We did some examples of counting the number of distinct paths from a given vertex S to a given vertex T in a DAG.
Then we discussed a general algorithm based on the following recurrence:
Define N(V) = the number of distinct paths from S to V.
Then N() satisfies the following recurrence relation:
We discussed a linear-time algorithm for computing the number of distinct S->T paths in a DAG using this recurrence.
Then we tried to convince ourselves that the recurrence was true.