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<div class="subTitle">org.jgrapht.alg</div>
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<h2 title="Class NaiveLcaFinder" class="title">Class NaiveLcaFinder<V,E></h2>
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<pre>public class <span class="strong">NaiveLcaFinder<V,E></span>
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extends <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></pre>
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<th class="colOne" scope="col">Constructor and Description</th>
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<td class="colOne"><code><strong><a href="../../../org/jgrapht/alg/NaiveLcaFinder.html#NaiveLcaFinder(org.jgrapht.DirectedGraph)">NaiveLcaFinder</a></strong>(<a href="../../../org/jgrapht/DirectedGraph.html" title="interface in org.jgrapht">DirectedGraph</a><<a href="../../../org/jgrapht/alg/NaiveLcaFinder.html" title="type parameter in NaiveLcaFinder">V</a>,<a href="../../../org/jgrapht/alg/NaiveLcaFinder.html" title="type parameter in NaiveLcaFinder">E</a>> graph)</code>
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<div class="block">Find the Lowest Common Ancestor of a directed graph.</div>
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</td>
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<th class="colFirst" scope="col">Modifier and Type</th>
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<td class="colFirst"><code><a href="../../../org/jgrapht/alg/NaiveLcaFinder.html" title="type parameter in NaiveLcaFinder">V</a></code></td>
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<td class="colLast"><code><strong><a href="../../../org/jgrapht/alg/NaiveLcaFinder.html#findLca(V,%20V)">findLca</a></strong>(<a href="../../../org/jgrapht/alg/NaiveLcaFinder.html" title="type parameter in NaiveLcaFinder">V</a> a,
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<a href="../../../org/jgrapht/alg/NaiveLcaFinder.html" title="type parameter in NaiveLcaFinder">V</a> b)</code>
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<div class="block">Return the first found LCA of a and b</div>
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</td>
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<td class="colFirst"><code><a href="http://docs.oracle.com/javase/7/docs/api/java/util/Set.html?is-external=true" title="class or interface in java.util">Set</a><<a href="../../../org/jgrapht/alg/NaiveLcaFinder.html" title="type parameter in NaiveLcaFinder">V</a>></code></td>
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<td class="colLast"><code><strong><a href="../../../org/jgrapht/alg/NaiveLcaFinder.html#findLcas(V,%20V)">findLcas</a></strong>(<a href="../../../org/jgrapht/alg/NaiveLcaFinder.html" title="type parameter in NaiveLcaFinder">V</a> a,
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<a href="../../../org/jgrapht/alg/NaiveLcaFinder.html" title="type parameter in NaiveLcaFinder">V</a> b)</code>
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<div class="block">Return all the LCA of a and b.</div>
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<h3>Methods inherited from class java.lang.<a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></h3>
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<code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#clone()" title="class or interface in java.lang">clone</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#equals(java.lang.Object)" title="class or interface in java.lang">equals</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#finalize()" title="class or interface in java.lang">finalize</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#getClass()" title="class or interface in java.lang">getClass</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#hashCode()" title="class or interface in java.lang">hashCode</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#notify()" title="class or interface in java.lang">notify</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#notifyAll()" title="class or interface in java.lang">notifyAll</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#toString()" title="class or interface in java.lang">toString</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait()" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait(long)" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait(long,%20int)" title="class or interface in java.lang">wait</a></code></li>
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<h3>Constructor Detail</h3>
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<a name="NaiveLcaFinder(org.jgrapht.DirectedGraph)">
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<h4>NaiveLcaFinder</h4>
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<pre>public NaiveLcaFinder(<a href="../../../org/jgrapht/DirectedGraph.html" title="interface in org.jgrapht">DirectedGraph</a><<a href="../../../org/jgrapht/alg/NaiveLcaFinder.html" title="type parameter in NaiveLcaFinder">V</a>,<a href="../../../org/jgrapht/alg/NaiveLcaFinder.html" title="type parameter in NaiveLcaFinder">E</a>> graph)</pre>
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<div class="block">Find the Lowest Common Ancestor of a directed graph.
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<p>Find the LCA, defined as <i>Let G = (V, E) be a DAG, and let x, y ∈ V
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. Let G x,y be the subgraph of G induced by the set of all common
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ancestors of x and y. Define SLCA (x, y) to be the set of out-degree 0
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nodes (leafs) in G x,y . The lowest common ancestors of x and y are the
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elements of SLCA (x, y). This naive algorithm simply starts at a and b,
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recursing upwards to the root(s) of the DAG. Wherever the recursion paths
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cross we have found our LCA.</i> from
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http://www.cs.sunysb.edu/~bender/pub/JALG05-daglca.pdf. The algorithm:
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<pre>
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1. Start at each of nodes you wish to find the lca for (a and b)
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2. Create sets aSet containing a, and bSet containing b
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3. If either set intersects with the union of the other sets previous values (i.e. the set of notes visited) then
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that intersection is LCA. if there are multiple intersections then the earliest one added is the LCA.
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4. Repeat from step 3, with aSet now the parents of everything in aSet, and bSet the parents of everything in bSet
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5. If there are no more parents to descend to then there is no LCA
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</pre>
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The rationale for this working is that in each iteration of the loop we
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are considering all the ancestors of a that have a path of length n back
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to a, where n is the depth of the recursion. The same is true of b.
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<p>We start by checking if a == b.<br>
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if not we look to see if there is any intersection between parents(a) and
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(parents(b) union b) (and the same with a and b swapped)<br>
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if not we look to see if there is any intersection between
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parents(parents(a)) and (parents(parents(b)) union parents(b) union b)
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(and the same with a and b swapped)<br>
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continues
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<p>This means at the end of recursion n, we know if there is an LCA that
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has a path of <=n to a and b. Of course we may have to wait longer if
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the path to a is of length n, but the path to b>n. at the first loop
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we have a path of 0 length from the nodes we are considering as LCA to
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their respective children which we wish to find the LCA for.</div>
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<h3>Method Detail</h3>
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<a name="findLca(java.lang.Object,java.lang.Object)">
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</a><a name="findLca(V, V)">
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<h4>findLca</h4>
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<pre>public <a href="../../../org/jgrapht/alg/NaiveLcaFinder.html" title="type parameter in NaiveLcaFinder">V</a> findLca(<a href="../../../org/jgrapht/alg/NaiveLcaFinder.html" title="type parameter in NaiveLcaFinder">V</a> a,
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<a href="../../../org/jgrapht/alg/NaiveLcaFinder.html" title="type parameter in NaiveLcaFinder">V</a> b)</pre>
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<div class="block">Return the first found LCA of a and b</div>
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<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - the first element to find LCA for</dd><dd><code>b</code> - the other element to find the LCA for</dd>
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<dt><span class="strong">Returns:</span></dt><dd>the first found LCA of a and b, or null if there is no LCA.</dd></dl>
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<a name="findLcas(java.lang.Object,java.lang.Object)">
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</a><a name="findLcas(V, V)">
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<h4>findLcas</h4>
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<pre>public <a href="http://docs.oracle.com/javase/7/docs/api/java/util/Set.html?is-external=true" title="class or interface in java.util">Set</a><<a href="../../../org/jgrapht/alg/NaiveLcaFinder.html" title="type parameter in NaiveLcaFinder">V</a>> findLcas(<a href="../../../org/jgrapht/alg/NaiveLcaFinder.html" title="type parameter in NaiveLcaFinder">V</a> a,
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<a href="../../../org/jgrapht/alg/NaiveLcaFinder.html" title="type parameter in NaiveLcaFinder">V</a> b)</pre>
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<div class="block">Return all the LCA of a and b. Currently not implemented</div>
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<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - the first element to find LCA for</dd><dd><code>b</code> - the other element to find the LCA for</dd>
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<dt><span class="strong">Returns:</span></dt><dd>the set of all LCA of a and b, or empty set if there is no LCA.</dd></dl>
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