From the project description, it seems that you want to implement two of the important algorithms in graph theory namely, Dijkstra's algorithm (to find a shortest path to all vertices given a source node) and a DFS algorithm using STL in C++. Also from the interface definition, it also seems that you want to use the adjacency list representation of graph to proceed with the program.
Given all of these specifications, I think the task can be easily completed within two days.
Waiting for your response...
Regards,
Atul Rajdhar