Mercurial > hg > octave-lyh
annotate scripts/sparse/treelayout.m @ 14459:a22a41ab6824
doc: Add Colin Macdonald and Mike Miller to contributors.in
author | Jordi Gutiérrez Hermoso <jordigh@octave.org> |
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date | Tue, 13 Mar 2012 01:30:26 -0400 |
parents | f3d52523cde1 |
children | 5d3a684236b0 |
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1 ## Copyright (C) 2008-2012 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 |
8507 | 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) |
8507 | 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 |
8506 | 38 ## Make it a row vector. |
8507 | 39 tree = tree(:)'; |
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40 |
8506 | 41 ## The count of nodes of the graph. |
8507 | 42 num_nodes = length (tree); |
8506 | 43 ## The number of children. |
8507 | 44 num_children = zeros (1, num_nodes + 1); |
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45 |
8506 | 46 ## Checking vector of predecessors. |
8507 | 47 for i = 1 : num_nodes |
48 if (tree(i) < i) | |
10549 | 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 |
8506 | 53 ## Try to find cicle in this part of graph using modified Floyd's |
54 ## cycle-finding algorithm. | |
8507 | 55 tortoise = tree(i); |
56 hare = tree(tortoise); | |
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57 |
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58 while (tortoise != hare) |
10549 | 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) |
8506 | 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 |
8507 | 66 tortoise = tree(tortoise); |
10549 | 67 ## Hare will move faster than tortoise so in cicle hare must |
68 ## reach tortoise. | |
8507 | 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) |
10549 | 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 |
8506 | 79 ## Vector of predecessors has right format. |
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80 |
8507 | 81 for i = 1:num_nodes |
82 ## vec_of_child is helping vector which is used to speed up the | |
8506 | 83 ## choice of descendant nodes. |
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84 |
8507 | 85 num_children(tree(i)+1) = num_children(tree(i)+1) + 1; |
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86 endfor |
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87 |
8507 | 88 pos = 1; |
89 start = zeros (1, num_nodes+1); | |
90 xhelp = zeros (1, num_nodes+1); | |
91 stop = zeros (1, num_nodes+1); | |
92 for i = 1 : num_nodes + 1 | |
93 start(i) = pos; | |
94 xhelp(i) = pos; | |
95 pos += num_children(i); | |
96 stop(i) = pos; | |
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97 endfor |
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98 |
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99 if (nargin == 1) |
8507 | 100 for i = 1:num_nodes |
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101 vec_of_child(xhelp(tree(i)+1)) = i; |
8507 | 102 xhelp(tree(i)+1) = xhelp(tree(i)+1) + 1; |
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103 endfor |
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104 else |
8507 | 105 vec_of_child = permutation; |
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106 endif |
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107 |
8506 | 108 ## The number of "parent" (actual) node (it's descendants will be |
109 ## browse in the next iteration). | |
8507 | 110 par_number = 0; |
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111 |
8506 | 112 ## The x-coordinate of the left most descendant of "parent node" |
113 ## this value is increased in each leaf. | |
8507 | 114 left_most = 0; |
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115 |
8507 | 116 ## The level of "parent" node (root level is num_nodes). |
117 level = num_nodes; | |
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118 |
8507 | 119 ## num_nodes - max_ht is the height of this graph. |
120 max_ht = num_nodes; | |
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121 |
8506 | 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 |
8506 | 124 ## there is "parent node". |
8507 | 125 stk = [-1, 0]; |
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126 |
8506 | 127 ## Number of vertices s in the top-level separator. |
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128 s = 0; |
8506 | 129 ## Flag which says if we are in top level separator. |
8507 | 130 top_level = 1; |
8506 | 131 ## The top of the stack. |
8507 | 132 while (par_number != -1) |
133 if (start(par_number+1) < stop(par_number+1)) | |
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 |
8506 | 139 ## Add to idx the vector of parent descendants. |
8507 | 140 stk = [stk; [idx', ones(fliplr(size(idx))) * par_number]]; |
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141 |
8506 | 142 ## We are in top level separator when we have one child and the |
143 ## flag is 1 | |
8507 | 144 if (columns(idx) == 1 && top_level == 1) |
145 s++; | |
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146 else |
8506 | 147 # We aren't in top level separator now. |
8507 | 148 top_level = 0; |
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149 endif |
8506 | 150 ## If there is not any descendant of "parent node": |
8507 | 151 if (stk(end,2) != par_number) |
152 left_most++; | |
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153 x_coordinate_r(par_number) = left_most; |
8507 | 154 max_ht = min (max_ht, level); |
155 if (length(stk) > 1 && find ((shift(stk,1)-stk) == 0) > 1 | |
10549 | 156 && stk(end,2) != stk(end-1,2)) |
157 ## Return to the nearest branching the position to return | |
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 |
8506 | 160 ## same parent node). |
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161 |
8507 | 162 position = (find ((shift (stk(:,2), 1) - stk(:,2)) == 0))(end) + 1; |
163 par_number_vec = stk(position:end,2); | |
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164 |
8506 | 165 ## The vector of removed nodes (the content of stack form |
166 ## position to end). | |
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167 |
8507 | 168 level += length (par_number_vec); |
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169 |
10549 | 170 ## The level have to be decreased. |
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171 |
8507 | 172 x_coordinate_r(par_number_vec) = left_most; |
173 stk(position:end,:) = []; | |
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174 endif |
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175 |
8506 | 176 ## Remove the next node from "searched branch". |
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177 |
8507 | 178 stk(end,:) = []; |
10549 | 179 ## Choose new "parent node". |
8507 | 180 par_number = stk(end,1); |
10549 | 181 ## If there is another branch start to search it. |
182 if (par_number != -1) | |
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183 y_coordinate(par_number) = level; |
8507 | 184 x_coordinate_l(par_number) = left_most + 1; |
10549 | 185 endif |
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186 else |
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187 |
8506 | 188 ## There were descendants of "parent nod" choose the last of |
189 ## them and go on through it. | |
8507 | 190 level--; |
191 par_number = stk(end,1); | |
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192 y_coordinate(par_number) = level; |
8507 | 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 |
8506 | 197 ## Calculate the x coordinates (the known values are the position |
198 ## of most left and most right descendants). | |
8507 | 199 x_coordinate = (x_coordinate_l + x_coordinate_r) / 2; |
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200 |
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202 endif |
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203 endfunction |
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204 |
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206 %!test |
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207 %! % Compute a simple tree layout |
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208 %! [x, y, h, s] = treelayout ([0, 1, 2, 2]); |
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209 %! assert (x, [1.5, 1.5, 2, 1]); |
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210 %! assert (y, [3, 2, 1, 1]); |
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211 %! assert (h, 2); |
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212 %! assert (s, 2); |
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213 |
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214 %!test |
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215 %! % Compute a simple tree layout with defined postorder permutation |
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216 %! [x, y, h, s] = treelayout ([0, 1, 2, 2], [1, 2, 4, 3]); |
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217 %! assert (x, [1.5, 1.5, 1, 2]); |
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218 %! assert (y, [3, 2, 1, 1]); |
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219 %! assert (h, 2); |
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220 %! assert (s, 2); |
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221 |
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222 %!test |
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223 %! % Compute a simple tree layout with defined postorder permutation |
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224 %! [x, y, h, s] = treelayout ([0, 1, 2, 2], [4, 2, 3, 1]); |
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225 %! assert (x, [0, 0, 0, 1]); |
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226 %! assert (y, [0, 0, 0, 3]); |
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227 %! assert (h, 0); |
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228 %! assert (s, 1); |
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229 |