topological-sort

Say, we have some items, and each defines some partial sorting rules, like this: I'm A and I want to be before B I'm C and I want to be after A but before D So we have items A,B,C,D with these rules: A>B C<A , C>D nothing else! So, B and D have no 'preferences' in ordering and are considered equal. As you see, transitive relation rules are not working here. However, if A>B it still means that B<A . So, there can be multiple possible results of sorting: A B C D A C D B A C B D A B C D How can I implement a sorting algorithm that handles such a situation? The reason: there're multiple loadable

Probably best illustrated with a small example. Given the relations A < B < C A < P < Q Correct outputs would be ABCPQ or APQBC or APBCQ ... etc. In other words, any ordering is valid in which the given relationships hold. I am most interested in the solution that is easiest to implement, but the best O(n) in speed and time is interesting as well. This is called topological sorting . The standard algorithm is to output a minimal element, then remove it and repeat until done. Do several sorts. First sort according to the first rule, then according to the second one and so on. Should work,

Some programming languages (like haskell ) allow cyclic dependencies between modules. Since the compiler needs to know all definitions of all modules imported while compiling one module, it usually has to do some extra work if some modules import each other mutually or any other kind of cycle occurs. In that case, the compiler may not be able to optimize code as much as in modules that have no import cycles, since imported functions may have not yet been analyzed. Usually only one module of a cycle has to be compiled that way, as a binary object has no dependecies. Let's call such a module

I'm trying to compute a partial "topological sort" of a dependency graph, which is actually a DAG (Directed Acyclic Graph) to be precise; so as to execute tasks without conflicting dependencies in parallel. I came up with this simple algorithm because what I found on Google wasn't all that helpful (I keep finding only algorithms that themselves run in parallel to compute a normal topological sort). visit(node) { maxdist = 0; foreach (e : in_edge(node)) { maxdist = max(maxdist, 1 + visit(source(e))) } distance[node] = maxdist; return distance[node]; } make_partial_ordering(node) { set all node

I want to use a PriorityQueue to do a topological sort on a graph. For brevity, I'd like to use an anonymous inner class for the comparator. However, I need access to the graph g in order to determine the in degree of the nodes I'm looking at. Is this possible? /** * topological sort * @param g must be a dag */ public static Queue<String> topoSort(DirectedGraph<String, DefaultEdge> g) { Queue<String> result = new PriorityQueue<String>(g.vertexSet().size(), new Comparator<String>() { DirectedGraph<String, DefaultEdge> g; @Override public int compare(String arg0, String arg1) { if (g.inDegreeOf