�>>> Hanoi towers
9�    Alain BROBECKER (baah/Arm's Tech) on ??-Jan-1998

(2�Algorithm is based upon the following fact...
2K�Moving the pile of N elements from stick I to stick J is equivalent to
</�  1) moving the N-1 elts' pile from I to K
F)�  2) moving the last elt from I to J
P/�  3) moving the N-1 elts' pile from K to J
Z$�9:�:�c%=1�15:�c%,c%*17,5*17,0:�
d)nb%=12                  :�nb of rings
n*s%=32                   :�size of ring
x2max%=(nb%+1)*s%         :�size of biggest ring
�6�size%(2):size%()=max%,0,0 :�sizes of bottom rings
�H�c%=1�nb%:�box(c%,0,(nb%+1-c%)*s%,c%*s%/2):� :�draw initial position
��
��Hanoi(nb%,0,1,2)
��
�
� ��Hanoi(nb%,from%,to%,temp%)
� �nb%�
�#  �Hanoi(nb%-1,from%,temp%,to%)
�  Ȗ
�)  �box(0,from%,size%(from%),nb%*s%/2)
�  size%(from%)-=s%
�  size%(to%)+=s%

'  �box(nb%,to%,size%(to%),nb%*s%/2)

#  �Hanoi(nb%-1,temp%,to%,from%)

 �

"�

,

6��box(col%,x%,y%,size%)

@
 �col%

J) ȓȐx%*400+200-size%,y%,2*size%,s%/2

T�
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00000000  0d 00 0a 15 f4 3e 3e 3e  20 48 61 6e 6f 69 20 74  |.....>>> Hanoi t|
00000010  6f 77 65 72 73 0d 00 14  39 f4 20 20 20 20 41 6c  |owers...9.    Al|
00000020  61 69 6e 20 42 52 4f 42  45 43 4b 45 52 20 28 62  |ain BROBECKER (b|
00000030  61 61 68 2f 41 72 6d 27  73 20 54 65 63 68 29 20  |aah/Arm's Tech) |
00000040  6f 6e 20 3f 3f 2d 4a 61  6e 2d 31 39 39 38 0d 00  |on ??-Jan-1998..|
00000050  1e 04 0d 00 28 32 f4 41  6c 67 6f 72 69 74 68 6d  |....(2.Algorithm|
00000060  20 69 73 20 62 61 73 65  64 20 75 70 6f 6e 20 74  | is based upon t|
00000070  68 65 20 66 6f 6c 6c 6f  77 69 6e 67 20 66 61 63  |he following fac|
00000080  74 2e 2e 2e 0d 00 32 4b  f4 4d 6f 76 69 6e 67 20  |t.....2K.Moving |
00000090  74 68 65 20 70 69 6c 65  20 6f 66 20 4e 20 65 6c  |the pile of N el|
000000a0  65 6d 65 6e 74 73 20 66  72 6f 6d 20 73 74 69 63  |ements from stic|
000000b0  6b 20 49 20 74 6f 20 73  74 69 63 6b 20 4a 20 69  |k I to stick J i|
000000c0  73 20 65 71 75 69 76 61  6c 65 6e 74 20 74 6f 0d  |s equivalent to.|
000000d0  00 3c 2f f4 20 20 31 29  20 6d 6f 76 69 6e 67 20  |.</.  1) moving |
000000e0  74 68 65 20 4e 2d 31 20  65 6c 74 73 27 20 70 69  |the N-1 elts' pi|
000000f0  6c 65 20 66 72 6f 6d 20  49 20 74 6f 20 4b 0d 00  |le from I to K..|
00000100  46 29 f4 20 20 32 29 20  6d 6f 76 69 6e 67 20 74  |F).  2) moving t|
00000110  68 65 20 6c 61 73 74 20  65 6c 74 20 66 72 6f 6d  |he last elt from|
00000120  20 49 20 74 6f 20 4a 0d  00 50 2f f4 20 20 33 29  | I to J..P/.  3)|
00000130  20 6d 6f 76 69 6e 67 20  74 68 65 20 4e 2d 31 20  | moving the N-1 |
00000140  65 6c 74 73 27 20 70 69  6c 65 20 66 72 6f 6d 20  |elts' pile from |
00000150  4b 20 74 6f 20 4a 0d 00  5a 24 eb 39 3a 87 3a e3  |K to J..Z$.9:.:.|
00000160  63 25 3d 31 b8 31 35 3a  fb 63 25 2c 63 25 2a 31  |c%=1.15:.c%,c%*1|
00000170  37 2c 35 2a 31 37 2c 30  3a ed 0d 00 64 29 6e 62  |7,5*17,0:...d)nb|
00000180  25 3d 31 32 20 20 20 20  20 20 20 20 20 20 20 20  |%=12            |
00000190  20 20 20 20 20 20 3a f4  6e 62 20 6f 66 20 72 69  |      :.nb of ri|
000001a0  6e 67 73 0d 00 6e 2a 73  25 3d 33 32 20 20 20 20  |ngs..n*s%=32    |
000001b0  20 20 20 20 20 20 20 20  20 20 20 20 20 20 20 3a  |               :|
000001c0  f4 73 69 7a 65 20 6f 66  20 72 69 6e 67 0d 00 78  |.size of ring..x|
000001d0  32 6d 61 78 25 3d 28 6e  62 25 2b 31 29 2a 73 25  |2max%=(nb%+1)*s%|
000001e0  20 20 20 20 20 20 20 20  20 3a f4 73 69 7a 65 20  |         :.size |
000001f0  6f 66 20 62 69 67 67 65  73 74 20 72 69 6e 67 0d  |of biggest ring.|
00000200  00 82 36 de 73 69 7a 65  25 28 32 29 3a 73 69 7a  |..6.size%(2):siz|
00000210  65 25 28 29 3d 6d 61 78  25 2c 30 2c 30 20 3a f4  |e%()=max%,0,0 :.|
00000220  73 69 7a 65 73 20 6f 66  20 62 6f 74 74 6f 6d 20  |sizes of bottom |
00000230  72 69 6e 67 73 0d 00 8c  48 e3 63 25 3d 31 b8 6e  |rings...H.c%=1.n|
00000240  62 25 3a f2 62 6f 78 28  63 25 2c 30 2c 28 6e 62  |b%:.box(c%,0,(nb|
00000250  25 2b 31 2d 63 25 29 2a  73 25 2c 63 25 2a 73 25  |%+1-c%)*s%,c%*s%|
00000260  2f 32 29 3a ed 20 3a f4  64 72 61 77 20 69 6e 69  |/2):. :.draw ini|
00000270  74 69 61 6c 20 70 6f 73  69 74 69 6f 6e 0d 00 96  |tial position...|
00000280  06 e7 a5 0d 00 a0 15 f2  48 61 6e 6f 69 28 6e 62  |........Hanoi(nb|
00000290  25 2c 30 2c 31 2c 32 29  0d 00 aa 05 e0 0d 00 b4  |%,0,1,2)........|
000002a0  04 0d 00 be 20 dd f2 48  61 6e 6f 69 28 6e 62 25  |.... ..Hanoi(nb%|
000002b0  2c 66 72 6f 6d 25 2c 74  6f 25 2c 74 65 6d 70 25  |,from%,to%,temp%|
000002c0  29 0d 00 c8 0b 20 e7 ac  6e 62 25 8c 0d 00 d2 23  |).... ..nb%....#|
000002d0  20 20 f2 48 61 6e 6f 69  28 6e 62 25 2d 31 2c 66  |  .Hanoi(nb%-1,f|
000002e0  72 6f 6d 25 2c 74 65 6d  70 25 2c 74 6f 25 29 0d  |rom%,temp%,to%).|
000002f0  00 dc 08 20 20 c8 96 0d  00 e6 29 20 20 f2 62 6f  |...  .....)  .bo|
00000300  78 28 30 2c 66 72 6f 6d  25 2c 73 69 7a 65 25 28  |x(0,from%,size%(|
00000310  66 72 6f 6d 25 29 2c 6e  62 25 2a 73 25 2f 32 29  |from%),nb%*s%/2)|
00000320  0d 00 f0 16 20 20 73 69  7a 65 25 28 66 72 6f 6d  |....  size%(from|
00000330  25 29 2d 3d 73 25 0d 00  fa 14 20 20 73 69 7a 65  |%)-=s%....  size|
00000340  25 28 74 6f 25 29 2b 3d  73 25 0d 01 04 27 20 20  |%(to%)+=s%...'  |
00000350  f2 62 6f 78 28 6e 62 25  2c 74 6f 25 2c 73 69 7a  |.box(nb%,to%,siz|
00000360  65 25 28 74 6f 25 29 2c  6e 62 25 2a 73 25 2f 32  |e%(to%),nb%*s%/2|
00000370  29 0d 01 0e 23 20 20 f2  48 61 6e 6f 69 28 6e 62  |)...#  .Hanoi(nb|
00000380  25 2d 31 2c 74 65 6d 70  25 2c 74 6f 25 2c 66 72  |%-1,temp%,to%,fr|
00000390  6f 6d 25 29 0d 01 18 06  20 cd 0d 01 22 05 e1 0d  |om%).... ..."...|
000003a0  01 2c 04 0d 01 36 1b dd  f2 62 6f 78 28 63 6f 6c  |.,...6...box(col|
000003b0  25 2c 78 25 2c 79 25 2c  73 69 7a 65 25 29 0d 01  |%,x%,y%,size%)..|
000003c0  40 0a 20 e6 63 6f 6c 25  0d 01 4a 29 20 c8 93 c8  |@. .col%..J) ...|
000003d0  90 78 25 2a 34 30 30 2b  32 30 30 2d 73 69 7a 65  |.x%*400+200-size|
000003e0  25 2c 79 25 2c 32 2a 73  69 7a 65 25 2c 73 25 2f  |%,y%,2*size%,s%/|
000003f0  32 0d 01 54 05 e1 0d ff                           |2..T....|
000003f8