algorithm - Number of paths between two nodes in a DAG

Question

I want to find number of paths between two nodes in a DAG. O(V^2) and O(V+E) are acceptable.

O(V+E) reminds me to somehow use BFS or DFS but I don't know how. Can somebody help?

Answer 1

Do a topological sort of the DAG, then scan the vertices from the target backwards to the source. For each vertex v, keep a count of the number of paths from v to the target. When you get to the source, the value of that count is the answer. That is O(V+E).