annotate scripts/sparse/treelayout.m @ 12575:d0b799dafede

Grammarcheck files for 3.4.1 release.
author Rik <octave@nomad.inbox5.com>
date Mon, 04 Apr 2011 15:33:46 -0700
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1 ## Copyright (C) 2008-2011 Ivana Varekova & Radek Salac
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or (at
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8 ## your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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13 ## General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {} treelayout (@var{tree})
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21 ## @deftypefnx {Function File} {} treelayout (@var{tree}, @var{permutation})
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22 ## treelayout lays out a tree or a forest. The first argument @var{tree} is a
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23 ## vector of
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24 ## predecessors, optional parameter @var{permutation} is an optional postorder
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25 ## permutation.
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26 ## The complexity of the algorithm is O(n) in
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27 ## terms of time and memory requirements.
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28 ## @seealso{etreeplot, gplot, treeplot}
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29 ## @end deftypefn
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30
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31 function [x_coordinate, y_coordinate, height, s] = treelayout (tree, permutation)
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32 if (nargin < 1 || nargin > 2 || nargout > 4)
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33 print_usage ();
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34 elseif (! isvector (tree) || rows (tree) != 1 || ! isnumeric (tree)
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35 || any (tree > length (tree)) || any (tree < 0))
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36 error ("treelayout: the first input argument must be a vector of predecessors");
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37 else
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38 ## Make it a row vector.
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39 tree = tree(:)';
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40
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41 ## The count of nodes of the graph.
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42 num_nodes = length (tree);
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43 ## The number of children.
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44 num_children = zeros (1, num_nodes + 1);
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45
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46 ## Checking vector of predecessors.
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47 for i = 1 : num_nodes
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48 if (tree(i) < i)
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49 ## This part of graph was checked before.
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50 continue;
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51 endif
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52
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53 ## Try to find cicle in this part of graph using modified Floyd's
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54 ## cycle-finding algorithm.
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55 tortoise = tree(i);
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56 hare = tree(tortoise);
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57
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58 while (tortoise != hare)
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59 ## End after finding a cicle or reaching a checked part of graph.
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60
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61 if (hare < i)
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62 ## This part of graph was checked before.
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63 break
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64 endif
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65
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66 tortoise = tree(tortoise);
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67 ## Hare will move faster than tortoise so in cicle hare must
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68 ## reach tortoise.
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69 hare = tree(tree(hare));
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70
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71 endwhile
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72
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73 if (tortoise == hare)
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74 ## If hare reach tortoise we found circle.
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75 error ("treelayout: vector of predecessors has bad format");
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76 endif
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77
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78 endfor
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79 ## Vector of predecessors has right format.
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80
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81 for i = 1:num_nodes
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82 ## vec_of_child is helping vector which is used to speed up the
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83 ## choice of descendant nodes.
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84
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85 num_children(tree(i)+1) = num_children(tree(i)+1) + 1;
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86 endfor
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87
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88 pos = 1;
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89 start = zeros (1, num_nodes+1);
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90 xhelp = zeros (1, num_nodes+1);
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91 stop = zeros (1, num_nodes+1);
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92 for i = 1 : num_nodes + 1
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93 start(i) = pos;
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94 xhelp(i) = pos;
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95 pos += num_children(i);
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96 stop(i) = pos;
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97 endfor
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98
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99 if (nargin == 1)
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100 for i = 1:num_nodes
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101 vec_of_child(xhelp(tree(i)+1)) = i;
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102 xhelp(tree(i)+1) = xhelp(tree(i)+1) + 1;
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103 endfor
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104 else
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105 vec_of_child = permutation;
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106 endif
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107
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108 ## The number of "parent" (actual) node (it's descendants will be
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109 ## browse in the next iteration).
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110 par_number = 0;
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111
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112 ## The x-coordinate of the left most descendant of "parent node"
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113 ## this value is increased in each leaf.
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114 left_most = 0;
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115
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116 ## The level of "parent" node (root level is num_nodes).
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117 level = num_nodes;
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118
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119 ## num_nodes - max_ht is the height of this graph.
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120 max_ht = num_nodes;
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121
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122 ## Main stack - each item consists of two numbers - the number of
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123 ## node and the number it's of parent node on the top of stack
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124 ## there is "parent node".
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125 stk = [-1, 0];
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126
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127 ## Number of vertices s in the top-level separator.
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128 s = 0;
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129 ## Flag which says if we are in top level separator.
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130 top_level = 1;
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131 ## The top of the stack.
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132 while (par_number != -1)
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133 if (start(par_number+1) < stop(par_number+1))
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134 idx = vec_of_child(start(par_number+1) : stop(par_number+1) - 1);
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135 else
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136 idx = zeros (1, 0);
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137 endif
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138
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139 ## Add to idx the vector of parent descendants.
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140 stk = [stk; [idx', ones(fliplr(size(idx))) * par_number]];
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141
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142 ## We are in top level separator when we have one child and the
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143 ## flag is 1
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144 if (columns(idx) == 1 && top_level == 1)
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145 s++;
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146 else
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147 # We aren't in top level separator now.
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148 top_level = 0;
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149 endif
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150 ## If there is not any descendant of "parent node":
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151 if (stk(end,2) != par_number)
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152 left_most++;
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153 x_coordinate_r(par_number) = left_most;
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154 max_ht = min (max_ht, level);
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155 if (length(stk) > 1 && find ((shift(stk,1)-stk) == 0) > 1
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156 && stk(end,2) != stk(end-1,2))
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157 ## Return to the nearest branching the position to return
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158 ## position is the position on the stack, where should be
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159 ## started further search (there are two nodes which has the
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160 ## same parent node).
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161
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162 position = (find ((shift (stk(:,2), 1) - stk(:,2)) == 0))(end) + 1;
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163 par_number_vec = stk(position:end,2);
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164
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165 ## The vector of removed nodes (the content of stack form
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166 ## position to end).
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167
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168 level += length (par_number_vec);
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169
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170 ## The level have to be decreased.
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171
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172 x_coordinate_r(par_number_vec) = left_most;
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173 stk(position:end,:) = [];
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174 endif
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175
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176 ## Remove the next node from "searched branch".
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177
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178 stk(end,:) = [];
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179 ## Choose new "parent node".
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180 par_number = stk(end,1);
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181 ## If there is another branch start to search it.
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182 if (par_number != -1)
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183 y_coordinate(par_number) = level;
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184 x_coordinate_l(par_number) = left_most + 1;
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185 endif
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186 else
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187
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188 ## There were descendants of "parent nod" choose the last of
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189 ## them and go on through it.
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190 level--;
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191 par_number = stk(end,1);
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192 y_coordinate(par_number) = level;
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193 x_coordinate_l(par_number) = left_most + 1;
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194 endif
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195 endwhile
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196
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197 ## Calculate the x coordinates (the known values are the position
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198 ## of most left and most right descendants).
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199 x_coordinate = (x_coordinate_l + x_coordinate_r) / 2;
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200
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201 height = num_nodes - max_ht - 1;
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202 endif
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203 endfunction
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204
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205 %!demo
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206 %! % Compute a simple tree layout
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207 %! [x,y,h,s]=treelayout([0 1 2 2])
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208
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209 %!demo
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210 %! % Compute a simple tree layout with defined postorder permutation
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211 %! [x,y,h,s]=treelayout([0 1 2 2],[1 2 3 4])