; Tower of Hanoi Model,
;
; Shows Tower of Hanoi Animation
;
; Copyright 2010 Shayryl Mae Ramos. All Rights Reserved.
;

globals[ 
         headx_disk ; indicates the x position of a particular disk
         rpt        ; used to indicate the appropriate x position of turtle(s) assigned in particular  disk
         container    ; this is used a container for disks, each disk may contain several turtles to form the ascending effect of disks
         step       ; indicates number of movements to be performed for particular number of disks
       ] 

to start

ca
set-default-shape turtles tiles
set step 1

;; the following will setup intial display of the screen
ask patches[
  if pycor >= -14 and pycor <= 14[set pcolor white]                                                           
  if (pxcor >= -9) and (pxcor <= 9) and (pycor = -12) [ set pcolor 109]                                       
  if (pxcor >= -33) and (pxcor <= -15) and (pycor = -12) [ set pcolor 109]
  if (pxcor >= 15) and (pxcor <= 33) and (pycor = -12) [ set pcolor 109]
  if (pycor >= -11 and pycor <= 5) and (pxcor = -24 or pxcor = 0 or pxcor = 24) [set pcolor 129]
  if (pycor = 12 and pxcor = 3) [ set plabel-color black set plabel "TOWER OF HANOI"]
  if (pycor = 7 and pxcor = -24) [ set plabel-color red set plabel "A"]
  if (pycor = 7 and pxcor = 0) [ set plabel-color red set plabel "B"]
  if (pycor = 7 and pxcor = 24) [ set plabel-color red set plabel "C"]
]

end

;; this will display the disks in the intial pole - A
to go
cd

let y -11                    ; the y position at the bottom of the pole
let num disks                ; the number of disks
set container[]              ; container for the disks, it contains sublist of of turtles


drawTurtles                  ; this will call drawTurtles function

  repeat disks[
    
    create-turtles 1[                                             ; this will create the first turtle of the current disk
      setxy headx_disk y                                          ; location of the first turtle
      hatch (2 * num) - 2                                         ; other turtles are created for the current disk
      set container lput [who] of turtles-here container          ; turtles are added to the container for proper ordering
    ]
   
       
   let x (headx_disk + 1)                                         ; this will create a new variable which will take headx_disk + 1 value
   
     ask turtles[                                                 ; for the newly created turtles in the current disk
      if count turtles-here != 1[ move-to patch x y set x x + 1 ] ; sets its location, y value is the same for all turtles in the current disk
      
    ] 
     
    set y y + 1                                                   ; increment the value of y for the next disk
    set num num - 1                                               ; decrement num for the next disk to tackle
    set headx_disk headx_disk + 1                                 ; increment headx_disk for the next disk
  ]
set container reverse container                                   ; this will arrange disks in ascending order


  
end


to drawTurtles
let base -24                                                      ; the center point for Pole A is -24 
ifelse disks = 1 [ set headx_disk base]                           ; if disk = 1, the turtle is placed at the center of the Pole A
[
  set headx_disk (base + 1) - disks                               ;  the leftmost turtle of the current disk will have this value
]

end

; this function contains x-values for disks for proper positioning
; num indicates the number of turtles in each disk
to-report checkloc[num w]

  if num = 19[ if w ="A"[set rpt -33] if w ="B"[set rpt -9] if w ="C"[set rpt 15] ]       ; disk 10
  if num = 17[ if w ="A"[set rpt -32] if w ="B"[set rpt -8] if w ="C"[set rpt 16] ]       ; disk 9
  if num = 15[ if w ="A"[set rpt -31] if w ="B"[set rpt -7] if w ="C"[set rpt 17] ]       ; disk 8
  if num = 13[ if w ="A"[set rpt -30] if w ="B"[set rpt -6] if w ="C"[set rpt 18] ]       ; disk 7
  if num = 11[ if w ="A"[set rpt -29] if w ="B"[set rpt -5] if w ="C"[set rpt 19] ]       ; disk 6
  if num = 9 [ if w ="A"[set rpt -28] if w ="B"[set rpt -4] if w ="C"[set rpt 20] ]       ; disk 5
  if num = 7 [ if w ="A"[set rpt -27] if w ="B"[set rpt -3] if w ="C"[set rpt 21] ]       ; disk 4
  if num = 5 [ if w ="A"[set rpt -26] if w ="B"[set rpt -2] if w ="C"[set rpt 22] ]       ; disk 3
  if num = 3 [ if w ="A"[set rpt -25] if w ="B"[set rpt -1] if w ="C"[set rpt 23] ]       ; disk 2
  if num = 1 [ if w ="A"[set rpt -24] if w ="B"[set rpt 0]  if w ="C"[set rpt 24] ]       ; disk 1
  report rpt
end

; this function will return 1 if the pole is not empty
to-report clear[ des ypos ]
let tt 0
let xl 0
let xb 0

if des = "A" [set xl -33 set xb -15]
if des = "B" [set xl -9 set xb 9]
if des = "C" [set xl 15 set xb 33]

if count turtles with [ycor = ypos and xcor >= xl and xcor <= xb] != 0 [set tt 1]

report tt

end


; this is used for y-coordinate positioning for each pole
; if there are any turtles in the current y position, ypos value will be incremented
to-report yPosition[ des ypos ]
let tt 0
let xl 0
let xb 0

if des = "A" [set xl -33 set xb -15]
if des = "B" [set xl -9 set xb 9]
if des = "C" [set xl 15 set xb 33]

while [count turtles with [ycor = ypos and xcor >= xl and xcor <= xb] != 0] [
   set ypos ypos + 1
  ]

report ypos

end

; this will start animation by calling hanoi function
to play                 
hanoi disks "A" "C" "B"  
end

; hanoi algorithm
to hanoi[p A C B]               

ifelse p = 0 [stop]
 [
  hanoi(p - 1) A B C 
  animate p A C                 ; animate function is called 
  hanoi(p - 1) B C A
 ]

end


to animate[d src des]
let l 0
let m 0
let y -11

let d1 (d - 1)                        ; this will be used to access conatainer. d1 indicated index value
let u item d1 container               ; u will get item value of index d1 in container
let v length item d1 container        ; the length indicates which varies according to disk numbers
let w yPosition des y                 ; destination pole y position value


; all disk movements will be displayed in the text area 
output-type "Step " output-type step 
output-type ". Move " output-type d
output-type " from "output-type  src 
output-type  " to " output-type  des 
output-print ""

set step step + 1                     ; increments step

wait 3                                ; will pause before moving

set m checkloc v des                  ; this will get the assigned x location for different disks

ifelse clear des y = 0 [ 
  foreach u [                         ; this will move all the turtles in a current disk to new position 
    ask turtle ?[ 
      setxy m w
      set m m + 1 
    ]
  ]
][animate2 d des y]

end

; this function is basically the same with the previous function, 
; created a duplicate function to terminate infinite looping.
to animate2[d des yl]
let l 0
let m 0
let y -11
let d1 (d - 1)

let u item d1 container
let v length item d1 container
let w yPosition des y

wait 3

set m checkloc v des

  foreach u [ 
    ask turtle ?[ 
      setxy m w
      set m m + 1 
    ]
  ]
end

;
; Copyright 2010 by Shayryl Mae Ramos.  All rights reserved.
;
; Permission to use, modify or redistribute this model is hereby granted,
; provided that both of the following requirements are followed:
; a) this copyright notice is included.
; b) this model will not be redistributed for profit without permission
;    from Shayryl Mae Ramos.
; Contact Shayryl Mae Ramos for appropriate licenses for redistribution for
; profit. Email at: shayrylmae@gmail.com
;
; To refer to this model in publications, please use:
;
; Ramos, S. L. (2010).  Tower of Hanoi.
;   
;

@#$#@#$#@
GRAPHICS-WINDOW
291
14
1176
377
43
16
10.061
1
10
1
1
1
0
0
0
1
-43
43
-16
16
0
0
1
ticks

BUTTON
11
10
74
43
NIL
start\n
NIL
1
T
OBSERVER
NIL
NIL
NIL
NIL

BUTTON
79
10
142
43
NIL
go
NIL
1
T
OBSERVER
NIL
NIL
NIL
NIL

SLIDER
117
58
209
91
disks
disks
1
10
3
1
1
NIL
HORIZONTAL

CHOOSER
15
55
107
100
tiles
tiles
"airplane" "arrow" "box" "bug" "butterfly" "car" "circle" "face happy" "fish" "flag" "flower" "house" "leaf" "pentagon" "person" "plant" "sheep" "square" "star" "target" "tree" "triangle" "x"
22

BUTTON
147
10
210
43
NIL
play
NIL
1
T
OBSERVER
NIL
NIL
NIL
NIL

MONITOR
65
110
170
159
No. of Steps
(2 ^ disks) - 1
17
1
12

OUTPUT
20
181
282
376
10

@#$#@#$#@
WHAT IS IT?
-----------
The Tower of Hanoi or Towers of Hanoi is a mathematical game or puzzle. It consists of three poles, and a number of disks of different sizes which can slide onto any poles. The puzzle starts with the disks in a stack in ascending order of size on pole A, the smallest at the top, thus making a conical shape.

The objective of the puzzle is to move the entire stack to another pole according to the following rules:

1. Only one disk may be moved at a time.
2. Each move consists of taking the upper disk from one of the poles and sliding it onto another pole, on top of the other disks that may already be present on that pole.
3.No disk may be placed on top of a smaller disk.

HOW IT WORKS
------------

In this program, set of turtles are used to represent a disk which are stored in a list. Once the disk number is called, the assiged set of turtles of that particular disk will be moved from one location to another. And to prevent overlapping of disks, a function will check if there are turtles on the desired region.


HOW TO USE IT
-------------
-Select the desired disk design in the drop-down box
-Adjust slider according to the number of disks

-Click START button to load background and poles
-Click GO button to display disks in Pole A
-Click PLAY button to run animation


THINGS TO NOTICE
----------------
Notice the turtles in each disks, these turtles will all move to the destination postion. Each of the turtles will move to their assigned locations in A, B and C.

Notice that all turtles in a disk have the same color, this is because color property of the leftmost turtle is copied.


THINGS TO TRY
-------------
Try to adjust disk size, the number of steps will also change, thus the amount of time to perform the animation will also increase. 


EXTENDING THE MODEL
-------------------
In the current implementation, all disks will move directly to the destination postion. Try enhancing the animation such that all disks must move up from the current pole, then left (or right) and then move down to the desired location. In this way, it will be more realistic.


NETLOGO FEATURES
----------------
Note the use of hatch and the positioning of turtles. These are used to create increasing disks.


CREDITS AND REFERENCES
----------------------
This model was created by Shayryl Mae Ramos. For concerns, email at shayrylmae@gmail.com

To refer to this model in publications, please use:

Tower of Hanoi. Ramos, S. L. (2010). 
@#$#@#$#@
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airplane
true
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Polygon -7500403 true true 150 0 135 15 120 60 120 105 15 165 15 195 120 180 135 240 105 270 120 285 150 270 180 285 210 270 165 240 180 180 285 195 285 165 180 105 180 60 165 15

arrow
true
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Polygon -7500403 true true 150 0 0 150 105 150 105 293 195 293 195 150 300 150

box
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Polygon -7500403 true true 150 285 285 225 285 75 150 135
Polygon -7500403 true true 150 135 15 75 150 15 285 75
Polygon -7500403 true true 15 75 15 225 150 285 150 135
Line -16777216 false 150 285 150 135
Line -16777216 false 150 135 15 75
Line -16777216 false 150 135 285 75

bug
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Circle -7500403 true true 96 182 108
Circle -7500403 true true 110 127 80
Circle -7500403 true true 110 75 80
Line -7500403 true 150 100 80 30
Line -7500403 true 150 100 220 30

butterfly
true
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Polygon -7500403 true true 150 165 209 199 225 225 225 255 195 270 165 255 150 240
Polygon -7500403 true true 150 165 89 198 75 225 75 255 105 270 135 255 150 240
Polygon -7500403 true true 139 148 100 105 55 90 25 90 10 105 10 135 25 180 40 195 85 194 139 163
Polygon -7500403 true true 162 150 200 105 245 90 275 90 290 105 290 135 275 180 260 195 215 195 162 165
Polygon -16777216 true false 150 255 135 225 120 150 135 120 150 105 165 120 180 150 165 225
Circle -16777216 true false 135 90 30
Line -16777216 false 150 105 195 60
Line -16777216 false 150 105 105 60

car
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Polygon -7500403 true true 300 180 279 164 261 144 240 135 226 132 213 106 203 84 185 63 159 50 135 50 75 60 0 150 0 165 0 225 300 225 300 180
Circle -16777216 true false 180 180 90
Circle -16777216 true false 30 180 90
Polygon -16777216 true false 162 80 132 78 134 135 209 135 194 105 189 96 180 89
Circle -7500403 true true 47 195 58
Circle -7500403 true true 195 195 58

circle
false
0
Circle -7500403 true true 0 0 300

circle 2
false
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Circle -7500403 true true 0 0 300
Circle -16777216 true false 30 30 240

cow
false
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Polygon -7500403 true true 200 193 197 249 179 249 177 196 166 187 140 189 93 191 78 179 72 211 49 209 48 181 37 149 25 120 25 89 45 72 103 84 179 75 198 76 252 64 272 81 293 103 285 121 255 121 242 118 224 167
Polygon -7500403 true true 73 210 86 251 62 249 48 208
Polygon -7500403 true true 25 114 16 195 9 204 23 213 25 200 39 123

cylinder
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Circle -7500403 true true 0 0 300

dot
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Circle -7500403 true true 90 90 120

face happy
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Circle -16777216 true false 60 75 60
Circle -16777216 true false 180 75 60
Polygon -16777216 true false 150 255 90 239 62 213 47 191 67 179 90 203 109 218 150 225 192 218 210 203 227 181 251 194 236 217 212 240

face neutral
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Circle -7500403 true true 8 7 285
Circle -16777216 true false 60 75 60
Circle -16777216 true false 180 75 60
Rectangle -16777216 true false 60 195 240 225

face sad
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Circle -7500403 true true 8 8 285
Circle -16777216 true false 60 75 60
Circle -16777216 true false 180 75 60
Polygon -16777216 true false 150 168 90 184 62 210 47 232 67 244 90 220 109 205 150 198 192 205 210 220 227 242 251 229 236 206 212 183

fish
false
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Polygon -1 true false 44 131 21 87 15 86 0 120 15 150 0 180 13 214 20 212 45 166
Polygon -1 true false 135 195 119 235 95 218 76 210 46 204 60 165
Polygon -1 true false 75 45 83 77 71 103 86 114 166 78 135 60
Polygon -7500403 true true 30 136 151 77 226 81 280 119 292 146 292 160 287 170 270 195 195 210 151 212 30 166
Circle -16777216 true false 215 106 30

flag
false
0
Rectangle -7500403 true true 60 15 75 300
Polygon -7500403 true true 90 150 270 90 90 30
Line -7500403 true 75 135 90 135
Line -7500403 true 75 45 90 45

flower
false
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Polygon -10899396 true false 135 120 165 165 180 210 180 240 150 300 165 300 195 240 195 195 165 135
Circle -7500403 true true 85 132 38
Circle -7500403 true true 130 147 38
Circle -7500403 true true 192 85 38
Circle -7500403 true true 85 40 38
Circle -7500403 true true 177 40 38
Circle -7500403 true true 177 132 38
Circle -7500403 true true 70 85 38
Circle -7500403 true true 130 25 38
Circle -7500403 true true 96 51 108
Circle -16777216 true false 113 68 74
Polygon -10899396 true false 189 233 219 188 249 173 279 188 234 218
Polygon -10899396 true false 180 255 150 210 105 210 75 240 135 240

house
false
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Rectangle -7500403 true true 45 120 255 285
Rectangle -16777216 true false 120 210 180 285
Polygon -7500403 true true 15 120 150 15 285 120
Line -16777216 false 30 120 270 120

leaf
false
0
Polygon -7500403 true true 150 210 135 195 120 210 60 210 30 195 60 180 60 165 15 135 30 120 15 105 40 104 45 90 60 90 90 105 105 120 120 120 105 60 120 60 135 30 150 15 165 30 180 60 195 60 180 120 195 120 210 105 240 90 255 90 263 104 285 105 270 120 285 135 240 165 240 180 270 195 240 210 180 210 165 195
Polygon -7500403 true true 135 195 135 240 120 255 105 255 105 285 135 285 165 240 165 195

line
true
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Line -7500403 true 150 0 150 300

line half
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Line -7500403 true 150 0 150 150

pentagon
false
0
Polygon -7500403 true true 150 15 15 120 60 285 240 285 285 120

person
false
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Circle -7500403 true true 110 5 80
Polygon -7500403 true true 105 90 120 195 90 285 105 300 135 300 150 225 165 300 195 300 210 285 180 195 195 90
Rectangle -7500403 true true 127 79 172 94
Polygon -7500403 true true 195 90 240 150 225 180 165 105
Polygon -7500403 true true 105 90 60 150 75 180 135 105

plant
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0
Rectangle -7500403 true true 135 90 165 300
Polygon -7500403 true true 135 255 90 210 45 195 75 255 135 285
Polygon -7500403 true true 165 255 210 210 255 195 225 255 165 285
Polygon -7500403 true true 135 180 90 135 45 120 75 180 135 210
Polygon -7500403 true true 165 180 165 210 225 180 255 120 210 135
Polygon -7500403 true true 135 105 90 60 45 45 75 105 135 135
Polygon -7500403 true true 165 105 165 135 225 105 255 45 210 60
Polygon -7500403 true true 135 90 120 45 150 15 180 45 165 90

sheep
false
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Rectangle -7500403 true true 151 225 180 285
Rectangle -7500403 true true 47 225 75 285
Rectangle -7500403 true true 15 75 210 225
Circle -7500403 true true 135 75 150
Circle -16777216 true false 165 76 116

square
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Rectangle -7500403 true true 30 30 270 270

square 2
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Rectangle -7500403 true true 30 30 270 270
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star
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Polygon -7500403 true true 151 1 185 108 298 108 207 175 242 282 151 216 59 282 94 175 3 108 116 108

target
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0
Circle -7500403 true true 0 0 300
Circle -16777216 true false 30 30 240
Circle -7500403 true true 60 60 180
Circle -16777216 true false 90 90 120
Circle -7500403 true true 120 120 60

tree
false
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Circle -7500403 true true 118 3 94
Rectangle -6459832 true false 120 195 180 300
Circle -7500403 true true 65 21 108
Circle -7500403 true true 116 41 127
Circle -7500403 true true 45 90 120
Circle -7500403 true true 104 74 152

triangle
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Polygon -7500403 true true 150 30 15 255 285 255

triangle 2
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truck
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Rectangle -7500403 true true 4 45 195 187
Polygon -7500403 true true 296 193 296 150 259 134 244 104 208 104 207 194
Rectangle -1 true false 195 60 195 105
Polygon -16777216 true false 238 112 252 141 219 141 218 112
Circle -16777216 true false 234 174 42
Rectangle -7500403 true true 181 185 214 194
Circle -16777216 true false 144 174 42
Circle -16777216 true false 24 174 42
Circle -7500403 false true 24 174 42
Circle -7500403 false true 144 174 42
Circle -7500403 false true 234 174 42

turtle
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Polygon -10899396 true false 215 204 240 233 246 254 228 266 215 252 193 210
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Polygon -10899396 true false 105 90 75 75 55 75 40 89 31 108 39 124 60 105 75 105 90 105
Polygon -10899396 true false 132 85 134 64 107 51 108 17 150 2 192 18 192 52 169 65 172 87
Polygon -10899396 true false 85 204 60 233 54 254 72 266 85 252 107 210
Polygon -7500403 true true 119 75 179 75 209 101 224 135 220 225 175 261 128 261 81 224 74 135 88 99

wheel
false
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Circle -7500403 true true 3 3 294
Circle -16777216 true false 30 30 240
Line -7500403 true 150 285 150 15
Line -7500403 true 15 150 285 150
Circle -7500403 true true 120 120 60
Line -7500403 true 216 40 79 269
Line -7500403 true 40 84 269 221
Line -7500403 true 40 216 269 79
Line -7500403 true 84 40 221 269

x
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Polygon -7500403 true true 270 75 225 30 30 225 75 270
Polygon -7500403 true true 30 75 75 30 270 225 225 270

@#$#@#$#@
NetLogo 4.1
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@#$#@#$#@
@#$#@#$#@
@#$#@#$#@
@#$#@#$#@
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Line -7500403 true 150 150 210 180

@#$#@#$#@
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@#$#@#$#@