Java: Count all possible Paths between two Vertices

Problem Statement:

Count the total number of ways or paths that exist between two vertices in a directed graph.

These paths don’t contain a cycle, the simple enough reason is that a cycle contains an infinite

number of paths and hence they create a problem

For the following Graph:

Input:

Count paths between A and E

Output:

Total paths between A and E are 4
The 4 paths between A and E are:
A -> E
A -> B -> E
A -> C -> E
A -> B -> D -> C -> E