The Graph and Vertex files contain the implementation for the
directed non-weighted graph used for this problem. The graph's edges
are stored as a Map with Vertex keys and lists of adjacent vertices as
values. A slightly modified version of the DFS algorithm has been
used to find if the graph contains a cycle or not. If the program detects
a back edge (and edge that points to an ancestor in the DFS tree, which
is represented by a GRAY colored node, meaning that we are not done
exploring that node) it means the graph contains a cycle.
For problems 2 and 3 the WeightedGraph implementation has been used,
which represents vertices by their Integer labels and uses the Edge
class to store adjacent vertices and the weights.
To find the shortest path from the source to all other nodes in a DAG, a Topological Sort is performed, and the nodes are traversed in that order, updating the distances accordingly until the end.
Because we know that the weights of the edges can be at most 30, we can use Dial's algorithm which is a modified version of Dijkstra that uses buckets instead of a priority queue or min-heap. A bucket i is used to store the nodes with distance i from the source. The buckets are traversed starting from 0 to the maximum distance value (the number of nodes * the maximum weight) and the distances and buckets are updated along the way similarly to dijkstra's algorithm.