Shortest Path Recovery

Mr. Biscuit is in trouble. He accidentally deleted all the programs in his server and his database is corrupted as a result. There was a graph contained in the database. The graph had a source node and  the shortest path from the source node to the other nodes was calculated using a function called SSSP. Mr. Biscuit has found the pseudocode of the function in his notebook. The pseudocode is given below:


This is a companion discussion topic for the original entry at https://toph.co/p/shortest-path-recovery