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  5. <title>GTL - Graph Template Library: topsort Class Reference</title>
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  35. <h1>topsort Class Reference</h1><!-- doxytag: class="topsort" --><!-- doxytag: inherits="dfs" -->Topological sorting.
  36. <a href="#_details">More...</a>
  37. <p>
  38. <div class="dynheader">
  39. Inheritance diagram for topsort:</div>
  40. <div class="dynsection">
  41. <p><center><img src="a00205.gif" border="0" usemap="#a00206" alt="Inheritance graph"></center>
  42. <map name="a00206">
  43. <area shape="rect" href="a00008.html" title="Depth&#45;First&#45;Search (DFS) algorithm." alt="" coords="24,81,64,105"><area shape="rect" href="a00001.html" title="Abstract baseclass for all algoritm&#45;classes." alt="" coords="5,7,83,31"></map>
  44. <center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center></div>
  45. <div class="dynheader">
  46. Collaboration diagram for topsort:</div>
  47. <div class="dynsection">
  48. <p><center><img src="a00207.gif" border="0" usemap="#a00208" alt="Collaboration graph"></center>
  49. <map name="a00208">
  50. <area shape="rect" href="a00008.html" title="Depth&#45;First&#45;Search (DFS) algorithm." alt="" coords="665,119,705,143"><area shape="rect" href="a00001.html" title="Abstract baseclass for all algoritm&#45;classes." alt="" coords="401,101,479,125"><area shape="rect" href="a00020.html" title="A node in a graph." alt="" coords="415,188,465,212"><area shape="rect" title="start" alt="" coords="463,188,471,196"><area shape="rect" title="start" alt="" coords="661,132,669,140"><area shape="rect" title="int_node" alt="" coords="411,185,419,193"><area shape="rect" title="int_node" alt="" coords="463,185,471,193"><area shape="rect" href="a00021.html" title="node_map\&lt; int \&gt;" alt="" coords="379,237,501,261"><area shape="rect" title="top_numbers" alt="" coords="497,240,505,248"><area shape="rect" title="top_numbers" alt="" coords="772,213,780,221"><area shape="rect" title="comp_number\ndfs_number" alt="" coords="497,235,505,243"><area shape="rect" title="comp_number\ndfs_number" alt="" coords="673,140,681,148"><area shape="rect" href="a00019.html" title="ne_map\&lt; node, int, graph, allocator\&lt; int \&gt; \&gt;" alt="" coords="21,237,304,261"><area shape="rect" href="a00011.html" title="edge_map\&lt; int \&gt;" alt="" coords="379,5,501,29"><area shape="rect" title="used" alt="" coords="497,20,505,28"><area shape="rect" title="used" alt="" coords="673,115,681,123"><area shape="rect" href="a00019.html" title="ne_map\&lt; edge, int, graph, allocator\&lt; int \&gt; \&gt;" alt="" coords="21,5,304,29"><area shape="rect" href="a00021.html" title="node_map\&lt; node \&gt;" alt="" coords="371,53,509,77"><area shape="rect" title="preds" alt="" coords="505,72,513,80"><area shape="rect" title="preds" alt="" coords="661,116,669,124"><area shape="rect" href="a00019.html" title="ne_map\&lt; node, node, graph, allocator\&lt; node \&gt; \&gt;" alt="" coords="5,53,320,77"></map>
  51. <center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center></div>
  52. <p>
  53. <a href="a00209.html">List of all members.</a><table border="0" cellpadding="0" cellspacing="0">
  54. <tr><td></td></tr>
  55. <tr><td colspan="2"><br><h2>Public Member Functions</h2></td></tr>
  56. <tr><td class="memItemLeft" nowrap align="right" valign="top">&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="a00028.html#76a9055969b9dbf006320040be9fd5e6">topsort</a> ()</td></tr>
  57. <tr><td class="memItemLeft" nowrap align="right" valign="top">int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="a00028.html#71069dab2159b75a324f3b8a44a88ced">top_num</a> (const <a class="el" href="a00020.html">node</a> &amp;n) const </td></tr>
  58. <tr><td class="memItemLeft" nowrap align="right" valign="top">bool&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="a00028.html#6df72e7e38299c30695e9391c3b04383">is_acyclic</a> () const </td></tr>
  59. <tr><td class="memItemLeft" nowrap align="right" valign="top">topsort_iterator&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="a00028.html#f2b446d051fceb0df31df7057e03025b">top_order_begin</a> () const </td></tr>
  60. <tr><td class="memItemLeft" nowrap align="right" valign="top">topsort_iterator&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="a00028.html#b4d0debf92c9e5eeceec48856af4b329">top_order_end</a> () const </td></tr>
  61. <tr><td class="memItemLeft" nowrap align="right" valign="top">virtual int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="a00028.html#d83c28909478d35c737a2c70506407dd">check</a> (<a class="el" href="a00014.html">graph</a> &amp;G)</td></tr>
  62. <tr><td class="memItemLeft" nowrap align="right" valign="top">virtual void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="a00028.html#403076f952ef640cb3f52c9b1a495a1f">reset</a> ()</td></tr>
  63. <tr><td class="memItemLeft" nowrap align="right" valign="top">virtual void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="a00028.html#1cd92994d564acf79c37e40bdb292827">init_handler</a> (<a class="el" href="a00014.html">graph</a> &amp;G)</td></tr>
  64. <tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Handler called before the start of DFS. <a href="#1cd92994d564acf79c37e40bdb292827"></a><br></td></tr>
  65. <tr><td class="memItemLeft" nowrap align="right" valign="top">virtual void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="a00028.html#4401a056e4310ca7eca47587f7da5daf">leave_handler</a> (<a class="el" href="a00014.html">graph</a> &amp;, <a class="el" href="a00020.html">node</a> &amp;, <a class="el" href="a00020.html">node</a> &amp;)</td></tr>
  66. <tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Handler called after all the adjacent edges of <em>n</em> have been examined. <a href="#4401a056e4310ca7eca47587f7da5daf"></a><br></td></tr>
  67. <tr><td class="memItemLeft" nowrap align="right" valign="top">virtual void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="a00028.html#97074494bbdb878a1e3b6da232e965dd">old_adj_node_handler</a> (<a class="el" href="a00014.html">graph</a> &amp;, <a class="el" href="a00010.html">edge</a> &amp;, <a class="el" href="a00020.html">node</a> &amp;)</td></tr>
  68. <tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Handler called when a already marked node <em>n</em> connected to the actual node by <em>e</em> is found during the search of all adjacent edges of the actual node. <a href="#97074494bbdb878a1e3b6da232e965dd"></a><br></td></tr>
  69. </table>
  70. <hr><a name="_details"></a><h2>Detailed Description</h2>
  71. Topological sorting.
  72. <p>
  73. Assigns to each <a class="el" href="a00020.html" title="A node in a graph.">node</a> <code>n</code> a number <code>top_num</code> such that for every <a class="el" href="a00010.html" title="An edge in a graph.">edge</a> <code>(u,v)</code> <code>top_num[u]</code> &lt; <code>top_num[v]</code>, if possible, i.e. iff the directed <a class="el" href="a00014.html" title="A directed or undirected graph.">graph</a> is acyclic.<p>
  74. Similar to the testing of <a class="el" href="a00004.html" title="Biconnectivity-test and low-numbers.">biconnectivity</a>, which extends DFS to calculate low-numbers, the topsort-algorithm extends DFS to calculate the new numbering (and thus to test whether such a numbering is possible).<p>
  75. In order to traverse all the nodes in the order of its top-numbers, a new iterator, <code>topsort_iterator</code> is provided. <hr><h2>Constructor &amp; Destructor Documentation</h2>
  76. <a class="anchor" name="76a9055969b9dbf006320040be9fd5e6"></a><!-- doxytag: member="topsort::topsort" ref="76a9055969b9dbf006320040be9fd5e6" args="()" -->
  77. <div class="memitem">
  78. <div class="memproto">
  79. <table class="memname">
  80. <tr>
  81. <td class="memname">topsort::topsort </td>
  82. <td>(</td>
  83. <td class="paramname"> </td>
  84. <td>&nbsp;)&nbsp;</td>
  85. <td width="100%"><code> [inline]</code></td>
  86. </tr>
  87. </table>
  88. </div>
  89. <div class="memdoc">
  90. <p>
  91. default constructor; enables scanning of the whole_graph.<p>
  92. <dl class="see" compact><dt><b>See also:</b></dt><dd><a class="el" href="a00008.html#2399808134dbabf6aa5e1b2e35a73954" title="Constructor.">dfs::dfs</a> </dd></dl>
  93. </div>
  94. </div><p>
  95. <hr><h2>Member Function Documentation</h2>
  96. <a class="anchor" name="71069dab2159b75a324f3b8a44a88ced"></a><!-- doxytag: member="topsort::top_num" ref="71069dab2159b75a324f3b8a44a88ced" args="(const node &amp;n) const " -->
  97. <div class="memitem">
  98. <div class="memproto">
  99. <table class="memname">
  100. <tr>
  101. <td class="memname">int topsort::top_num </td>
  102. <td>(</td>
  103. <td class="paramtype">const <a class="el" href="a00020.html">node</a> &amp;&nbsp;</td>
  104. <td class="paramname"> <em>n</em> </td>
  105. <td>&nbsp;)&nbsp;</td>
  106. <td width="100%"> const<code> [inline]</code></td>
  107. </tr>
  108. </table>
  109. </div>
  110. <div class="memdoc">
  111. <p>
  112. Number in topological order.<p>
  113. <dl compact><dt><b>Parameters:</b></dt><dd>
  114. <table border="0" cellspacing="2" cellpadding="0">
  115. <tr><td valign="top"></td><td valign="top"><em>&lt;code&gt;n&lt;/code&gt;</em>&nbsp;</td><td><a class="el" href="a00020.html" title="A node in a graph.">node</a>. </td></tr>
  116. </table>
  117. </dl>
  118. <dl class="return" compact><dt><b>Returns:</b></dt><dd>number in topological order. </dd></dl>
  119. </div>
  120. </div><p>
  121. <a class="anchor" name="6df72e7e38299c30695e9391c3b04383"></a><!-- doxytag: member="topsort::is_acyclic" ref="6df72e7e38299c30695e9391c3b04383" args="() const " -->
  122. <div class="memitem">
  123. <div class="memproto">
  124. <table class="memname">
  125. <tr>
  126. <td class="memname">bool topsort::is_acyclic </td>
  127. <td>(</td>
  128. <td class="paramname"> </td>
  129. <td>&nbsp;)&nbsp;</td>
  130. <td width="100%"> const<code> [inline]</code></td>
  131. </tr>
  132. </table>
  133. </div>
  134. <div class="memdoc">
  135. <p>
  136. Tests if <a class="el" href="a00014.html" title="A directed or undirected graph.">graph</a> was acyclic.<p>
  137. <dl class="return" compact><dt><b>Returns:</b></dt><dd>true iff <a class="el" href="a00014.html" title="A directed or undirected graph.">graph</a> was acyclic. </dd></dl>
  138. </div>
  139. </div><p>
  140. <a class="anchor" name="f2b446d051fceb0df31df7057e03025b"></a><!-- doxytag: member="topsort::top_order_begin" ref="f2b446d051fceb0df31df7057e03025b" args="() const " -->
  141. <div class="memitem">
  142. <div class="memproto">
  143. <table class="memname">
  144. <tr>
  145. <td class="memname">topsort_iterator topsort::top_order_begin </td>
  146. <td>(</td>
  147. <td class="paramname"> </td>
  148. <td>&nbsp;)&nbsp;</td>
  149. <td width="100%"> const<code> [inline]</code></td>
  150. </tr>
  151. </table>
  152. </div>
  153. <div class="memdoc">
  154. <p>
  155. Iterate through nodes in topsort-order.<p>
  156. <dl class="return" compact><dt><b>Returns:</b></dt><dd>start-iterator. </dd></dl>
  157. </div>
  158. </div><p>
  159. <a class="anchor" name="b4d0debf92c9e5eeceec48856af4b329"></a><!-- doxytag: member="topsort::top_order_end" ref="b4d0debf92c9e5eeceec48856af4b329" args="() const " -->
  160. <div class="memitem">
  161. <div class="memproto">
  162. <table class="memname">
  163. <tr>
  164. <td class="memname">topsort_iterator topsort::top_order_end </td>
  165. <td>(</td>
  166. <td class="paramname"> </td>
  167. <td>&nbsp;)&nbsp;</td>
  168. <td width="100%"> const<code> [inline]</code></td>
  169. </tr>
  170. </table>
  171. </div>
  172. <div class="memdoc">
  173. <p>
  174. Iterate through nodes in topsort-order.<p>
  175. <dl class="return" compact><dt><b>Returns:</b></dt><dd>end-iterator. </dd></dl>
  176. </div>
  177. </div><p>
  178. <a class="anchor" name="d83c28909478d35c737a2c70506407dd"></a><!-- doxytag: member="topsort::check" ref="d83c28909478d35c737a2c70506407dd" args="(graph &amp;G)" -->
  179. <div class="memitem">
  180. <div class="memproto">
  181. <table class="memname">
  182. <tr>
  183. <td class="memname">virtual int topsort::check </td>
  184. <td>(</td>
  185. <td class="paramtype"><a class="el" href="a00014.html">graph</a> &amp;&nbsp;</td>
  186. <td class="paramname"> <em>G</em> </td>
  187. <td>&nbsp;)&nbsp;</td>
  188. <td width="100%"><code> [virtual]</code></td>
  189. </tr>
  190. </table>
  191. </div>
  192. <div class="memdoc">
  193. <p>
  194. Preconditions: <ul>
  195. <li>
  196. <code>G</code> is directed. </li>
  197. <li>
  198. DFS may be applied </li>
  199. </ul>
  200. <p>
  201. <dl compact><dt><b>Parameters:</b></dt><dd>
  202. <table border="0" cellspacing="2" cellpadding="0">
  203. <tr><td valign="top"></td><td valign="top"><em>&lt;code&gt;G&lt;/code&gt;</em>&nbsp;</td><td><a class="el" href="a00014.html" title="A directed or undirected graph.">graph</a>. </td></tr>
  204. </table>
  205. </dl>
  206. <dl class="return" compact><dt><b>Returns:</b></dt><dd><code><a class="el" href="a00001.html#f1a0078e153aa99c24f9bdf0d97f67105114c20e4a96a76b5de9f28bf15e282b">algorithm::GTL_OK</a></code> if <a class="el" href="a00028.html" title="Topological sorting.">topsort</a> may be applied to <code>G</code>. </dd></dl>
  207. <dl class="see" compact><dt><b>See also:</b></dt><dd><a class="el" href="a00008.html#908f4ea617ed59767ed334b39a2771d0" title="Checks whether the preconditions for DFS are satisfied.">dfs::check</a> </dd></dl>
  208. <p>Reimplemented from <a class="el" href="a00008.html#908f4ea617ed59767ed334b39a2771d0">dfs</a>.</p>
  209. </div>
  210. </div><p>
  211. <a class="anchor" name="403076f952ef640cb3f52c9b1a495a1f"></a><!-- doxytag: member="topsort::reset" ref="403076f952ef640cb3f52c9b1a495a1f" args="()" -->
  212. <div class="memitem">
  213. <div class="memproto">
  214. <table class="memname">
  215. <tr>
  216. <td class="memname">virtual void topsort::reset </td>
  217. <td>(</td>
  218. <td class="paramname"> </td>
  219. <td>&nbsp;)&nbsp;</td>
  220. <td width="100%"><code> [virtual]</code></td>
  221. </tr>
  222. </table>
  223. </div>
  224. <div class="memdoc">
  225. <p>
  226. Reset <dl class="see" compact><dt><b>See also:</b></dt><dd><a class="el" href="a00008.html#1c893f699517cc72624cf171b7bc4da4" title="Resets algorithm.">dfs::reset</a> </dd></dl>
  227. <p>Reimplemented from <a class="el" href="a00008.html#1c893f699517cc72624cf171b7bc4da4">dfs</a>.</p>
  228. </div>
  229. </div><p>
  230. <a class="anchor" name="1cd92994d564acf79c37e40bdb292827"></a><!-- doxytag: member="topsort::init_handler" ref="1cd92994d564acf79c37e40bdb292827" args="(graph &amp;G)" -->
  231. <div class="memitem">
  232. <div class="memproto">
  233. <table class="memname">
  234. <tr>
  235. <td class="memname">virtual void topsort::init_handler </td>
  236. <td>(</td>
  237. <td class="paramtype"><a class="el" href="a00014.html">graph</a> &amp;&nbsp;</td>
  238. <td class="paramname"> <em>G</em> </td>
  239. <td>&nbsp;)&nbsp;</td>
  240. <td width="100%"><code> [virtual]</code></td>
  241. </tr>
  242. </table>
  243. </div>
  244. <div class="memdoc">
  245. <p>
  246. Handler called before the start of DFS.
  247. <p>
  248. <dl compact><dt><b>Parameters:</b></dt><dd>
  249. <table border="0" cellspacing="2" cellpadding="0">
  250. <tr><td valign="top"></td><td valign="top"><em>G</em>&nbsp;</td><td>graph for which DFS was invoked. </td></tr>
  251. </table>
  252. </dl>
  253. <p>Reimplemented from <a class="el" href="a00008.html#cc82574cd42ab8256e685374bee5fabb">dfs</a>.</p>
  254. </div>
  255. </div><p>
  256. <a class="anchor" name="4401a056e4310ca7eca47587f7da5daf"></a><!-- doxytag: member="topsort::leave_handler" ref="4401a056e4310ca7eca47587f7da5daf" args="(graph &amp;, node &amp;, node &amp;)" -->
  257. <div class="memitem">
  258. <div class="memproto">
  259. <table class="memname">
  260. <tr>
  261. <td class="memname">virtual void topsort::leave_handler </td>
  262. <td>(</td>
  263. <td class="paramtype"><a class="el" href="a00014.html">graph</a> &amp;&nbsp;</td>
  264. <td class="paramname"> <em>G</em>, </td>
  265. </tr>
  266. <tr>
  267. <td class="paramkey"></td>
  268. <td></td>
  269. <td class="paramtype"><a class="el" href="a00020.html">node</a> &amp;&nbsp;</td>
  270. <td class="paramname"> <em>n</em>, </td>
  271. </tr>
  272. <tr>
  273. <td class="paramkey"></td>
  274. <td></td>
  275. <td class="paramtype"><a class="el" href="a00020.html">node</a> &amp;&nbsp;</td>
  276. <td class="paramname"> <em>f</em></td><td>&nbsp;</td>
  277. </tr>
  278. <tr>
  279. <td></td>
  280. <td>)</td>
  281. <td></td><td></td><td width="100%"><code> [virtual]</code></td>
  282. </tr>
  283. </table>
  284. </div>
  285. <div class="memdoc">
  286. <p>
  287. Handler called after all the adjacent edges of <em>n</em> have been examined.
  288. <p>
  289. <dl compact><dt><b>Parameters:</b></dt><dd>
  290. <table border="0" cellspacing="2" cellpadding="0">
  291. <tr><td valign="top"></td><td valign="top"><em>G</em>&nbsp;</td><td>graph for which DFS was invoked. </td></tr>
  292. <tr><td valign="top"></td><td valign="top"><em>n</em>&nbsp;</td><td>actual node. </td></tr>
  293. <tr><td valign="top"></td><td valign="top"><em>f</em>&nbsp;</td><td>predecessor. </td></tr>
  294. </table>
  295. </dl>
  296. <p>Reimplemented from <a class="el" href="a00008.html#8071fc4e82deff7ceb2790cd4eb42280">dfs</a>.</p>
  297. </div>
  298. </div><p>
  299. <a class="anchor" name="97074494bbdb878a1e3b6da232e965dd"></a><!-- doxytag: member="topsort::old_adj_node_handler" ref="97074494bbdb878a1e3b6da232e965dd" args="(graph &amp;, edge &amp;, node &amp;)" -->
  300. <div class="memitem">
  301. <div class="memproto">
  302. <table class="memname">
  303. <tr>
  304. <td class="memname">virtual void topsort::old_adj_node_handler </td>
  305. <td>(</td>
  306. <td class="paramtype"><a class="el" href="a00014.html">graph</a> &amp;&nbsp;</td>
  307. <td class="paramname"> <em>G</em>, </td>
  308. </tr>
  309. <tr>
  310. <td class="paramkey"></td>
  311. <td></td>
  312. <td class="paramtype"><a class="el" href="a00010.html">edge</a> &amp;&nbsp;</td>
  313. <td class="paramname"> <em>e</em>, </td>
  314. </tr>
  315. <tr>
  316. <td class="paramkey"></td>
  317. <td></td>
  318. <td class="paramtype"><a class="el" href="a00020.html">node</a> &amp;&nbsp;</td>
  319. <td class="paramname"> <em>n</em></td><td>&nbsp;</td>
  320. </tr>
  321. <tr>
  322. <td></td>
  323. <td>)</td>
  324. <td></td><td></td><td width="100%"><code> [virtual]</code></td>
  325. </tr>
  326. </table>
  327. </div>
  328. <div class="memdoc">
  329. <p>
  330. Handler called when a already marked node <em>n</em> connected to the actual node by <em>e</em> is found during the search of all adjacent edges of the actual node.
  331. <p>
  332. <dl compact><dt><b>Parameters:</b></dt><dd>
  333. <table border="0" cellspacing="2" cellpadding="0">
  334. <tr><td valign="top"></td><td valign="top"><em>G</em>&nbsp;</td><td>graph for which DFS was invoked. </td></tr>
  335. <tr><td valign="top"></td><td valign="top"><em>e</em>&nbsp;</td><td>edge connecting the actual node to the old one. </td></tr>
  336. <tr><td valign="top"></td><td valign="top"><em>n</em>&nbsp;</td><td>used node. </td></tr>
  337. </table>
  338. </dl>
  339. <p>Reimplemented from <a class="el" href="a00008.html#df1c667188e632761c63f529537c544c">dfs</a>.</p>
  340. </div>
  341. </div><p>
  342. <p class="links">
  343. <a href="http://www.uni-passau.de/">University of Passau</a>
  344. &nbsp;-&nbsp;
  345. <a href="http://www.fmi.uni-passau.de/">FMI</a>
  346. &nbsp;-&nbsp;
  347. <a href="http://www.fmi.uni-passau.de/fmi/lehrstuehle/brandenburg/">Theoretical
  348. Computer Science</a>
  349. </p>
  350. <div class="copyright">
  351. Design &copy; 2002, 2003 <a href="mailto:raitner@fmi.uni-passau.de">Marcus Raitner</a>, University of Passau
  352. </div>
  353. </body>
  354. </html>