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1 " These macros 'solve' any maze produced by the a-maze-ing maze.c program.
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2 "
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3 " First, a bit of maze theory.
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4 " If you were put into a maze, a guaranteed method of finding your way
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5 " out of the maze is to put your left hand onto a wall and just keep walking,
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6 " never taking your hand off the wall. This technique is only guaranteed to
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7 " work if the maze does not have any 'islands', or if the 'exit' is on the
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8 " same island as your starting point. These conditions hold for the mazes
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9 " under consideration.
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10 "
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11 " Assuming that the maze is made up of horizontal and vertical walls spaced
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12 " one step apart and that you can move either north, south, east or west,
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13 " then you can automate this procedure by carrying out the following steps.
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14 "
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15 " 1. Put yourself somewhere in the maze near a wall.
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16 " 2. Check if you have a wall on your left. If so, go to step 4.
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17 " 3. There is no wall on your left, so turn on the spot to your left and step
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18 " forward by one step and repeat step 2.
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19 " 4. Check what is directly in front of you. If it is a wall, turn on the
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20 " spot to your right by 90 degrees and repeat step 4.
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21 " 5. There is no wall in front of you, so step forward one step and
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22 " go to step 2.
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23 "
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24 " In this way you will cover all the corridors of the maze (until you get back
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25 " to where you started from, if you do not stop).
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26 "
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27 " By examining a maze produced by the maze.c program you will see that
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28 " each square of the maze is one character high and two characters wide.
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29 " To go north or south, you move by a one character step, but to move east or
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30 " west you move by a two character step. Also note that in any position
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31 " there are four places where walls could be put - to the north, to the south,
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32 " to the east and to the west.
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33 " A wall exists to the north of you if the character to the north of
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34 " you is a _ (otherwise it is a space).
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35 " A wall exists to the east of you if the character to the east of you
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36 " is a | (otherwise it is a .).
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37 " A wall exists to the west of you if the character to the west of you
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38 " is a | (otherwise it is a .).
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39 " A wall exists to the south of you if the character where you are
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40 " is a _ (otherwise it is a space).
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41 "
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42 " Note the difference for direction south, where we must examine the character
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43 " where the cursor is rather than an adjacent cell.
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44 "
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45 " If you were implementing the above procedure is a normal computer language
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46 " you could use a loop with if statements and continue statements,
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47 " However, these constructs are not available in vi macros so I have used
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48 " a state machine with 8 states. Each state signifies the direction you
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49 " are going in and whether or not you have checked if there is a wall on
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50 " your left.
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51 "
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52 " The transition from state to state and the actions taken on each transition
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53 " are given in the state table below.
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54 " The names of the states are N1, N2, S1, S2, E1, E2, W1, W2, where each letter
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55 " stands for a direction of the compass, the number 1 indicates that the we
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56 " have not yet checked to see if there is a wall on our left and the number 2
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57 " indicates that we have checked and there is a wall on our left.
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58 "
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59 " For each state we must consider the existence or not of a wall in a
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60 " particular direction. This direction is given in the following table.
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61 "
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62 " NextChar table:
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63 " state direction vi commands
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64 " N1 W hF
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65 " N2 N kF
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66 " S1 E lF
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67 " S2 S F
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68 " E1 N kF
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69 " E2 E lF
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70 " W1 S F
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71 " W2 W hF
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72 "
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73 " where F is a macro which yanks the character under the cursor into
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74 " the NextChar register (n).
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75 "
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76 " State table:
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77 " In the 'vi commands' column is given the actions to carry out when in
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78 " this state and the NextChar is as given. The commands k, j, ll, hh move
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79 " the current position north, south, east and west respectively. The
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80 " command mm is used as a no-op command.
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81 " In the 'next state' column is given the new state of the machine after
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82 " the action is carried out.
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83 "
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84 " current state NextChar vi commands next state
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85 " N1 . hh W1
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86 " N1 | mm N2
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87 " N2 _ mm E1
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88 " N2 space k N1
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89 " S1 . ll E1
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90 " S1 | mm S2
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91 " S2 _ mm W1
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92 " S2 space j S1
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93 " E1 space k N1
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94 " E1 _ mm E2
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95 " E2 | mm S1
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96 " E2 . ll E1
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97 " W1 space j S1
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98 " W1 _ mm W2
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99 " W2 | mm N1
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100 " W2 . hh W1
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101 "
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102 "
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103 " Complaint about vi macros:
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104 " It seems that you cannot have more than one 'undo-able' vi command
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105 " in the one macro, so you have to make lots of little macros and
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106 " put them together.
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107 "
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108 " I'll explain what I mean by an example. Edit a file and
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109 " type ':map Q rXY'. This should map the Q key to 'replace the
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110 " character under the cursor with X and yank the line'.
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111 " But when I type Q, vi tells me 'Can't yank inside global/macro' and
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112 " goes into ex mode. However if I type ':map Q rXT' and ':map T Y',
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113 " everything is OK. I`m doing all this on a Sparcstation.
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114 " If anyone reading this has an answer to this problem, the author would
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115 " love to find out. Mail to gregm@otc.otca.oz.au.
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116 "
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117 " The macros:
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118 " The macro to run the maze solver is 'g'. This simply calls two other
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119 " macros: I, to initialise everything, and L, to loop forever running
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120 " through the state table.
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121 " Both of these macros are long sequences of calls to other macros. All
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122 " of these other macros are quite simple and so to understand how this
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123 " works, all you need to do is examine macros I and L and learn what they
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124 " do (a simple sequence of vi actions) and how L loops (by calling U, which
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125 " simply calls L again).
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126 "
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127 " Macro I sets up the state table and NextChar table at the end of the file.
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128 " Macro L then searches these tables to find out what actions to perform and
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129 " what state changes to make.
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130 "
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131 " The entries in the state table all begin with a key consisting of the
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132 " letter 's', the current state and the NextChar. After this is the
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133 " action to take in this state and after this is the next state to change to.
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134 "
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135 " The entries in the NextChar table begin with a key consisting of the
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136 " letter 'n' and the current state. After this is the action to take to
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137 " obtain NextChar - the character that must be examined to change state.
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138 "
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139 " One way to see what each part of the macros is doing is to type in the
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140 " body of the macros I and L manually (instead of typing 'g') and see
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141 " what happens at each step.
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142 "
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143 " Good luck.
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144 "
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145 " Registers used by the macros:
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146 " s (State) - holds the state the machine is in
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147 " c (Char) - holds the character under the current position
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148 " m (Macro) - holds a vi command string to be executed later
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149 " n (NextChar) - holds the character we must examine to change state
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150 " r (Second Macro) - holds a second vi command string to be executed later
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151 "
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152 set remap
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153 set nomagic
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154 set noterse
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155 set wrapscan
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156 "
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157 "================================================================
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158 " g - go runs the whole show
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159 " I - initialise
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160 " L - then loop forever
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161 map g IL
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162 "
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163 "================================================================
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164 " I - initialise everything before running the loop
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165 " G$?.^M - find the last . in the maze
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166 " ^ - replace it with an X (the goal)
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167 " GYKeDP - print the state table and next char table at the end of the file
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168 " 0S - initialise the state of the machine to E1
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169 " 2Gl - move to the top left cell of the maze
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170 map I G$?.
^GYKeDP0S2Gl
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171 "
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172 "================================================================
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173 " L - the loop which is executed forever
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174 " Q - save the current character in the Char register
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175 " A - replace the current character with an 'O'
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176 " ma - mark the current position with mark 'a'
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177 " GNB - on bottom line, create a command to search the NextChar table
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178 " for the current state
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179 " 0M0E@m^M - yank the command into the Macro register and execute it
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180 " wX - we have now found the entry in the table, now yank the
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181 " following word into the Macro register
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182 " `a@m - go back to the current position and execute the macro, this will
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183 " yank the NextChar in register n
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184 " GT$B$R - on bottom line, create a command to search the state table
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185 " for the current state and NextChar
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186 " 0M0E@m^M - yank the command into the Macro register and execute it
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187 " 2WS - we have now found the entry in the table, now yank the
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188 " next state into the State macro
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189 " bX - and yank the action corresponding to this state table entry
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190 " into the Macro register
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191 " GVJ - on bottom line, create a command to restore the current character
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192 " 0H - and save the command into the second Macro register
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193 " `a@r - go back to the current position and exectute the macro to restore
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194 " the current character
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195 " @m - execute the action associated with this state
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196 " U - and repeat
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197 map L QAmaGNB0M0E@m
wX`a@mGT$B$R0M0E@m
2WSbXGVJ0H`a@r@mU
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198 "
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199 "================================================================
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200 " U - no tail recursion allowed in vi macros so cheat and set U = L
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201 map U L
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202 "
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203 "================================================================
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204 " S - yank the next two characters into the State register
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205 map S "sy2l
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206 "
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207 "================================================================
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208 " Q - save the current character in the Char register
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209 map Q "cyl
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210 "
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211 "================================================================
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212 " A - replace the current character with an 'O'
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213 map A rO
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214 "
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215 "================================================================
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216 " N - replace this line with the string 'n'
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217 map N C/n
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218 "
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219 "================================================================
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220 " B - put the current state
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221 map B "sp
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222 "
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223 "================================================================
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224 " M - yank this line into the Macro register
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225 map M "my$
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226 "
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227 "================================================================
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228 " E - delete to the end of the line
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229 map E d$
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230 "
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231 "================================================================
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232 " X - yank this word into the Macro register
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233 map X "myt
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234 "
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235 "================================================================
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236 " T - replace this line with the string 's'
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237 map T C/s
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238 "
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239 "================================================================
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240 " R - put NextChar
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241 map R "np
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242 "
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243 "================================================================
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244 " V - add the letter 'r' (the replace vi command)
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245 map V ar
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246 "
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247 "================================================================
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248 " J - restore the current character
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249 map J "cp
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250 "
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251 "================================================================
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252 " H - yank this line into the second Macro register
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253 map H "ry$
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254 "
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255 "================================================================
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256 " F - yank NextChar (this macro is called from the Macro register)
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257 map F "nyl
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258 "
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259 "================================================================
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260 " ^ - replace the current character with an 'X'
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261 map ^ rX
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262 "
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263 "================================================================
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264 " YKeDP - create the state table, NextChar table and initial state
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265 " Note that you have to escape the bar character, since it is special to
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266 " the map command (it indicates a new line).
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267 map Y osE1 k N1 sE1_ mm E2 sE2| mm S1 sE2. ll E1
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268 map K osW1 j S1 sW1_ mm W2 sW2| mm N1 sW2. hh W1
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269 map e osN1. hh W1 sN1| mm N2 sN2 k N1 sN2_ mm E1
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270 map D osS1. ll E1 sS1| mm S2 sS2 j S1 sS2_ mm W1
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271 map P onE1 kF nE2 lF nW1 G$JF nW2 hF nN1 hF nN2 kF nS1 lF nS2 G$JF
E1
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