- The problem is solved using modification of Floyd-Warshall algorithm. Shortest path calculation is done when the program starts.
- Complexity of the initial step(calculating all shortest paths from each stations) is O(|stations|^3)
- Worst case complexity of each query is O(|stations|)
- It is assumed that travel time can't be greater than Int.MaxValue
- To exit the program type END
You are asked to develop a new routing solution for public transport system that lets people search for the quickest route between to given stations. Your customer is also asking for the posibility to find stations nearby a given station that can be reached within a given time.
The transport network is modelled as a directed graph with edges that represent a connection between the two stations and are labelled with the travel time in seconds. If a transport line can be used in two directions it is modelled as two distinct, opposing edges. The stations are identified with alphanumeric strings without special characters or whitespace, such as “A” or “B” or “EXAMPLESTATION”. To keep things simple the train schedule and changing times at stations will be ignored.
###Input
The routing program starts by reading the transport network graph. The first line of input is the number of edges in the graph. The edges are defined on a single line each in the form: <source> -> <destination>: <travel time>
Where <source> and <destination> are station identifiers and <travel time> is a decimal number representing the travel time between source and destination in seconds. After the graph has been defined the routing program is ready to process routing queries. Each query is followed by a newline. There are two kinds of queries. A routing query which asks for the shortest route between two stations takes the following form: route <source> -> <destination>
A nearby query which asks for all the stations that can be reached from a given station within a given time looks as follows: nearby <source>, <maximum travel time>
###Output
The output for each query goes to a separate line. The output for a routing query is the ->- separated route followed by a colon and the travel time: <source> -> <waypoint1> -> ... <destination> : <travel time>
If no route exists an error message is printed. Error: No route from <source> to <destination>
For nearby queries the output is a comma separated list of stations with the travel times ordered by ascending travel times. <destination1>:<travel time>, <destinationation2>:<travel time>, ...
###Test Input
8
A -> B: 240
A -> C: 70
A -> D: 120
C -> B: 60
D -> E: 480
C -> E: 240
B -> E: 210
E -> A: 300
route A -> B
nearby A, 130
###Expected Output
A -> C -> B: 130
C: 70, D: 120, B: 130