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1 ;;; hanoi.el --- towers of hanoi in GNUmacs
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2
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3 ;; Author: Damon Anton Permezel
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4 ;; Maintainer: FSF
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5 ;; Keywords: games
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6
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7 ; Author (a) 1985, Damon Anton Permezel
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8 ; This is in the public domain
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9 ; since he distributed it without copyright notice in 1985.
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10
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11 ;;; Synched up with: FSF 19.30.
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12
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13 ;;; Commentary:
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14
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15 ;; Solves the Towers of Hanoi puzzle while-U-wait.
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16 ;;
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17 ;; The puzzle: Start with N rings, decreasing in sizes from bottom to
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18 ;; top, stacked around a post. There are two other posts. Your mission,
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19 ;; should you choose to accept it, is to shift the pile, stacked in its
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20 ;; original order, to another post.
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21 ;;
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22 ;; The challenge is to do it in the fewest possible moves. Each move
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23 ;; shifts one ring to a different post. But there's a rule; you can
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24 ;; only stack a ring on top of a larger one.
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25 ;;
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26 ;; The simplest nontrivial version of this puzzle is N = 3. Solution
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27 ;; time rises as 2**N, and programs to solve it have long been considered
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28 ;; classic introductory exercises in the use of recursion.
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29 ;;
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30 ;; The puzzle is called `Towers of Hanoi' because an early popular
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31 ;; presentation wove a fanciful legend around it. According to this
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32 ;; myth (uttered long before the Vietnam War), there is a Buddhist
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33 ;; monastery at Hanoi which contains a large room with three time-worn
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34 ;; posts in it surrounded by 21 golden discs. Monks, acting out the
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35 ;; command of an ancient prophecy, have been moving these disks, in
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36 ;; accordance with the rules of the puzzle, once every day since the
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37 ;; monastery was founded over a thousand years ago. They are said
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38 ;; believe that when the last move of the puzzle is completed, the
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39 ;; world will end in a clap of thunder. Fortunately, they are nowhere
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40 ;; even close to being done...
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41
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42 ;;; Code:
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43
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44 ;;;
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45 ;;; hanoi-topos - direct cursor addressing
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46 ;;;
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47 (defun hanoi-topos (row col)
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48 (goto-line row)
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49 (beginning-of-line)
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50 (forward-char col))
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51
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52 ;;;
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53 ;;; hanoi - user callable Towers of Hanoi
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54 ;;;
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55 ;;;###autoload
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56 (defun hanoi (nrings)
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57 "Towers of Hanoi diversion. Argument is number of rings."
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58 (interactive
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59 (list (if (null current-prefix-arg)
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60 3
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61 (prefix-numeric-value current-prefix-arg))))
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62 (if (<= nrings 0) (error "Negative number of rings"))
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63 (let* (floor-row
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64 fly-row
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65 (window-height (window-height (selected-window)))
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66 (window-width (window-width (selected-window)))
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67
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68 ;; This is the unit of spacing to use between poles. It
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69 ;; must be even. We round down, since rounding up might
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70 ;; cause us to draw off the edge of the window.
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71 (pole-spacing (logand (/ window-width 6) (lognot 1))))
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72 (let (
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73 ;; The poles are (1+ NRINGS) rows high; we also want an
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74 ;; empty row at the top for the flying rings, a base, and a
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75 ;; blank line underneath that.
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76 (h (+ nrings 4))
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77
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78 ;; If we have NRINGS rings, we label them with the numbers 0
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79 ;; through NRINGS-1. The width of ring i is 2i+3; it pokes
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80 ;; out i spaces on either side of the pole. Rather than
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81 ;; checking if the window is wide enough to accommodate this,
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82 ;; we make sure pole-spacing is large enough, since that
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83 ;; works even when we have decremented pole-spacing to make
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84 ;; it even.
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85 (w (1+ nrings)))
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86 (if (not (and (>= window-height h)
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87 (> pole-spacing w)))
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88 (progn
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89 (delete-other-windows)
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90 (if (not (and (>= (setq window-height
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91 (window-height (selected-window)))
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92 h)
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93 (> (setq pole-spacing
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94 (logand (/ window-width 6) (lognot 1)))
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95 w)))
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96 (error "Screen is too small (need at least %dx%d)" w h))))
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97 (setq floor-row (if (> (- window-height 3) h)
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98 (- window-height 3) window-height)))
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99 (let ((fly-row (- floor-row nrings 1))
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100 ;; pole: column . fill height
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101 (pole-1 (cons pole-spacing floor-row))
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102 (pole-2 (cons (* 3 pole-spacing) floor-row))
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103 (pole-3 (cons (* 5 pole-spacing) floor-row))
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104 (rings (make-vector nrings nil)))
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105 ;; construct the ring list
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106 (let ((i 0))
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107 (while (< i nrings)
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108 ;; ring: [pole-number string empty-string]
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109 (aset rings i (vector nil
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110 (make-string (+ i i 3) (+ ?0 i))
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111 (make-string (+ i i 3) ?\ )))
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112 (setq i (1+ i))))
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113 ;;
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114 ;; init the screen
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115 ;;
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116 (switch-to-buffer "*Hanoi*")
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117 (setq buffer-read-only nil)
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118 (buffer-disable-undo (current-buffer))
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119 (erase-buffer)
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120 (let ((i 0))
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121 (while (< i floor-row)
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122 (setq i (1+ i))
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123 (insert-char ?\ (1- window-width))
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124 (insert ?\n)))
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125 (insert-char ?= (1- window-width))
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126
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127 (let ((n 1))
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128 (while (< n 6)
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129 (hanoi-topos fly-row (* n pole-spacing))
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130 (setq n (+ n 2))
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131 (let ((i fly-row))
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132 (while (< i floor-row)
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133 (setq i (1+ i))
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134 (next-line 1)
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135 (insert ?\|)
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136 (delete-char 1)
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137 (backward-char 1)))))
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138 ;(sit-for 0)
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139 ;;
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140 ;; now draw the rings in their initial positions
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141 ;;
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142 (let ((i 0)
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143 ring)
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144 (while (< i nrings)
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145 (setq ring (aref rings (- nrings 1 i)))
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146 (aset ring 0 (- floor-row i))
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147 (hanoi-topos (cdr pole-1)
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148 (- (car pole-1) (- nrings i)))
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149 (hanoi-draw-ring ring t nil)
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150 (setcdr pole-1 (1- (cdr pole-1)))
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151 (setq i (1+ i))))
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152 (setq buffer-read-only t)
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153 (sit-for 0)
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154 ;;
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155 ;; do it!
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156 ;;
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157 (hanoi0 (1- nrings) pole-1 pole-2 pole-3)
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158 (goto-char (point-min))
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159 (message "Done")
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160 (setq buffer-read-only t)
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161 (force-mode-line-update)
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162 (sit-for 0))))
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163
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164 ;;;
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165 ;;; hanoi0 - work horse of hanoi
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166 ;;;
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167 (defun hanoi0 (n from to work)
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168 (cond ((input-pending-p)
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169 (signal 'quit (list "I can tell you've had enough")))
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170 ((< n 0))
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171 (t
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172 (hanoi0 (1- n) from work to)
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173 (hanoi-move-ring n from to)
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174 (hanoi0 (1- n) work to from))))
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175
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176 ;;;
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177 ;;; hanoi-move-ring - move ring 'n' from 'from' to 'to'
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178 ;;;
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179 ;;;
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180 (defun hanoi-move-ring (n from to)
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181 (let ((ring (aref rings n)) ; ring <- ring: (ring# . row)
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182 (buffer-read-only nil))
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183 (let ((row (aref ring 0)) ; row <- row ring is on
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184 (col (- (car from) n 1)) ; col <- left edge of ring
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185 (dst-col (- (car to) n 1)) ; dst-col <- dest col for left edge
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186 (dst-row (cdr to))) ; dst-row <- dest row for ring
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187 (hanoi-topos row col)
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188 (while (> row fly-row) ; move up to the fly row
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189 (hanoi-draw-ring ring nil t) ; blank out ring
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190 (previous-line 1) ; move up a line
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191 (hanoi-draw-ring ring t nil) ; redraw
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192 (sit-for 0)
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193 (setq row (1- row)))
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194 (setcdr from (1+ (cdr from))) ; adjust top row
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195 ;;
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196 ;; fly the ring over to the right pole
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197 ;;
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198 (while (not (equal dst-col col))
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199 (cond ((> dst-col col) ; dst-col > col: right shift
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200 (end-of-line 1)
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201 (delete-backward-char 2)
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202 (beginning-of-line 1)
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203 (insert ?\ ?\ )
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204 (sit-for 0)
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205 (setq col (1+ (1+ col))))
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206 ((< dst-col col) ; dst-col < col: left shift
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207 (beginning-of-line 1)
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208 (delete-char 2)
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209 (end-of-line 1)
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210 (insert ?\ ?\ )
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211 (sit-for 0)
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212 (setq col (1- (1- col))))))
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213 ;;
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214 ;; let the ring float down
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215 ;;
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216 (hanoi-topos fly-row dst-col)
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217 (while (< row dst-row) ; move down to the dest row
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218 (hanoi-draw-ring ring nil (> row fly-row)) ; blank out ring
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219 (next-line 1) ; move down a line
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220 (hanoi-draw-ring ring t nil) ; redraw ring
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221 (sit-for 0)
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222 (setq row (1+ row)))
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223 (aset ring 0 dst-row)
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224 (setcdr to (1- (cdr to)))))) ; adjust top row
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225
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226 ;;;
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227 ;;; draw-ring - draw the ring at point, leave point unchanged
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228 ;;;
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229 ;;; Input:
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230 ;;; ring
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231 ;;; f1 - flag: t -> draw, nil -> erase
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232 ;;; f2 - flag: t -> erasing and need to draw ?\|
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233 ;;;
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234 (defun hanoi-draw-ring (ring f1 f2)
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235 (save-excursion
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236 (let* ((string (if f1 (aref ring 1) (aref ring 2)))
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237 (len (length string)))
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238 (delete-char len)
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239 (insert string)
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240 (if f2
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241 (progn
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242 (backward-char (/ (+ len 1) 2))
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243 (delete-char 1) (insert ?\|))))))
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244
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245 (provide 'hanoi)
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246
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247 ;;; hanoi.el ends here
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