algorithm,graph,vertex,directed-acyclic-graphs,topological-sort

a. Prove that for every DAG the above function is uniquely defined, i.e. it's the only function that satisfies conditions 1,2 and 3. Maybe I am missing something, but this seems really obvious to me: if you define it as the minimum that satisfies those conditions, how can there...

def dfs(graph,start) Function declaration creates local scope for variables. To access any variable from outside you'll need to pass it as an argument to this function....

algorithm,topological-sort,connected-components

Yes, it's technically correct, because a digraph without self-loops is acyclic (i.e., topologically sortable) iff all strong components have size 1. The most common topological sorts do cycle detection as an easy byproduct, though.

algorithm,sorting,pseudocode,topological-sort

Recall the procedure of the topological sort, which is in short: result <- [] //empty list Find a node n which is a sink in the graph remove all edges connecting to n, and n from the graph result.addFirst(n) if there are nodes left, return to 2 If at any...

python,networkx,topological-sort

One approach is to build a dependency graph containing a directed edge between A and B if and only if A strongly depends upon B, or A weakly depends upon B and B is strongly depended upon by some other task. Here's some code that does just that. In this...

c++,algorithm,recursion,graph,topological-sort

Obviously, you'd use a stack but you wouldn't put all adjacent nodes anyway: that would yield a DFS with the wrong size complexity anyway (it would be quadratic in the number of nodes assuming non-parallel edges, otherwise potentially worse). Instead, you'd store the current node together with a state indicating...

graph,topological-sort,longest-path

If we don't sort it, we don't know which adjacent vertex to choose first and it may lead to a situation where we use distance of a vertex v to update distances of its adjacent vertices adj[v], but after that, the distance of vertex v gets updated, so vertices from...

c++,graph,graph-algorithm,topological-sort

First, for the number of edges, it would be simpler to count them directly when you build the graph (just add a counter in your Digraph class and increment it each time you add an edge … ) For the topological sort, first I have a question: your edges are...

Topological Sorting is mainly used for scheduling jobs from the given dependencies among jobs. In computer science, applications of this type arise in instruction scheduling, ordering of formula cell evaluation when recomputing formula values in spreadsheets, logic synthesis, determining the order of compilation tasks to perform in makefiles, data serialization,...

algorithm,pseudocode,directed-graph,topological-sort

There's no particular reason to use a stack as opposed to some other kind of collection. If we pop elements nondeterministically, then we can realize all possible topological orders. Thus, the topological order is unique if and only if the collection contains one element each time we pop (except when...

c++,priority-queue,depth-first-search,topological-sort

The problem seems to be that pq.top is called before all outgoing edges of the current node have been checked. Consider the following graph: Nodes: A, B, C; Edges A->B, A-C. Let C have a smaller priority value, i.e. it should come first. During dfs(A), you check B before C....