com.salesforce.jgrapht.alg.NaiveLcaFinder Maven / Gradle / Ivy
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/*
* (C) Copyright 2013-2017, by Leo Crawford and Contributors.
*
* JGraphT : a free Java graph-theory library
*
* This program and the accompanying materials are dual-licensed under
* either
*
* (a) the terms of the GNU Lesser General Public License version 2.1
* as published by the Free Software Foundation, or (at your option) any
* later version.
*
* or (per the licensee's choosing)
*
* (b) the terms of the Eclipse Public License v1.0 as published by
* the Eclipse Foundation.
*/
package com.salesforce.jgrapht.alg;
import java.util.*;
import com.salesforce.jgrapht.*;
/**
* Find the Lowest Common Ancestor of a directed graph.
*
*
* Find the LCA, defined as Let G = (V, E) be a DAG, and let x, y ∈ V . Let G x,y be the subgraph
* of G induced by the set of all common ancestors of x and y. Define SLCA (x, y) to be the set of
* out-degree 0 nodes (leafs) in G x,y . The lowest common ancestors of x and y are the elements of
* SLCA (x, y). This naive algorithm simply starts at a and b, recursing upwards to the root(s) of
* the DAG. Wherever the recursion paths cross we have found our LCA. from
* http://www.cs.sunysb.edu/~bender/pub/JALG05-daglca.pdf. The algorithm:
*
*
* 1. Start at each of nodes you wish to find the lca for (a and b)
* 2. Create sets aSet containing a, and bSet containing b
* 3. If either set intersects with the union of the other sets previous values (i.e. the set of notes visited) then
* that intersection is LCA. if there are multiple intersections then the earliest one added is the LCA.
* 4. Repeat from step 3, with aSet now the parents of everything in aSet, and bSet the parents of everything in bSet
* 5. If there are no more parents to descend to then there is no LCA
*
*
* The rationale for this working is that in each iteration of the loop we are considering all the
* ancestors of a that have a path of length n back to a, where n is the depth of the recursion. The
* same is true of b.
*
*
* We start by checking if a == b.
* if not we look to see if there is any intersection between parents(a) and (parents(b) union b)
* (and the same with a and b swapped)
* if not we look to see if there is any intersection between parents(parents(a)) and
* (parents(parents(b)) union parents(b) union b) (and the same with a and b swapped)
* continues
*
*
* This means at the end of recursion n, we know if there is an LCA that has a path of <=n to a
* and b. Of course we may have to wait longer if the path to a is of length n, but the path to
* b>n. at the first loop we have a path of 0 length from the nodes we are considering as LCA to
* their respective children which we wish to find the LCA for.
*
* @param the graph vertex type
* @param the graph edge type
*
*/
public class NaiveLcaFinder
{
private DirectedGraph graph;
/**
* Create a new instance of the native LCA finder.
*
* @param graph the input graph
*/
public NaiveLcaFinder(DirectedGraph graph)
{
this.graph = graph;
}
/**
* Return the first found LCA of a and b
*
* @param a the first element to find LCA for
* @param b the other element to find the LCA for
*
* @return the first found LCA of a and b, or null if there is no LCA.
*/
public V findLca(V a, V b)
{
return findLca(
Collections.singleton(a), Collections.singleton(b), new LinkedHashSet<>(),
new LinkedHashSet<>());
}
/**
* Return all the LCA of a and b. Currently not implemented
*
* @param a the first element to find LCA for
* @param b the other element to find the LCA for
*
* @return the set of all LCA of a and b, or empty set if there is no LCA.
*/
public Set findLcas(V a, V b)
{
throw new UnsupportedOperationException("findLcas has not yet been implemented");
}
/**
* Recurse through the descendants of aSet and bSet looking for the LCA of a and b, which are
* members of sets aSeenSet and bSeenSet respectively, along with all elements on the paths from
* every member of aSet and bSet
*/
private V findLca(
Set aSet, Set bSet, LinkedHashSet aSeenSet, LinkedHashSet bSeenSet)
{
// if there is no LCA...
if ((aSet.size() == 0) && (bSet.size() == 0)) {
return null;
}
// does aSet intersect with bSeenSet
if (!Collections.disjoint(aSet, bSeenSet)) {
return overlappingMember(aSet, bSeenSet);
}
// does bSet intersect with aSeenSet
if (!Collections.disjoint(bSet, aSeenSet)) {
return overlappingMember(bSet, aSeenSet);
}
if (!Collections.disjoint(aSet, bSet)) {
return overlappingMember(aSet, bSet);
}
aSeenSet.addAll(aSet);
bSeenSet.addAll(bSet);
aSet = allParents(aSet);
// no point doing the same again (and it can stop us getting stuck in
// an infinite loop)
aSet.removeAll(aSeenSet);
bSet = allParents(bSet);
bSet.removeAll(bSeenSet);
return findLca(aSet, bSet, aSeenSet, bSeenSet);
}
/**
* Find the immediate parents of every item in the given set, and return a set containing all
* those parents
*
* @param vertexSet the set of vertex to find parents of
*
* @return a set of every parent of every vertex passed in
*/
private Set allParents(Set vertexSet)
{
HashSet result = new HashSet<>();
for (V e : vertexSet) {
for (E edge : graph.incomingEdgesOf(e)) {
if (graph.getEdgeTarget(edge).equals(e)) {
result.add(graph.getEdgeSource(edge));
}
}
}
return result;
}
/**
* Return a single vertex that is both in x and y. If there is more than one then select the
* first element from the iterator returned from y, after all the elements of x have been
* removed. this allows an orderedSet to be passed in to give predictable results.
*
* @param x set containing vertex
* @param y set containing vertex, which may be ordered to give predictable results
*
* @return the first element of y that is also in x, or null if no such element
*/
private V overlappingMember(Set x, Set y)
{
y.retainAll(x);
return y.iterator().next();
}
}
// End NaiveLcaFinder.java