Question

I have to write an algorithm that find the path in DAG with single source and single sink…
I really don’t know what to do ( tried to use DSF and topological sort but nothing…)
I don’t want anyone to solve it for me but just some guidance.

Thank you

Answer 1

BFS finds shortest path in general unweighted graph – and also specifically in DAG [since it is also a graph]. It is also pretty simple to code it.

Note that DFS will find a path – but it doesn’t have to be the shortest one.

You might also want to have a look at this post to see how to get the actual path from BFS after running it.

EDIT: according to your comments, it seems you want O(|V|) solution, and it doesn’t have to be shortest. a modification of DFS is the way to do then, since the DAG has a single source and a single sink, every path from the source reaches the sink.

Note that since your graph is a DAG and since we established that every path from the source reaches the sink, you don’t need to go backward after exploring a certain path [so no recursion or stack is needed].

pseudo-code:

modifiedDFS(source,target):
  map <- new map
  current <- source
  while (current != target):
    next <- current.getNextVertex() //just chose an arbitrary edge and follow it, doesn't matter which
    map.put(next,current) //we "discovered" next by following current
    current <- next

after running this algorithm, you need to follow back the map from the target to the
source – and you get the actual path [reversed of course]

The complexity is indeed O(n) because we visit each node at most once. In order to maintain O(n) the map has to be a hashmap [and not a treemap]. If the vertices are enumerated – you can even implement the map as an array.