64 20 63 65 6c 6c 73 2e 0a 0a 49 66 20 74 over.the.two.topped.cells...If.t
2d60 68 69 73 20 68 65 61 70 20 69 6e 76 61 72 69 61 6e 74 20 69 73 20 70 72 6f 74 65 63 74 65 64 20 his.heap.invariant.is.protected.
2d80 61 74 20 61 6c 6c 20 74 69 6d 65 2c 20 69 6e 64 65 78 20 30 20 69 73 20 63 6c 65 61 72 6c 79 0a at.all.time,.index.0.is.clearly.
2da0 74 68 65 20 6f 76 65 72 61 6c 6c 20 77 69 6e 6e 65 72 2e 20 20 54 68 65 20 73 69 6d 70 6c 65 73 the.overall.winner...The.simples
2dc0 74 20 61 6c 67 6f 72 69 74 68 6d 69 63 20 77 61 79 20 74 6f 20 72 65 6d 6f 76 65 20 69 74 20 61 t.algorithmic.way.to.remove.it.a
2de0 6e 64 0a 66 69 6e 64 20 74 68 65 20 22 6e 65 78 74 22 20 77 69 6e 6e 65 72 20 69 73 20 74 6f 20 nd.find.the."next".winner.is.to.
2e00 6d 6f 76 65 20 73 6f 6d 65 20 6c 6f 73 65 72 20 28 6c 65 74 27 73 20 73 61 79 20 63 65 6c 6c 20 move.some.loser.(let's.say.cell.
2e20 33 30 20 69 6e 20 74 68 65 0a 64 69 61 67 72 61 6d 20 61 62 6f 76 65 29 20 69 6e 74 6f 20 74 68 30.in.the.diagram.above).into.th
2e40 65 20 30 20 70 6f 73 69 74 69 6f 6e 2c 20 61 6e 64 20 74 68 65 6e 20 70 65 72 63 6f 6c 61 74 65 e.0.position,.and.then.percolate
2e60 20 74 68 69 73 20 6e 65 77 20 30 20 64 6f 77 6e 0a 74 68 65 20 74 72 65 65 2c 20 65 78 63 68 61 .this.new.0.down.the.tree,.excha
2e80 6e 67 69 6e 67 20 76 61 6c 75 65 73 2c 20 75 6e 74 69 6c 20 74 68 65 20 69 6e 76 61 72 69 61 6e nging.values,.until.the.invarian
2ea0 74 20 69 73 20 72 65 2d 65 73 74 61 62 6c 69 73 68 65 64 2e 0a 54 68 69 73 20 69 73 20 63 6c 65 t.is.re-established..This.is.cle
2ec0 61 72 6c 79 20 6c 6f 67 61 72 69 74 68 6d 69 63 20 6f 6e 20 74 68 65 20 74 6f 74 61 6c 20 6e 75 arly.logarithmic.on.the.total.nu
2ee0 6d 62 65 72 20 6f 66 20 69 74 65 6d 73 20 69 6e 20 74 68 65 20 74 72 65 65 2e 0a 42 79 20 69 74 mber.of.items.in.the.tree..By.it
2f00 65 72 61 74 69 6e 67 20 6f 76 65 72 20 61 6c 6c 20 69 74 65 6d 73 2c 20 79 6f 75 20 67 65 74 20 erating.over.all.items,.you.get.
2f20 61 6e 20 4f 28 6e 20 6c 6e 20 6e 29 20 73 6f 72 74 2e 0a 0a 41 20 6e 69 63 65 20 66 65 61 74 75 an.O(n.ln.n).sort...A.nice.featu
2f40 72 65 20 6f 66 20 74 68 69 73 20 73 6f 72 74 20 69 73 20 74 68 61 74 20 79 6f 75 20 63 61 6e 20 re.of.this.sort.is.that.you.can.
2f60 65 66 66 69 63 69 65 6e 74 6c 79 20 69 6e 73 65 72 74 20 6e 65 77 0a 69 74 65 6d 73 20 77 68 69 efficiently.insert.new.items.whi
2f80 6c 65 20 74 68 65 20 73 6f 72 74 20 69 73 20 67 6f 69 6e 67 20 6f 6e 2c 20 70 72 6f 76 69 64 65 le.the.sort.is.going.on,.provide
2fa0 64 20 74 68 61 74 20 74 68 65 20 69 6e 73 65 72 74 65 64 20 69 74 65 6d 73 20 61 72 65 0a 6e 6f d.that.the.inserted.items.are.no
2fc0 74 20 22 62 65 74 74 65 72 22 20 74 68 61 6e 20 74 68 65 20 6c 61 73 74 20 30 27 74 68 20 65 6c t."better".than.the.last.0'th.el
2fe0 65 6d 65 6e 74 20 79 6f 75 20 65 78 74 72 61 63 74 65 64 2e 20 20 54 68 69 73 20 69 73 0a 65 73 ement.you.extracted...This.is.es
3000 70 65 63 69 61 6c 6c 79 20 75 73 65 66 75 6c 20 69 6e 20 73 69 6d 75 6c 61 74 69 6f 6e 20 63 6f pecially.useful.in.simulation.co
3020 6e 74 65 78 74 73 2c 20 77 68 65 72 65 20 74 68 65 20 74 72 65 65 20 68 6f 6c 64 73 20 61 6c 6c ntexts,.where.the.tree.holds.all
3040 0a 69 6e 63 6f 6d 69 6e 67 20 65 76 65 6e 74 73 2c 20 61 6e 64 20 74 68 65 20 22 77 69 6e 22 20 .incoming.events,.and.the."win".
3060 63 6f 6e 64 69 74 69 6f 6e 20 6d 65 61 6e 73 20 74 68 65 20 73 6d 61 6c 6c 65 73 74 20 73 63 68 condition.means.the.smallest.sch
3080 65 64 75 6c 65 64 0a 74 69 6d 65 2e 20 20 57 68 65 6e 20 61 6e 20 65 76 65 6e 74 20 73 63 68 65 eduled.time...When.an.event.sche
30a0 64 75 6c 65 20 6f 74 68 65 72 20 65 76 65 6e 74 73 20 66 6f 72 20 65 78 65 63 75 74 69 6f 6e 2c dule.other.events.for.execution,
30c0 20 74 68 65 79 20 61 72 65 0a 73 63 68 65 64 75 6c 65 64 20 69 6e 74 6f 20 74 68 65 20 66 75 74 .they.are.scheduled.into.the.fut
30e0 75 72 65 2c 20 73 6f 20 74 68 65 79 20 63 61 6e 20 65 61 73 69 6c 79 20 67 6f 20 69 6e 74 6f 20 ure,.so.they.can.easily.go.into.
3100 74 68 65 20 68 65 61 70 2e 20 20 53 6f 2c 20 61 0a 68 65 61 70 20 69 73 20 61 20 67 6f 6f 64 20 the.heap...So,.a.heap.is.a.good.
3120 73 74 72 75 63 74 75 72 65 20 66 6f 72 20 69 6d 70 6c 65 6d 65 6e 74 69 6e 67 20 73 63 68 65 64 structure.for.implementing.sched
3140 75 6c 65 72 73 20 28 74 68 69 73 20 69 73 20 77 68 61 74 20 49 0a 75 73 65 64 20 66 6f 72 20 6d ulers.(this.is.what.I.used.for.m
3160 79 20 4d 49 44 49 20 73 65 71 75 65 6e 63 65 72 20 3a 2d 29 2e 0a 0a 56 61 72 69 6f 75 73 20 73 y.MIDI.sequencer.:-)...Various.s
3180 74 72 75 63 74 75 72 65 73 20 66 6f 72 20 69 6d 70 6c 65 6d 65 6e 74 69 6e 67 20 73 63 68 65 64 tructures.for.implementing.sched
31a0 75 6c 65 72 73 20 68 61 76 65 20 62 65 65 6e 20 65 78 74 65 6e 73 69 76 65 6c 79 0a 73 74 75 64 ulers.have.been.extensively.stud
31c0 69 65 64 2c 20 61 6e 64 20 68 65 61 70 73 20 61 72 65 20 67 6f 6f 64 20 66 6f 72 20 74 68 69 73 ied,.and.heaps.are.good.for.this
31e0 2c 20 61 73 20 74 68 65 79 20 61 72 65 20 72 65 61 73 6f 6e 61 62 6c 79 20 73 70 65 65 64 79 2c ,.as.they.are.reasonably.speedy,
3200 0a 74 68 65 20 73 70 65 65 64 20 69 73 20 61 6c 6d 6f 73 74 20 63 6f 6e 73 74 61 6e 74 2c 20 61 .the.speed.is.almost.constant,.a
3220 6e 64 20 74 68 65 20 77 6f 72 73 74 20 63 61 73 65 20 69 73 20 6e 6f 74 20 6d 75 63 68 20 64 69 nd.the.worst.case.is.not.much.di
3240 66 66 65 72 65 6e 74 0a 74 68 61 6e 20 74 68 65 20 61 76 65 72 61 67 65 20 63 61 73 65 2e 20 20 fferent.than.the.average.case...
3260 48 6f 77 65 76 65 72 2c 20 74 68 65 72 65 20 61 72 65 20 6f 74 68 65 72 20 72 65 70 72 65 73 65 However,.there.are.other.represe
3280 6e 74 61 74 69 6f 6e 73 20 77 68 69 63 68 0a 61 72 65 20 6d 6f 72 65 20 65 66 66 69 63 69 65 6e ntations.which.are.more.efficien
32a0 74 20 6f 76 65 72 61 6c 6c 2c 20 79 65 74 20 74 68 65 20 77 6f 72 73 74 20 63 61 73 65 73 20 6d t.overall,.yet.the.worst.cases.m
32c0 69 67 68 74 20 62 65 20 74 65 72 72 69 62 6c 65 2e 0a 0a 48 65 61 70 73 20 61 72 65 20 61 6c 73 ight.be.terrible...Heaps.are.als
32e0 6f 20 76 65 72 79 20 75 73 65 66 75 6c 20 69 6e 20 62 69 67 20 64 69 73 6b 20 73 6f 72 74 73 2e o.very.useful.in.big.disk.sorts.
3300 20 20 59 6f 75 20 6d 6f 73 74 20 70 72 6f 62 61 62 6c 79 20 61 6c 6c 0a 6b 6e 6f 77 20 74 68 61 ..You.most.probably.all.know.tha
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6aa0 00 60 00 00 10 00 00 00 30 31 34 31 38 31 00 00 00 b0 00 00 10 00 00 00 0c 30 18 30 1c 30 00 00 .`......014181...........0.0.0..
6ac0 00 c0 00 00 10 00 00 00 04 30 08 30 0c 30 10 30 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .........0.0.0.0................
6ae0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................................
6b00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................................
6b20 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................................
6b40 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................................
6b60 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................................
6b80 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................................
6ba0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................................
6bc0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................................
6be0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................................