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<link title="CCSexp" rel="Chapter" href="CCSexp.html">
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<link title="CCSexpM" rel="Chapter" href="CCSexpM.html"><link title="Interfaces for graphs" rel="Section" href="#2_Interfacesforgraphs">
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<link title="Bags of vertices" rel="Section" href="#2_Bagsofvertices">
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<link title="Traversals" rel="Section" href="#2_Traversals">
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<link title="Mutable Graph" rel="Section" href="#2_MutableGraph">
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<title>Containers doc : CCGraph</title>
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<h1>Module <a href="type_CCGraph.html">CCGraph</a></h1>
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<pre><span class="keyword">module</span> CCGraph: <code class="code"><span class="keyword">sig</span></code> <a href="CCGraph.html">..</a> <code class="code"><span class="keyword">end</span></code></pre><div class="info module top">
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<h1 id="1_SimpleGraphInterface">Simple Graph Interface</h1>
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<p>
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A collections of algorithms on (mostly read-only) graph structures.
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The user provides her own graph structure as a <code class="code">(<span class="keywordsign">'</span>v, <span class="keywordsign">'</span>e) <span class="constructor">CCGraph</span>.t</code>,
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where <code class="code"><span class="keywordsign">'</span>v</code> is the type of vertices and <code class="code"><span class="keywordsign">'</span>e</code> the type of edges
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(for instance, <code class="code"><span class="keywordsign">'</span>e = (<span class="keywordsign">'</span>v * <span class="keywordsign">'</span>v)</code> is perfectly fine in many cases).
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<p>
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Such a <code class="code">(<span class="keywordsign">'</span>v, <span class="keywordsign">'</span>e) <span class="constructor">CCGraph</span>.t</code> structure is a record containing
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three functions: two relate edges to their origin and destination,
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and one maps vertices to their outgoing edges.
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This abstract notion of graph makes it possible to run the algorithms
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on any user-specific type that happens to have a graph structure.
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<p>
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Many graph algorithms here take a sequence of vertices as input.
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If the user only has a single vertex (e.g., for a topological sort
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from a given vertex), she can use <code class="code"><span class="constructor">Seq</span>.return x</code> to build a sequence
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of one element.
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<p>
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<b>status: unstable</b><br>
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<b>Since</b> 0.12<br>
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</div>
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<hr width="100%">
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<pre><span id="TYPEsequence"><span class="keyword">type</span> <code class="type">'a</code> sequence</span> = <code class="type">('a -> unit) -> unit</code> </pre>
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<div class="info ">
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A sequence of items of type <code class="code"><span class="keywordsign">'</span>a</code>, possibly infinite<br>
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</div>
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<pre><span id="TYPEsequence_once"><span class="keyword">type</span> <code class="type">'a</code> sequence_once</span> = <code class="type">'a <a href="CCGraph.html#TYPEsequence">sequence</a></code> </pre>
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<div class="info ">
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Sequence that should be used only once<br>
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</div>
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<pre><span id="EXCEPTIONSequence_once"><span class="keyword">exception</span> Sequence_once</span></pre>
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<div class="info ">
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Raised when a sequence meant to be used once is used several times<br>
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</div>
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<pre><span class="keyword">module</span> <a href="CCGraph.Seq.html">Seq</a>: <code class="code"><span class="keyword">sig</span></code> <a href="CCGraph.Seq.html">..</a> <code class="code"><span class="keyword">end</span></code></pre><br>
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<h2 id="2_Interfacesforgraphs">Interfaces for graphs</h2><br>
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<pre><code><span id="TYPEt"><span class="keyword">type</span> <code class="type">('v, 'e)</code> t</span> = {</code></pre><table class="typetable">
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<tr>
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<td align="left" valign="top" >
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<code> </code></td>
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<td align="left" valign="top" >
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<code><span id="TYPEELTt.children">children</span> : <code class="type">'v -> 'e <a href="CCGraph.html#TYPEsequence">sequence</a></code>;</code></td>
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</tr>
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<tr>
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<td align="left" valign="top" >
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<code> </code></td>
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<td align="left" valign="top" >
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<code><span id="TYPEELTt.origin">origin</span> : <code class="type">'e -> 'v</code>;</code></td>
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</tr>
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<tr>
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<td align="left" valign="top" >
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<code> </code></td>
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<td align="left" valign="top" >
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<code><span id="TYPEELTt.dest">dest</span> : <code class="type">'e -> 'v</code>;</code></td>
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</tr></table>
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}
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<div class="info ">
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Directed graph with vertices of type <code class="code"><span class="keywordsign">'</span>v</code> and edges of type <code class="code">e'</code><br>
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</div>
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<pre><span id="TYPEgraph"><span class="keyword">type</span> <code class="type">('v, 'e)</code> graph</span> = <code class="type">('v, 'e) <a href="CCGraph.html#TYPEt">t</a></code> </pre>
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<pre><span id="VALmake"><span class="keyword">val</span> make</span> : <code class="type">origin:('e -> 'v) -><br> dest:('e -> 'v) -> ('v -> 'e <a href="CCGraph.html#TYPEsequence">sequence</a>) -> ('v, 'e) <a href="CCGraph.html#TYPEt">t</a></code></pre><div class="info ">
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Make a graph by providing its fields<br>
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<b>Since</b> 0.16<br>
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</div>
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<pre><span id="VALmake_labelled_tuple"><span class="keyword">val</span> make_labelled_tuple</span> : <code class="type">('v -> ('a * 'v) <a href="CCGraph.html#TYPEsequence">sequence</a>) -> ('v, 'v * 'a * 'v) <a href="CCGraph.html#TYPEt">t</a></code></pre><div class="info ">
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Make a graph with edges being triples <code class="code">(origin,label,dest)</code><br>
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<b>Since</b> 0.16<br>
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</div>
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<pre><span id="VALmake_tuple"><span class="keyword">val</span> make_tuple</span> : <code class="type">('v -> 'v <a href="CCGraph.html#TYPEsequence">sequence</a>) -> ('v, 'v * 'v) <a href="CCGraph.html#TYPEt">t</a></code></pre><div class="info ">
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Make a graph with edges being pairs <code class="code">(origin,dest)</code><br>
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<b>Since</b> 0.16<br>
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</div>
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<pre><code><span id="TYPEtag_set"><span class="keyword">type</span> <code class="type">'v</code> tag_set</span> = {</code></pre><table class="typetable">
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<tr>
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<td align="left" valign="top" >
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<code> </code></td>
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<td align="left" valign="top" >
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<code><span id="TYPEELTtag_set.get_tag">get_tag</span> : <code class="type">'v -> bool</code>;</code></td>
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</tr>
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<tr>
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<td align="left" valign="top" >
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<code> </code></td>
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<td align="left" valign="top" >
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<code><span id="TYPEELTtag_set.set_tag">set_tag</span> : <code class="type">'v -> unit</code>;</code></td>
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<td class="typefieldcomment" align="left" valign="top" ><code>(*</code></td><td class="typefieldcomment" align="left" valign="top" ><div class="info ">
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Set tag for the given element<br>
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</div>
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</td><td class="typefieldcomment" align="left" valign="bottom" ><code>*)</code></td>
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</tr></table>
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}
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<div class="info ">
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Mutable tags from values of type <code class="code"><span class="keywordsign">'</span>v</code> to tags of type <code class="code">bool</code><br>
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</div>
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<pre><code><span id="TYPEtable"><span class="keyword">type</span> <code class="type">('k, 'a)</code> table</span> = {</code></pre><table class="typetable">
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<tr>
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<td align="left" valign="top" >
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<code> </code></td>
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<td align="left" valign="top" >
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<code><span id="TYPEELTtable.mem">mem</span> : <code class="type">'k -> bool</code>;</code></td>
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</tr>
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<tr>
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<td align="left" valign="top" >
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<code> </code></td>
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<td align="left" valign="top" >
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<code><span id="TYPEELTtable.find">find</span> : <code class="type">'k -> 'a</code>;</code></td>
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<td class="typefieldcomment" align="left" valign="top" ><code>(*</code></td><td class="typefieldcomment" align="left" valign="top" ><div class="info ">
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<b>Raises</b> <code>Not_found</code> if element not added before<br>
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</div>
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</td><td class="typefieldcomment" align="left" valign="bottom" ><code>*)</code></td>
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</tr>
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<tr>
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<td align="left" valign="top" >
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<code> </code></td>
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<td align="left" valign="top" >
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<code><span id="TYPEELTtable.add">add</span> : <code class="type">'k -> 'a -> unit</code>;</code></td>
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<td class="typefieldcomment" align="left" valign="top" ><code>(*</code></td><td class="typefieldcomment" align="left" valign="top" ><div class="info ">
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Erases previous binding<br>
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</div>
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</td><td class="typefieldcomment" align="left" valign="bottom" ><code>*)</code></td>
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</tr></table>
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}
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<div class="info ">
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Mutable table with keys <code class="code"><span class="keywordsign">'</span>k</code> and values <code class="code"><span class="keywordsign">'</span>a</code><br>
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</div>
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<pre><span id="TYPEset"><span class="keyword">type</span> <code class="type">'a</code> set</span> = <code class="type">('a, unit) <a href="CCGraph.html#TYPEtable">table</a></code> </pre>
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<div class="info ">
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Mutable set<br>
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</div>
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<pre><span id="VALmk_table"><span class="keyword">val</span> mk_table</span> : <code class="type">?eq:('k -> 'k -> bool) -> ?hash:('k -> int) -> int -> ('k, 'a) <a href="CCGraph.html#TYPEtable">table</a></code></pre><div class="info ">
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Default implementation for <a href="CCGraph.html#TYPEtable"><code class="code"><span class="constructor">CCGraph</span>.table</code></a>: a <code class="code"><span class="constructor">Hashtbl</span>.t</code><br>
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</div>
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<pre><span id="VALmk_map"><span class="keyword">val</span> mk_map</span> : <code class="type">?cmp:('k -> 'k -> int) -> unit -> ('k, 'a) <a href="CCGraph.html#TYPEtable">table</a></code></pre><div class="info ">
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Use a <code class="code"><span class="constructor">Map</span>.<span class="constructor">S</span></code> underneath<br>
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</div>
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<br>
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<h2 id="2_Bagsofvertices">Bags of vertices</h2><br>
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<pre><code><span id="TYPEbag"><span class="keyword">type</span> <code class="type">'a</code> bag</span> = {</code></pre><table class="typetable">
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<tr>
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<td align="left" valign="top" >
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<code> </code></td>
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<td align="left" valign="top" >
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<code><span id="TYPEELTbag.push">push</span> : <code class="type">'a -> unit</code>;</code></td>
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</tr>
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<tr>
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<td align="left" valign="top" >
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<code> </code></td>
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<td align="left" valign="top" >
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<code><span id="TYPEELTbag.is_empty">is_empty</span> : <code class="type">unit -> bool</code>;</code></td>
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</tr>
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<tr>
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<td align="left" valign="top" >
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<code> </code></td>
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<td align="left" valign="top" >
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<code><span id="TYPEELTbag.pop">pop</span> : <code class="type">unit -> 'a</code>;</code></td>
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<td class="typefieldcomment" align="left" valign="top" ><code>(*</code></td><td class="typefieldcomment" align="left" valign="top" ><div class="info ">
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raises some exception is empty<br>
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</div>
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</td><td class="typefieldcomment" align="left" valign="bottom" ><code>*)</code></td>
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</tr></table>
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}
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<div class="info ">
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Bag of elements of type <code class="code"><span class="keywordsign">'</span>a</code><br>
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</div>
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<pre><span id="VALmk_queue"><span class="keyword">val</span> mk_queue</span> : <code class="type">unit -> 'a <a href="CCGraph.html#TYPEbag">bag</a></code></pre>
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<pre><span id="VALmk_stack"><span class="keyword">val</span> mk_stack</span> : <code class="type">unit -> 'a <a href="CCGraph.html#TYPEbag">bag</a></code></pre>
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<pre><span id="VALmk_heap"><span class="keyword">val</span> mk_heap</span> : <code class="type">leq:('a -> 'a -> bool) -> 'a <a href="CCGraph.html#TYPEbag">bag</a></code></pre><div class="info ">
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<code class="code">mk_heap ~leq</code> makes a priority queue where <code class="code">leq x y = <span class="keyword">true</span></code> means that
|
|
<code class="code">x</code> is smaller than <code class="code">y</code> and should be prioritary<br>
|
|
</div>
|
|
<br>
|
|
<h2 id="2_Traversals">Traversals</h2><br>
|
|
|
|
<pre><span class="keyword">module</span> <a href="CCGraph.Traverse.html">Traverse</a>: <code class="code"><span class="keyword">sig</span></code> <a href="CCGraph.Traverse.html">..</a> <code class="code"><span class="keyword">end</span></code></pre><br>
|
|
<h2 id="2_Cycles">Cycles</h2><br>
|
|
|
|
<pre><span id="VALis_dag"><span class="keyword">val</span> is_dag</span> : <code class="type">?tbl:'v <a href="CCGraph.html#TYPEset">set</a> -><br> graph:('v, 'a) <a href="CCGraph.html#TYPEt">t</a> -> 'v <a href="CCGraph.html#TYPEsequence">sequence</a> -> bool</code></pre><div class="info ">
|
|
<code class="code">is_dag ~graph vs</code> returns <code class="code"><span class="keyword">true</span></code> if the subset of <code class="code">graph</code> reachable
|
|
from <code class="code">vs</code> is acyclic.<br>
|
|
<b>Since</b> 0.18<br>
|
|
</div>
|
|
<br>
|
|
<h2 id="2_TopologicalSort">Topological Sort</h2><br>
|
|
|
|
<pre><span id="EXCEPTIONHas_cycle"><span class="keyword">exception</span> Has_cycle</span></pre>
|
|
|
|
<pre><span id="VALtopo_sort"><span class="keyword">val</span> topo_sort</span> : <code class="type">?eq:('v -> 'v -> bool) -><br> ?rev:bool -><br> ?tbl:'v <a href="CCGraph.html#TYPEset">set</a> -><br> graph:('v, 'e) <a href="CCGraph.html#TYPEt">t</a> -> 'v <a href="CCGraph.html#TYPEsequence">sequence</a> -> 'v list</code></pre><div class="info ">
|
|
<code class="code">topo_sort ~graph seq</code> returns a list of vertices <code class="code">l</code> where each
|
|
element of <code class="code">l</code> is reachable from <code class="code">seq</code>.
|
|
The list is sorted in a way such that if <code class="code">v <span class="keywordsign">-></span> v'</code> in the graph, then
|
|
<code class="code">v</code> comes before <code class="code">v'</code> in the list (i.e. has a smaller index).
|
|
Basically <code class="code">v <span class="keywordsign">-></span> v'</code> means that <code class="code">v</code> is smaller than <code class="code">v'</code>
|
|
see <a href=" https://en.wikipedia.org/wiki/Topological_sorting"> wikipedia</a><br>
|
|
<b>Raises</b> <code>Has_cycle</code> if the graph is not a DAG<br>
|
|
</div>
|
|
<div class="param_info"><code class="code">eq</code> : equality predicate on vertices (default <code class="code">(=)</code>)</div>
|
|
<div class="param_info"><code class="code">rev</code> : if true, the dependency relation is inverted (<code class="code">v <span class="keywordsign">-></span> v'</code> means
|
|
<code class="code">v'</code> occurs before <code class="code">v</code>)</div>
|
|
|
|
<pre><span id="VALtopo_sort_tag"><span class="keyword">val</span> topo_sort_tag</span> : <code class="type">?eq:('v -> 'v -> bool) -><br> ?rev:bool -><br> tags:'v <a href="CCGraph.html#TYPEtag_set">tag_set</a> -><br> graph:('v, 'e) <a href="CCGraph.html#TYPEt">t</a> -> 'v <a href="CCGraph.html#TYPEsequence">sequence</a> -> 'v list</code></pre><div class="info ">
|
|
Same as <a href="CCGraph.html#VALtopo_sort"><code class="code"><span class="constructor">CCGraph</span>.topo_sort</code></a> but uses an explicit tag set<br>
|
|
</div>
|
|
<br>
|
|
<h2 id="2_LazySpanningTree">Lazy Spanning Tree</h2><br>
|
|
|
|
<pre><span class="keyword">module</span> <a href="CCGraph.LazyTree.html">LazyTree</a>: <code class="code"><span class="keyword">sig</span></code> <a href="CCGraph.LazyTree.html">..</a> <code class="code"><span class="keyword">end</span></code></pre>
|
|
<pre><span id="VALspanning_tree"><span class="keyword">val</span> spanning_tree</span> : <code class="type">?tbl:'v <a href="CCGraph.html#TYPEset">set</a> -><br> graph:('v, 'e) <a href="CCGraph.html#TYPEt">t</a> -> 'v -> ('v, 'e) <a href="CCGraph.LazyTree.html#TYPEt">LazyTree.t</a></code></pre><div class="info ">
|
|
<code class="code">spanning_tree ~graph v</code> computes a lazy spanning tree that has <code class="code">v</code>
|
|
as a root. The table <code class="code">tbl</code> is used for the memoization part<br>
|
|
</div>
|
|
|
|
<pre><span id="VALspanning_tree_tag"><span class="keyword">val</span> spanning_tree_tag</span> : <code class="type">tags:'v <a href="CCGraph.html#TYPEtag_set">tag_set</a> -><br> graph:('v, 'e) <a href="CCGraph.html#TYPEt">t</a> -> 'v -> ('v, 'e) <a href="CCGraph.LazyTree.html#TYPEt">LazyTree.t</a></code></pre><br>
|
|
<h2 id="2_StronglyConnectedComponents">Strongly Connected Components</h2><br>
|
|
|
|
<pre><span id="TYPEscc_state"><span class="keyword">type</span> <code class="type">'v</code> scc_state</span> </pre>
|
|
<div class="info ">
|
|
Hidden state for <a href="CCGraph.html#VALscc"><code class="code"><span class="constructor">CCGraph</span>.scc</code></a><br>
|
|
</div>
|
|
|
|
|
|
<pre><span id="VALscc"><span class="keyword">val</span> scc</span> : <code class="type">?tbl:('v, 'v <a href="CCGraph.html#TYPEscc_state">scc_state</a>) <a href="CCGraph.html#TYPEtable">table</a> -><br> graph:('v, 'e) <a href="CCGraph.html#TYPEt">t</a> -><br> 'v <a href="CCGraph.html#TYPEsequence">sequence</a> -> 'v list <a href="CCGraph.html#TYPEsequence_once">sequence_once</a></code></pre><div class="info ">
|
|
Strongly connected components reachable from the given vertices.
|
|
Each component is a list of vertices that are all mutually reachable
|
|
in the graph.
|
|
The components are explored in a topological order (if C1 and C2 are
|
|
components, and C1 points to C2, then C2 will be yielded before C1).
|
|
Uses <a href=" https://en.wikipedia.org/wiki/Tarjan's_strongly_connected_components_algorithm"> Tarjan's algorithm</a><br>
|
|
<b>Raises</b> <code>Sequence_once</code> if the result is iterated on more than once.<br>
|
|
</div>
|
|
<div class="param_info"><code class="code">tbl</code> : table used to map nodes to some hidden state</div>
|
|
<br>
|
|
<h2 id="2_PrettyprintingintheDOTgraphvizformat">Pretty printing in the DOT (graphviz) format</h2>
|
|
<p>
|
|
|
|
Example (print divisors from <code class="code">42</code>):
|
|
<p>
|
|
|
|
<pre class="codepre"><code class="code"> <span class="keyword">let</span> <span class="keyword">open</span> <span class="constructor">CCGraph</span> <span class="keyword">in</span><br>
|
|
<span class="keyword">let</span> <span class="keyword">open</span> <span class="constructor">Dot</span> <span class="keyword">in</span><br>
|
|
with_out <span class="string">"/tmp/truc.dot"</span><br>
|
|
(<span class="keyword">fun</span> out <span class="keywordsign">-></span><br>
|
|
pp ~attrs_v:(<span class="keyword">fun</span> i <span class="keywordsign">-></span> [<span class="keywordsign">`</span><span class="constructor">Label</span> (string_of_int i)]) ~graph:divisors_graph out 42<br>
|
|
)<br>
|
|
</code></pre><br>
|
|
|
|
<pre><span class="keyword">module</span> <a href="CCGraph.Dot.html">Dot</a>: <code class="code"><span class="keyword">sig</span></code> <a href="CCGraph.Dot.html">..</a> <code class="code"><span class="keyword">end</span></code></pre><br>
|
|
<h2 id="2_MutableGraph">Mutable Graph</h2><br>
|
|
|
|
<pre><span id="TYPEmut_graph"><span class="keyword">type</span> <code class="type">('v, 'e)</code> mut_graph</span> = <</pre><table class="typetable">
|
|
<tr>
|
|
<td align="left" valign="top" >
|
|
<code> </code></td>
|
|
<td align="left" valign="top" >
|
|
<code><span id="TYPEELTmut_graph.add_edge">add_edge</span> : <code class="type">'e -> unit</code>;</code></td>
|
|
|
|
</tr>
|
|
<tr>
|
|
<td align="left" valign="top" >
|
|
<code> </code></td>
|
|
<td align="left" valign="top" >
|
|
<code><span id="TYPEELTmut_graph.graph">graph</span> : <code class="type">('v, 'e) <a href="CCGraph.html#TYPEt">t</a></code>;</code></td>
|
|
|
|
</tr>
|
|
<tr>
|
|
<td align="left" valign="top" >
|
|
<code> </code></td>
|
|
<td align="left" valign="top" >
|
|
<code><span id="TYPEELTmut_graph.remove">remove</span> : <code class="type">'v -> unit</code>;</code></td>
|
|
|
|
</tr></table>
|
|
>
|
|
</pre>
|
|
|
|
|
|
<pre><span id="VALmk_mut_tbl"><span class="keyword">val</span> mk_mut_tbl</span> : <code class="type">?eq:('v -> 'v -> bool) -><br> ?hash:('v -> int) -> int -> ('v, 'v * 'a * 'v) <a href="CCGraph.html#TYPEmut_graph">mut_graph</a></code></pre><div class="info ">
|
|
Make a new mutable graph from a Hashtbl. Edges are labelled with type <code class="code"><span class="keywordsign">'</span>a</code><br>
|
|
</div>
|
|
<br>
|
|
<h2 id="2_ImmutableGraph">Immutable Graph</h2>
|
|
<p>
|
|
|
|
A classic implementation of a graph structure on totally ordered vertices,
|
|
with unlabelled edges. The graph allows to add and remove edges and vertices,
|
|
and to iterate on edges and vertices.<br>
|
|
|
|
<pre><span class="keyword">module type</span> <a href="CCGraph.MAP.html">MAP</a> = <code class="code"><span class="keyword">sig</span></code> <a href="CCGraph.MAP.html">..</a> <code class="code"><span class="keyword">end</span></code></pre>
|
|
<pre><span class="keyword">module</span> <a href="CCGraph.Map.html">Map</a> <code class="code">(</code><code class="code"><span class="constructor">O</span></code><code class="code"> : </code><code class="type">Map.OrderedType</code><code class="code">) </code>: <code class="type"><a href="CCGraph.MAP.html">MAP</a></code><code class="type"> with type vertex = O.t</code></pre><br>
|
|
<h2 id="2_Misc">Misc</h2><br>
|
|
|
|
<pre><span id="VALof_list"><span class="keyword">val</span> of_list</span> : <code class="type">?eq:('v -> 'v -> bool) -> ('v * 'v) list -> ('v, 'v * 'v) <a href="CCGraph.html#TYPEt">t</a></code></pre><div class="info ">
|
|
<code class="code">of_list l</code> makes a graph from a list of pairs of vertices.
|
|
Each pair <code class="code">(a,b)</code> is an edge from <code class="code">a</code> to <code class="code">b</code>.<br>
|
|
</div>
|
|
<div class="param_info"><code class="code">eq</code> : equality used to compare vertices</div>
|
|
|
|
<pre><span id="VALof_hashtbl"><span class="keyword">val</span> of_hashtbl</span> : <code class="type">('v, 'v list) Hashtbl.t -> ('v, 'v * 'v) <a href="CCGraph.html#TYPEt">t</a></code></pre><div class="info ">
|
|
<code class="code">of_hashtbl tbl</code> makes a graph from a hashtable that maps vertices
|
|
to lists of children<br>
|
|
</div>
|
|
|
|
<pre><span id="VALof_fun"><span class="keyword">val</span> of_fun</span> : <code class="type">('v -> 'v list) -> ('v, 'v * 'v) <a href="CCGraph.html#TYPEt">t</a></code></pre><div class="info ">
|
|
<code class="code">of_fun f</code> makes a graph out of a function that maps a vertex to
|
|
the list of its children. The function is assumed to be deterministic.<br>
|
|
</div>
|
|
|
|
<pre><span id="VALdivisors_graph"><span class="keyword">val</span> divisors_graph</span> : <code class="type">(int, int * int) <a href="CCGraph.html#TYPEt">t</a></code></pre><div class="info ">
|
|
<code class="code">n</code> points to all its strict divisors<br>
|
|
</div>
|
|
</body></html> |