ofs | hex dump | ascii |
---|
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0060 | 5a 06 00 6d 07 00 5a 07 00 6d 08 00 5a 08 00 6d 09 00 5a 09 00 01 64 0a 00 64 0c 00 6c 0a 00 6d | Z..m..Z..m..Z..m..Z...d..d..l..m |
0080 | 0b 00 5a 0b 00 01 64 0d 00 84 00 00 5a 0c 00 64 0e 00 84 00 00 5a 0d 00 64 0f 00 84 00 00 5a 0e | ..Z...d.....Z..d.....Z..d.....Z. |
00a0 | 00 64 10 00 84 00 00 5a 0f 00 64 11 00 84 00 00 5a 10 00 64 12 00 84 00 00 5a 11 00 64 13 00 84 | .d.....Z..d.....Z..d.....Z..d... |
00c0 | 00 00 5a 12 00 64 14 00 84 00 00 5a 13 00 64 15 00 84 00 00 5a 14 00 64 16 00 84 00 00 5a 15 00 | ..Z..d.....Z..d.....Z..d.....Z.. |
00e0 | 64 17 00 84 00 00 5a 16 00 64 18 00 84 00 00 5a 17 00 64 19 00 84 00 00 5a 18 00 64 1a 00 84 00 | d.....Z..d.....Z..d.....Z..d.... |
0100 | 00 5a 19 00 79 0e 00 64 0a 00 64 1b 00 6c 1a 00 54 57 6e 11 00 04 65 1b 00 6b 0a 00 72 07 01 01 | .Z..y..d..d..l..TWn...e..k..r... |
0120 | 01 01 6e 01 00 58 64 1c 00 84 00 00 5a 1c 00 65 15 00 5a 1d 00 64 2a 00 64 1d 00 84 01 00 5a 15 | ..n..Xd.....Z..e..Z..d*.d.....Z. |
0140 | 00 65 14 00 5a 1f 00 64 2a 00 64 1e 00 84 01 00 5a 14 00 65 20 00 64 1f 00 6b 02 00 72 cd 01 67 | .e..Z..d*.d.....Z..e..d..k..r..g |
0160 | 00 00 5a 21 00 64 20 00 64 21 00 64 22 00 64 23 00 64 24 00 64 25 00 64 26 00 64 27 00 64 28 00 | ..Z!.d..d!.d".d#.d$.d%.d&.d'.d(. |
0180 | 64 29 00 67 0a 00 5a 22 00 78 1b 00 65 22 00 44 5d 13 00 5a 23 00 65 0d 00 65 21 00 65 23 00 83 | d).g..Z".x..e".D]..Z#.e..e!.e#.. |
01a0 | 02 00 01 71 72 01 57 67 00 00 5a 24 00 78 1d 00 65 21 00 72 ae 01 65 24 00 6a 25 00 65 0e 00 65 | ...qr.Wg..Z$.x..e!.r..e$.j%.e..e |
01c0 | 21 00 83 01 00 83 01 00 01 71 92 01 57 65 24 00 47 48 64 0a 00 64 2a 00 6c 26 00 5a 26 00 65 26 | !........q..We$.GHd..d*.l&.Z&.e& |
01e0 | 00 6a 27 00 83 00 00 01 6e 00 00 64 2a 00 53 28 2b 00 00 00 73 ef 04 00 00 48 65 61 70 20 71 75 | .j'.....n..d*.S(+...s....Heap.qu |
0200 | 65 75 65 20 61 6c 67 6f 72 69 74 68 6d 20 28 61 2e 6b 2e 61 2e 20 70 72 69 6f 72 69 74 79 20 71 | eue.algorithm.(a.k.a..priority.q |
0220 | 75 65 75 65 29 2e 0a 0a 48 65 61 70 73 20 61 72 65 20 61 72 72 61 79 73 20 66 6f 72 20 77 68 69 | ueue)...Heaps.are.arrays.for.whi |
0240 | 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 5b 6b 5d 20 3c 3d 20 | ch.a[k].<=.a[2*k+1].and.a[k].<=. |
0260 | 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 69 6e 67 20 65 6c 65 | a[2*k+2].for.all.k,.counting.ele |
0280 | 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 6b 65 20 6f 66 20 63 | ments.from.0...For.the.sake.of.c |
02a0 | 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 6c 65 6d 65 6e 74 73 | omparison,.non-existing.elements |
02c0 | 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 69 6e 69 74 65 2e 20 | .are.considered.to.be.infinite.. |
02e0 | 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 20 6f 66 20 61 20 68 | .The.interesting.property.of.a.h |
0300 | 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 73 20 69 74 73 20 73 | eap.is.that.a[0].is.always.its.s |
0320 | 6d 61 6c 6c 65 73 74 20 65 6c 65 6d 65 6e 74 2e 0a 0a 55 73 61 67 65 3a 0a 0a 68 65 61 70 20 3d | mallest.element...Usage:..heap.= |
0340 | 20 5b 5d 20 20 20 20 20 20 20 20 20 20 20 20 23 20 63 72 65 61 74 65 73 20 61 6e 20 65 6d 70 74 | .[]............#.creates.an.empt |
0360 | 79 20 68 65 61 70 0a 68 65 61 70 70 75 73 68 28 68 65 61 70 2c 20 69 74 65 6d 29 20 23 20 70 75 | y.heap.heappush(heap,.item).#.pu |
0380 | 73 68 65 73 20 61 20 6e 65 77 20 69 74 65 6d 20 6f 6e 20 74 68 65 20 68 65 61 70 0a 69 74 65 6d | shes.a.new.item.on.the.heap.item |
03a0 | 20 3d 20 68 65 61 70 70 6f 70 28 68 65 61 70 29 20 23 20 70 6f 70 73 20 74 68 65 20 73 6d 61 6c | .=.heappop(heap).#.pops.the.smal |
03c0 | 6c 65 73 74 20 69 74 65 6d 20 66 72 6f 6d 20 74 68 65 20 68 65 61 70 0a 69 74 65 6d 20 3d 20 68 | lest.item.from.the.heap.item.=.h |
03e0 | 65 61 70 5b 30 5d 20 20 20 20 20 20 20 23 20 73 6d 61 6c 6c 65 73 74 20 69 74 65 6d 20 6f 6e 20 | eap[0].......#.smallest.item.on. |
0400 | 74 68 65 20 68 65 61 70 20 77 69 74 68 6f 75 74 20 70 6f 70 70 69 6e 67 20 69 74 0a 68 65 61 70 | the.heap.without.popping.it.heap |
0420 | 69 66 79 28 78 29 20 20 20 20 20 20 20 20 20 20 20 23 20 74 72 61 6e 73 66 6f 72 6d 73 20 6c 69 | ify(x)...........#.transforms.li |
0440 | 73 74 20 69 6e 74 6f 20 61 20 68 65 61 70 2c 20 69 6e 2d 70 6c 61 63 65 2c 20 69 6e 20 6c 69 6e | st.into.a.heap,.in-place,.in.lin |
0460 | 65 61 72 20 74 69 6d 65 0a 69 74 65 6d 20 3d 20 68 65 61 70 72 65 70 6c 61 63 65 28 68 65 61 70 | ear.time.item.=.heapreplace(heap |
0480 | 2c 20 69 74 65 6d 29 20 23 20 70 6f 70 73 20 61 6e 64 20 72 65 74 75 72 6e 73 20 73 6d 61 6c 6c | ,.item).#.pops.and.returns.small |
04a0 | 65 73 74 20 69 74 65 6d 2c 20 61 6e 64 20 61 64 64 73 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 | est.item,.and.adds.............. |
04c0 | 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 23 20 6e 65 77 20 69 74 65 6d 3b 20 74 68 | ..................#.new.item;.th |
04e0 | 65 20 68 65 61 70 20 73 69 7a 65 20 69 73 20 75 6e 63 68 61 6e 67 65 64 0a 0a 4f 75 72 20 41 50 | e.heap.size.is.unchanged..Our.AP |
0500 | 49 20 64 69 66 66 65 72 73 20 66 72 6f 6d 20 74 65 78 74 62 6f 6f 6b 20 68 65 61 70 20 61 6c 67 | I.differs.from.textbook.heap.alg |
0520 | 6f 72 69 74 68 6d 73 20 61 73 20 66 6f 6c 6c 6f 77 73 3a 0a 0a 2d 20 57 65 20 75 73 65 20 30 2d | orithms.as.follows:..-.We.use.0- |
0540 | 62 61 73 65 64 20 69 6e 64 65 78 69 6e 67 2e 20 20 54 68 69 73 20 6d 61 6b 65 73 20 74 68 65 20 | based.indexing...This.makes.the. |
0560 | 72 65 6c 61 74 69 6f 6e 73 68 69 70 20 62 65 74 77 65 65 6e 20 74 68 65 0a 20 20 69 6e 64 65 78 | relationship.between.the...index |
0580 | 20 66 6f 72 20 61 20 6e 6f 64 65 20 61 6e 64 20 74 68 65 20 69 6e 64 65 78 65 73 20 66 6f 72 20 | .for.a.node.and.the.indexes.for. |
05a0 | 69 74 73 20 63 68 69 6c 64 72 65 6e 20 73 6c 69 67 68 74 6c 79 20 6c 65 73 73 0a 20 20 6f 62 76 | its.children.slightly.less...obv |
05c0 | 69 6f 75 73 2c 20 62 75 74 20 69 73 20 6d 6f 72 65 20 73 75 69 74 61 62 6c 65 20 73 69 6e 63 65 | ious,.but.is.more.suitable.since |
05e0 | 20 50 79 74 68 6f 6e 20 75 73 65 73 20 30 2d 62 61 73 65 64 20 69 6e 64 65 78 69 6e 67 2e 0a 0a | .Python.uses.0-based.indexing... |
0600 | 2d 20 4f 75 72 20 68 65 61 70 70 6f 70 28 29 20 6d 65 74 68 6f 64 20 72 65 74 75 72 6e 73 20 74 | -.Our.heappop().method.returns.t |
0620 | 68 65 20 73 6d 61 6c 6c 65 73 74 20 69 74 65 6d 2c 20 6e 6f 74 20 74 68 65 20 6c 61 72 67 65 73 | he.smallest.item,.not.the.larges |
0640 | 74 2e 0a 0a 54 68 65 73 65 20 74 77 6f 20 6d 61 6b 65 20 69 74 20 70 6f 73 73 69 62 6c 65 20 74 | t...These.two.make.it.possible.t |
0660 | 6f 20 76 69 65 77 20 74 68 65 20 68 65 61 70 20 61 73 20 61 20 72 65 67 75 6c 61 72 20 50 79 74 | o.view.the.heap.as.a.regular.Pyt |
0680 | 68 6f 6e 20 6c 69 73 74 0a 77 69 74 68 6f 75 74 20 73 75 72 70 72 69 73 65 73 3a 20 68 65 61 70 | hon.list.without.surprises:.heap |
06a0 | 5b 30 5d 20 69 73 20 74 68 65 20 73 6d 61 6c 6c 65 73 74 20 69 74 65 6d 2c 20 61 6e 64 20 68 65 | [0].is.the.smallest.item,.and.he |
06c0 | 61 70 2e 73 6f 72 74 28 29 0a 6d 61 69 6e 74 61 69 6e 73 20 74 68 65 20 68 65 61 70 20 69 6e 76 | ap.sort().maintains.the.heap.inv |
06e0 | 61 72 69 61 6e 74 21 0a 73 6f 12 00 00 48 65 61 70 20 71 75 65 75 65 73 0a 0a 5b 65 78 70 6c 61 | ariant!.so...Heap.queues..[expla |
0700 | 6e 61 74 69 6f 6e 20 62 79 20 46 72 61 6e e7 6f 69 73 20 50 69 6e 61 72 64 5d 0a 0a 48 65 61 70 | nation.by.Fran.ois.Pinard]..Heap |
0720 | 73 20 61 72 65 20 61 72 72 61 79 73 20 66 6f 72 20 77 68 69 63 68 20 61 5b 6b 5d 20 3c 3d 20 61 | s.are.arrays.for.which.a[k].<=.a |
0740 | 5b 32 2a 6b 2b 31 5d 20 61 6e 64 20 61 5b 6b 5d 20 3c 3d 20 61 5b 32 2a 6b 2b 32 5d 20 66 6f 72 | [2*k+1].and.a[k].<=.a[2*k+2].for |
0760 | 0a 61 6c 6c 20 6b 2c 20 63 6f 75 6e 74 69 6e 67 20 65 6c 65 6d 65 6e 74 73 20 66 72 6f 6d 20 30 | .all.k,.counting.elements.from.0 |
0780 | 2e 20 20 46 6f 72 20 74 68 65 20 73 61 6b 65 20 6f 66 20 63 6f 6d 70 61 72 69 73 6f 6e 2c 0a 6e | ...For.the.sake.of.comparison,.n |
07a0 | 6f 6e 2d 65 78 69 73 74 69 6e 67 20 65 6c 65 6d 65 6e 74 73 20 61 72 65 20 63 6f 6e 73 69 64 65 | on-existing.elements.are.conside |
07c0 | 72 65 64 20 74 6f 20 62 65 20 69 6e 66 69 6e 69 74 65 2e 20 20 54 68 65 20 69 6e 74 65 72 65 73 | red.to.be.infinite...The.interes |
07e0 | 74 69 6e 67 0a 70 72 6f 70 65 72 74 79 20 6f 66 20 61 20 68 65 61 70 20 69 73 20 74 68 61 74 20 | ting.property.of.a.heap.is.that. |
0800 | 61 5b 30 5d 20 69 73 20 61 6c 77 61 79 73 20 69 74 73 20 73 6d 61 6c 6c 65 73 74 20 65 6c 65 6d | a[0].is.always.its.smallest.elem |
0820 | 65 6e 74 2e 0a 0a 54 68 65 20 73 74 72 61 6e 67 65 20 69 6e 76 61 72 69 61 6e 74 20 61 62 6f 76 | ent...The.strange.invariant.abov |
0840 | 65 20 69 73 20 6d 65 61 6e 74 20 74 6f 20 62 65 20 61 6e 20 65 66 66 69 63 69 65 6e 74 20 6d 65 | e.is.meant.to.be.an.efficient.me |
0860 | 6d 6f 72 79 0a 72 65 70 72 65 73 65 6e 74 61 74 69 6f 6e 20 66 6f 72 20 61 20 74 6f 75 72 6e 61 | mory.representation.for.a.tourna |
0880 | 6d 65 6e 74 2e 20 20 54 68 65 20 6e 75 6d 62 65 72 73 20 62 65 6c 6f 77 20 61 72 65 20 60 6b 27 | ment...The.numbers.below.are.`k' |
08a0 | 2c 20 6e 6f 74 20 61 5b 6b 5d 3a 0a 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | ,.not.a[k]:..................... |
08c0 | 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 30 0a 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 | ................0............... |
08e0 | 20 20 20 20 20 31 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 | .....1.......................... |
0900 | 20 20 20 20 20 20 20 32 0a 0a 20 20 20 20 20 20 20 20 20 20 33 20 20 20 20 20 20 20 20 20 20 20 | .......2............3........... |
0920 | 20 20 20 20 34 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 35 20 20 20 20 20 20 20 20 20 20 | ....4................5.......... |
0940 | 20 20 20 20 20 36 0a 0a 20 20 20 20 20 20 37 20 20 20 20 20 20 20 38 20 20 20 20 20 20 20 39 20 | .....6........7.......8.......9. |
0960 | 20 20 20 20 20 20 31 30 20 20 20 20 20 20 31 31 20 20 20 20 20 20 31 32 20 20 20 20 20 20 31 33 | ......10......11......12......13 |
0980 | 20 20 20 20 20 20 31 34 0a 0a 20 20 20 20 31 35 20 31 36 20 20 20 31 37 20 31 38 20 20 20 31 39 | ......14......15.16...17.18...19 |
09a0 | 20 32 30 20 20 20 32 31 20 32 32 20 20 20 32 33 20 32 34 20 20 20 32 35 20 32 36 20 20 20 32 37 | .20...21.22...23.24...25.26...27 |
09c0 | 20 32 38 20 20 20 32 39 20 33 30 0a 0a 0a 49 6e 20 74 68 65 20 74 72 65 65 20 61 62 6f 76 65 2c | .28...29.30...In.the.tree.above, |
09e0 | 20 65 61 63 68 20 63 65 6c 6c 20 60 6b 27 20 69 73 20 74 6f 70 70 69 6e 67 20 60 32 2a 6b 2b 31 | .each.cell.`k'.is.topping.`2*k+1 |
0a00 | 27 20 61 6e 64 20 60 32 2a 6b 2b 32 27 2e 20 20 49 6e 0a 61 6e 20 75 73 75 61 6c 20 62 69 6e 61 | '.and.`2*k+2'...In.an.usual.bina |
0a20 | 72 79 20 74 6f 75 72 6e 61 6d 65 6e 74 20 77 65 20 73 65 65 20 69 6e 20 73 70 6f 72 74 73 2c 20 | ry.tournament.we.see.in.sports,. |
0a40 | 65 61 63 68 20 63 65 6c 6c 20 69 73 20 74 68 65 20 77 69 6e 6e 65 72 0a 6f 76 65 72 20 74 68 65 | each.cell.is.the.winner.over.the |
0a60 | 20 74 77 6f 20 63 65 6c 6c 73 20 69 74 20 74 6f 70 73 2c 20 61 6e 64 20 77 65 20 63 61 6e 20 74 | .two.cells.it.tops,.and.we.can.t |
0a80 | 72 61 63 65 20 74 68 65 20 77 69 6e 6e 65 72 20 64 6f 77 6e 20 74 68 65 20 74 72 65 65 0a 74 6f | race.the.winner.down.the.tree.to |
0aa0 | 20 73 65 65 20 61 6c 6c 20 6f 70 70 6f 6e 65 6e 74 73 20 73 2f 68 65 20 68 61 64 2e 20 20 48 6f | .see.all.opponents.s/he.had...Ho |
0ac0 | 77 65 76 65 72 2c 20 69 6e 20 6d 61 6e 79 20 63 6f 6d 70 75 74 65 72 20 61 70 70 6c 69 63 61 74 | wever,.in.many.computer.applicat |
0ae0 | 69 6f 6e 73 0a 6f 66 20 73 75 63 68 20 74 6f 75 72 6e 61 6d 65 6e 74 73 2c 20 77 65 20 64 6f 20 | ions.of.such.tournaments,.we.do. |
0b00 | 6e 6f 74 20 6e 65 65 64 20 74 6f 20 74 72 61 63 65 20 74 68 65 20 68 69 73 74 6f 72 79 20 6f 66 | not.need.to.trace.the.history.of |
0b20 | 20 61 20 77 69 6e 6e 65 72 2e 0a 54 6f 20 62 65 20 6d 6f 72 65 20 6d 65 6d 6f 72 79 20 65 66 66 | .a.winner..To.be.more.memory.eff |
0b40 | 69 63 69 65 6e 74 2c 20 77 68 65 6e 20 61 20 77 69 6e 6e 65 72 20 69 73 20 70 72 6f 6d 6f 74 65 | icient,.when.a.winner.is.promote |
0b60 | 64 2c 20 77 65 20 74 72 79 20 74 6f 0a 72 65 70 6c 61 63 65 20 69 74 20 62 79 20 73 6f 6d 65 74 | d,.we.try.to.replace.it.by.somet |
0b80 | 68 69 6e 67 20 65 6c 73 65 20 61 74 20 61 20 6c 6f 77 65 72 20 6c 65 76 65 6c 2c 20 61 6e 64 20 | hing.else.at.a.lower.level,.and. |
0ba0 | 74 68 65 20 72 75 6c 65 20 62 65 63 6f 6d 65 73 0a 74 68 61 74 20 61 20 63 65 6c 6c 20 61 6e 64 | the.rule.becomes.that.a.cell.and |
0bc0 | 20 74 68 65 20 74 77 6f 20 63 65 6c 6c 73 20 69 74 20 74 6f 70 73 20 63 6f 6e 74 61 69 6e 20 74 | .the.two.cells.it.tops.contain.t |
0be0 | 68 72 65 65 20 64 69 66 66 65 72 65 6e 74 20 69 74 65 6d 73 2c 0a 62 75 74 20 74 68 65 20 74 6f | hree.different.items,.but.the.to |
0c00 | 70 20 63 65 6c 6c 20 22 77 69 6e 73 22 20 6f 76 65 72 20 74 68 65 20 74 77 6f 20 74 6f 70 70 65 | p.cell."wins".over.the.two.toppe |
0c20 | 64 20 63 65 6c 6c 73 2e 0a 0a 49 66 20 74 68 69 73 20 68 65 61 70 20 69 6e 76 61 72 69 61 6e 74 | d.cells...If.this.heap.invariant |
0c40 | 20 69 73 20 70 72 6f 74 65 63 74 65 64 20 61 74 20 61 6c 6c 20 74 69 6d 65 2c 20 69 6e 64 65 78 | .is.protected.at.all.time,.index |
0c60 | 20 30 20 69 73 20 63 6c 65 61 72 6c 79 0a 74 68 65 20 6f 76 65 72 61 6c 6c 20 77 69 6e 6e 65 72 | .0.is.clearly.the.overall.winner |
0c80 | 2e 20 20 54 68 65 20 73 69 6d 70 6c 65 73 74 20 61 6c 67 6f 72 69 74 68 6d 69 63 20 77 61 79 20 | ...The.simplest.algorithmic.way. |
0ca0 | 74 6f 20 72 65 6d 6f 76 65 20 69 74 20 61 6e 64 0a 66 69 6e 64 20 74 68 65 20 22 6e 65 78 74 22 | to.remove.it.and.find.the."next" |
0cc0 | 20 77 69 6e 6e 65 72 20 69 73 20 74 6f 20 6d 6f 76 65 20 73 6f 6d 65 20 6c 6f 73 65 72 20 28 6c | .winner.is.to.move.some.loser.(l |
0ce0 | 65 74 27 73 20 73 61 79 20 63 65 6c 6c 20 33 30 20 69 6e 20 74 68 65 0a 64 69 61 67 72 61 6d 20 | et's.say.cell.30.in.the.diagram. |
0d00 | 61 62 6f 76 65 29 20 69 6e 74 6f 20 74 68 65 20 30 20 70 6f 73 69 74 69 6f 6e 2c 20 61 6e 64 20 | above).into.the.0.position,.and. |
0d20 | 74 68 65 6e 20 70 65 72 63 6f 6c 61 74 65 20 74 68 69 73 20 6e 65 77 20 30 20 64 6f 77 6e 0a 74 | then.percolate.this.new.0.down.t |
0d40 | 68 65 20 74 72 65 65 2c 20 65 78 63 68 61 6e 67 69 6e 67 20 76 61 6c 75 65 73 2c 20 75 6e 74 69 | he.tree,.exchanging.values,.unti |
0d60 | 6c 20 74 68 65 20 69 6e 76 61 72 69 61 6e 74 20 69 73 20 72 65 2d 65 73 74 61 62 6c 69 73 68 65 | l.the.invariant.is.re-establishe |
0d80 | 64 2e 0a 54 68 69 73 20 69 73 20 63 6c 65 61 72 6c 79 20 6c 6f 67 61 72 69 74 68 6d 69 63 20 6f | d..This.is.clearly.logarithmic.o |
0da0 | 6e 20 74 68 65 20 74 6f 74 61 6c 20 6e 75 6d 62 65 72 20 6f 66 20 69 74 65 6d 73 20 69 6e 20 74 | n.the.total.number.of.items.in.t |
0dc0 | 68 65 20 74 72 65 65 2e 0a 42 79 20 69 74 65 72 61 74 69 6e 67 20 6f 76 65 72 20 61 6c 6c 20 69 | he.tree..By.iterating.over.all.i |
0de0 | 74 65 6d 73 2c 20 79 6f 75 20 67 65 74 20 61 6e 20 4f 28 6e 20 6c 6e 20 6e 29 20 73 6f 72 74 2e | tems,.you.get.an.O(n.ln.n).sort. |
0e00 | 0a 0a 41 20 6e 69 63 65 20 66 65 61 74 75 72 65 20 6f 66 20 74 68 69 73 20 73 6f 72 74 20 69 73 | ..A.nice.feature.of.this.sort.is |
0e20 | 20 74 68 61 74 20 79 6f 75 20 63 61 6e 20 65 66 66 69 63 69 65 6e 74 6c 79 20 69 6e 73 65 72 74 | .that.you.can.efficiently.insert |
0e40 | 20 6e 65 77 0a 69 74 65 6d 73 20 77 68 69 6c 65 20 74 68 65 20 73 6f 72 74 20 69 73 20 67 6f 69 | .new.items.while.the.sort.is.goi |
0e60 | 6e 67 20 6f 6e 2c 20 70 72 6f 76 69 64 65 64 20 74 68 61 74 20 74 68 65 20 69 6e 73 65 72 74 65 | ng.on,.provided.that.the.inserte |
0e80 | 64 20 69 74 65 6d 73 20 61 72 65 0a 6e 6f 74 20 22 62 65 74 74 65 72 22 20 74 68 61 6e 20 74 68 | d.items.are.not."better".than.th |
0ea0 | 65 20 6c 61 73 74 20 30 27 74 68 20 65 6c 65 6d 65 6e 74 20 79 6f 75 20 65 78 74 72 61 63 74 65 | e.last.0'th.element.you.extracte |
0ec0 | 64 2e 20 20 54 68 69 73 20 69 73 0a 65 73 70 65 63 69 61 6c 6c 79 20 75 73 65 66 75 6c 20 69 6e | d...This.is.especially.useful.in |
0ee0 | 20 73 69 6d 75 6c 61 74 69 6f 6e 20 63 6f 6e 74 65 78 74 73 2c 20 77 68 65 72 65 20 74 68 65 20 | .simulation.contexts,.where.the. |
0f00 | 74 72 65 65 20 68 6f 6c 64 73 20 61 6c 6c 0a 69 6e 63 6f 6d 69 6e 67 20 65 76 65 6e 74 73 2c 20 | tree.holds.all.incoming.events,. |
0f20 | 61 6e 64 20 74 68 65 20 22 77 69 6e 22 20 63 6f 6e 64 69 74 69 6f 6e 20 6d 65 61 6e 73 20 74 68 | and.the."win".condition.means.th |
0f40 | 65 20 73 6d 61 6c 6c 65 73 74 20 73 63 68 65 64 75 6c 65 64 0a 74 69 6d 65 2e 20 20 57 68 65 6e | e.smallest.scheduled.time...When |
0f60 | 20 61 6e 20 65 76 65 6e 74 20 73 63 68 65 64 75 6c 65 20 6f 74 68 65 72 20 65 76 65 6e 74 73 20 | .an.event.schedule.other.events. |
0f80 | 66 6f 72 20 65 78 65 63 75 74 69 6f 6e 2c 20 74 68 65 79 20 61 72 65 0a 73 63 68 65 64 75 6c 65 | for.execution,.they.are.schedule |
0fa0 | 64 20 69 6e 74 6f 20 74 68 65 20 66 75 74 75 72 65 2c 20 73 6f 20 74 68 65 79 20 63 61 6e 20 65 | d.into.the.future,.so.they.can.e |
0fc0 | 61 73 69 6c 79 20 67 6f 20 69 6e 74 6f 20 74 68 65 20 68 65 61 70 2e 20 20 53 6f 2c 20 61 0a 68 | asily.go.into.the.heap...So,.a.h |
0fe0 | 65 61 70 20 69 73 20 61 20 67 6f 6f 64 20 73 74 72 75 63 74 75 72 65 20 66 6f 72 20 69 6d 70 6c | eap.is.a.good.structure.for.impl |
1000 | 65 6d 65 6e 74 69 6e 67 20 73 63 68 65 64 75 6c 65 72 73 20 28 74 68 69 73 20 69 73 20 77 68 61 | ementing.schedulers.(this.is.wha |
1020 | 74 20 49 0a 75 73 65 64 20 66 6f 72 20 6d 79 20 4d 49 44 49 20 73 65 71 75 65 6e 63 65 72 20 3a | t.I.used.for.my.MIDI.sequencer.: |
1040 | 2d 29 2e 0a 0a 56 61 72 69 6f 75 73 20 73 74 72 75 63 74 75 72 65 73 20 66 6f 72 20 69 6d 70 6c | -)...Various.structures.for.impl |
1060 | 65 6d 65 6e 74 69 6e 67 20 73 63 68 65 64 75 6c 65 72 73 20 68 61 76 65 20 62 65 65 6e 20 65 78 | ementing.schedulers.have.been.ex |
1080 | 74 65 6e 73 69 76 65 6c 79 0a 73 74 75 64 69 65 64 2c 20 61 6e 64 20 68 65 61 70 73 20 61 72 65 | tensively.studied,.and.heaps.are |
10a0 | 20 67 6f 6f 64 20 66 6f 72 20 74 68 69 73 2c 20 61 73 20 74 68 65 79 20 61 72 65 20 72 65 61 73 | .good.for.this,.as.they.are.reas |
10c0 | 6f 6e 61 62 6c 79 20 73 70 65 65 64 79 2c 0a 74 68 65 20 73 70 65 65 64 20 69 73 20 61 6c 6d 6f | onably.speedy,.the.speed.is.almo |
10e0 | 73 74 20 63 6f 6e 73 74 61 6e 74 2c 20 61 6e 64 20 74 68 65 20 77 6f 72 73 74 20 63 61 73 65 20 | st.constant,.and.the.worst.case. |
1100 | 69 73 20 6e 6f 74 20 6d 75 63 68 20 64 69 66 66 65 72 65 6e 74 0a 74 68 61 6e 20 74 68 65 20 61 | is.not.much.different.than.the.a |
1120 | 76 65 72 61 67 65 20 63 61 73 65 2e 20 20 48 6f 77 65 76 65 72 2c 20 74 68 65 72 65 20 61 72 65 | verage.case...However,.there.are |
1140 | 20 6f 74 68 65 72 20 72 65 70 72 65 73 65 6e 74 61 74 69 6f 6e 73 20 77 68 69 63 68 0a 61 72 65 | .other.representations.which.are |
1160 | 20 6d 6f 72 65 20 65 66 66 69 63 69 65 6e 74 20 6f 76 65 72 61 6c 6c 2c 20 79 65 74 20 74 68 65 | .more.efficient.overall,.yet.the |
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11a0 | 0a 48 65 61 70 73 20 61 72 65 20 61 6c 73 6f 20 76 65 72 79 20 75 73 65 66 75 6c 20 69 6e 20 62 | .Heaps.are.also.very.useful.in.b |
11c0 | 69 67 20 64 69 73 6b 20 73 6f 72 74 73 2e 20 20 59 6f 75 20 6d 6f 73 74 20 70 72 6f 62 61 62 6c | ig.disk.sorts...You.most.probabl |
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1240 | 69 73 20 75 73 75 61 6c 6c 79 20 72 65 6c 61 74 65 64 20 74 6f 20 74 68 65 20 61 6d 6f 75 6e 74 | is.usually.related.to.the.amount |
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12c0 | 6c 79 20 6f 72 67 61 6e 69 73 65 64 5b 31 5d 2e 20 20 49 74 20 69 73 20 76 65 72 79 20 69 6d 70 | ly.organised[1]...It.is.very.imp |
12e0 | 6f 72 74 61 6e 74 20 74 68 61 74 20 74 68 65 20 69 6e 69 74 69 61 6c 0a 73 6f 72 74 20 70 72 6f | ortant.that.the.initial.sort.pro |
1300 | 64 75 63 65 73 20 74 68 65 20 6c 6f 6e 67 65 73 74 20 72 75 6e 73 20 70 6f 73 73 69 62 6c 65 2e | duces.the.longest.runs.possible. |
1320 | 20 20 54 6f 75 72 6e 61 6d 65 6e 74 73 20 61 72 65 20 61 20 67 6f 6f 64 20 77 61 79 0a 74 6f 20 | ..Tournaments.are.a.good.way.to. |
1340 | 74 68 61 74 2e 20 20 49 66 2c 20 75 73 69 6e 67 20 61 6c 6c 20 74 68 65 20 6d 65 6d 6f 72 79 20 | that...If,.using.all.the.memory. |
1360 | 61 76 61 69 6c 61 62 6c 65 20 74 6f 20 68 6f 6c 64 20 61 20 74 6f 75 72 6e 61 6d 65 6e 74 2c 20 | available.to.hold.a.tournament,. |
1380 | 79 6f 75 0a 72 65 70 6c 61 63 65 20 61 6e 64 20 70 65 72 63 6f 6c 61 74 65 20 69 74 65 6d 73 20 | you.replace.and.percolate.items. |
13a0 | 74 68 61 74 20 68 61 70 70 65 6e 20 74 6f 20 66 69 74 20 74 68 65 20 63 75 72 72 65 6e 74 20 72 | that.happen.to.fit.the.current.r |
13c0 | 75 6e 2c 20 79 6f 75 27 6c 6c 0a 70 72 6f 64 75 63 65 20 72 75 6e 73 20 77 68 69 63 68 20 61 72 | un,.you'll.produce.runs.which.ar |
13e0 | 65 20 74 77 69 63 65 20 74 68 65 20 73 69 7a 65 20 6f 66 20 74 68 65 20 6d 65 6d 6f 72 79 20 66 | e.twice.the.size.of.the.memory.f |
1400 | 6f 72 20 72 61 6e 64 6f 6d 20 69 6e 70 75 74 2c 0a 61 6e 64 20 6d 75 63 68 20 62 65 74 74 65 72 | or.random.input,.and.much.better |
1420 | 20 66 6f 72 20 69 6e 70 75 74 20 66 75 7a 7a 69 6c 79 20 6f 72 64 65 72 65 64 2e 0a 0a 4d 6f 72 | .for.input.fuzzily.ordered...Mor |
1440 | 65 6f 76 65 72 2c 20 69 66 20 79 6f 75 20 6f 75 74 70 75 74 20 74 68 65 20 30 27 74 68 20 69 74 | eover,.if.you.output.the.0'th.it |
1460 | 65 6d 20 6f 6e 20 64 69 73 6b 20 61 6e 64 20 67 65 74 20 61 6e 20 69 6e 70 75 74 20 77 68 69 63 | em.on.disk.and.get.an.input.whic |
1480 | 68 0a 6d 61 79 20 6e 6f 74 20 66 69 74 20 69 6e 20 74 68 65 20 63 75 72 72 65 6e 74 20 74 6f 75 | h.may.not.fit.in.the.current.tou |
14a0 | 72 6e 61 6d 65 6e 74 20 28 62 65 63 61 75 73 65 20 74 68 65 20 76 61 6c 75 65 20 22 77 69 6e 73 | rnament.(because.the.value."wins |
14c0 | 22 20 6f 76 65 72 0a 74 68 65 20 6c 61 73 74 20 6f 75 74 70 75 74 20 76 61 6c 75 65 29 2c 20 69 | ".over.the.last.output.value),.i |
14e0 | 74 20 63 61 6e 6e 6f 74 20 66 69 74 20 69 6e 20 74 68 65 20 68 65 61 70 2c 20 73 6f 20 74 68 65 | t.cannot.fit.in.the.heap,.so.the |
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1520 | 65 20 66 72 65 65 64 20 6d 65 6d 6f 72 79 20 63 6f 75 6c 64 20 62 65 20 63 6c 65 76 65 72 6c 79 | e.freed.memory.could.be.cleverly |
1540 | 20 72 65 75 73 65 64 20 69 6d 6d 65 64 69 61 74 65 6c 79 0a 66 6f 72 20 70 72 6f 67 72 65 73 73 | .reused.immediately.for.progress |
1560 | 69 76 65 6c 79 20 62 75 69 6c 64 69 6e 67 20 61 20 73 65 63 6f 6e 64 20 68 65 61 70 2c 20 77 68 | ively.building.a.second.heap,.wh |
1580 | 69 63 68 20 67 72 6f 77 73 20 61 74 20 65 78 61 63 74 6c 79 20 74 68 65 0a 73 61 6d 65 20 72 61 | ich.grows.at.exactly.the.same.ra |
15a0 | 74 65 20 74 68 65 20 66 69 72 73 74 20 68 65 61 70 20 69 73 20 6d 65 6c 74 69 6e 67 2e 20 20 57 | te.the.first.heap.is.melting...W |
15c0 | 68 65 6e 20 74 68 65 20 66 69 72 73 74 20 68 65 61 70 20 63 6f 6d 70 6c 65 74 65 6c 79 0a 76 61 | hen.the.first.heap.completely.va |
15e0 | 6e 69 73 68 65 73 2c 20 79 6f 75 20 73 77 69 74 63 68 20 68 65 61 70 73 20 61 6e 64 20 73 74 61 | nishes,.you.switch.heaps.and.sta |
1600 | 72 74 20 61 20 6e 65 77 20 72 75 6e 2e 20 20 43 6c 65 76 65 72 20 61 6e 64 20 71 75 69 74 65 0a | rt.a.new.run...Clever.and.quite. |
1620 | 65 66 66 65 63 74 69 76 65 21 0a 0a 49 6e 20 61 20 77 6f 72 64 2c 20 68 65 61 70 73 20 61 72 65 | effective!..In.a.word,.heaps.are |
1640 | 20 75 73 65 66 75 6c 20 6d 65 6d 6f 72 79 20 73 74 72 75 63 74 75 72 65 73 20 74 6f 20 6b 6e 6f | .useful.memory.structures.to.kno |
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1720 | 6e 6e 6f 79 69 6e 67 20 74 68 61 6e 20 63 6c 65 76 65 72 2c 20 61 6e 64 20 74 68 69 73 20 69 73 | nnoying.than.clever,.and.this.is |
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17a0 | 0a 74 61 70 65 20 64 72 69 76 65 73 2c 20 74 68 65 20 73 74 6f 72 79 20 77 61 73 20 71 75 69 74 | .tape.drives,.the.story.was.quit |
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1860 | 65 20 61 74 0a 22 70 72 6f 67 72 65 73 73 69 6e 67 22 20 74 68 65 20 6d 65 72 67 65 29 2e 20 20 | e.at."progressing".the.merge)... |
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