Programm für den HP-42S zum Lösen des Puzzles ‚Türme von Hanoi‘.

Bedienung

• XEQ ‚HANOI‘
• Anzahl Scheiben [1..7] eingeben und R/S drücken
• Die Scheiben werden jetzt umgeschichtet
• Wenn das Puzzle gelöst ist, R/S drücken für Neustart

Programm

(Jetzt auch auf Github verfügbar)

{ 262-Byte Prgm }

;----------------------------------------------------------
; Towers of Hanoi

001 § LBL "HANOI"

; ask user to enter number of disks and limit it to
; the supported range [1..7]

002   INPUT "DISKS"
003   7
004   X>Y?
005   X<>Y
006   1
007   X<Y?
008   X<>Y
009   STO "DISKS"

010   STO 08             ; current disk size

; smallest disk is moved to the right if number of disks
; is even, otherwise it is moved to the left

011   1
012   AND
013   LASTX
014   +
015   STO 07

; disk 8 represents the basement and acts as a sentinel
; when moving disks

016   8
017   STO 00
018   STO 01
019   STO 02

; initialize other data registers to zero

020   CLX
021   STO 03
022   STO 04
023   STO 05
024   STO 06
025   STO 09

; set default AGRAPH mode

026   CF 34
027   CF 35

; draw basement

028   CLLCD
029   -15
030   X<>Y
031   PIXEL
032   -16
033   X<>Y
034   PIXEL

; set up initial tower

035 § LBL 00
036   XEQ 04
037   XEQ 02
038   DSE 08
039   GTO 00

; start solving puzzle

040   TONE 3
041   TONE 1
042   GTO 08

;----------------------------------------------------------
; remove disk of size R08 from pile R09

043 § LBL 01

; erase disk

044   SF 34
045   XEQ 03

; decrease tower height

046   RCL 09
047   3
048   +
049   DSE IND ST X
050   CLX

; update tower configuration
; (4 bits per disk)

051   RCL IND 09
052   16
053   ÷
054   IP
055   STO IND 09

056   RTN

;----------------------------------------------------------
; put disk of size R08 onto pile R09

057 § LBL 02

; update tower configuration
; (4 bits per disk)

058   RCL IND 09
059   16
060   x
061   RCL 08
062   +
063   STO IND 09

; increase tower height

064   RCL 09
065   3
066   +
067   ISG IND ST X
068   CLX

; draw disk and return

069   CF 34

;----------------------------------------------------------
; draw topmost disk of size R08 on pile R09
; assumes ALPHA register contains disk pattern
; SF 34, CF 35 will erase the disk

070 § LBL 03

; compute display row
; r := 15 - 2h(p)

071   RCL 09
072   3
073   +
074   15
075   RCL IND ST Y
076   ENTER
077   +
078   -

; compute display column
; c := 35p + 31 - 2s

079   RCL 09
080   35
081   x
082   31
083   +
084   RCL 08
085   ENTER
086   +
087   -

; finally, draw the disk

088   AGRAPH
089   RTN

;----------------------------------------------------------
; build string for drawing disk of size R08

090 § LBL 04

; width of disk in pixels := 4s + 1

091   "x"                ; hex 01
092   RCL 08
093   LBL 05
094   |-"xxxx"           ; hex 01 01 01 01
095   DSE ST X
096   GTO 05

097   RTN

;----------------------------------------------------------
; main loop

098 § LBL 06

; determine the one and only possible move after the
; smallest disk has been moved

; get indices of piles next to smallest disk

099   RCL 06
100   1
101   +
102   3
103   MOD
104   STO 09

105   1
106   +
107   3
108   MOD
109   STO 10

; get sizes of topmost disks on these piles

110   RCL IND 09
111   15
112   AND
113   STO 08

114   LASTX
115   RCL IND 10
116   AND

; test which move is legal

117   X>Y?
118   GTO 07

; move disk from pile R10 to pile R09

119   STO 08
120   RCL 10
121   X<> 09
122   STO 10

; move disk from pile R09 to pile R10

123 § LBL 07
124   XEQ 04
125   XEQ 01
126   RCL 10
127   STO 09
128   XEQ 02

129 § LBL 08

; remove smallest disk

130   1
131   STO 08
132   RCL 06
133   STO 09
134   XEQ 04
135   XEQ 01

; move it to the next pile

136   RCL 06
137   RCL 07
138   +
139   3
140   MOD
141   STO 06
142   STO 09
143   XEQ 02

; puzzle solved if all disk are on target pile

144   RCL "DISKS"
145   RCL 05
146   X<Y?
147   GTO 06

148   TONE 5
149   TONE 8
150   END

Register Usage
--------------
R00   configuration of tower 1
R01   configuration of tower 2
R02   configuration of tower 3
R03   height of tower 1
R04   height of tower 2
R05   height of tower 3
R06   pile with smallest disk
R07   smallest disk move
R08   current disk
R09   current pile
R10   destination pile

Definitions
-----------
s     size of disk [1..7]
p     pile number [0..2]
h     height of pile p
w     width of disk in pixels
      w := 4s + 1
r     display row of topmost disk on pile p
      r := 15 - 2h
c     display column of topmost disk on pile p
      c := 35p + 31 - 2s