Question

I have data in database which is in the form of:

A -> B
C -> D
B -> C
F -> G
G -> J
X -> Z

This basically means that A goes to B, C goes to D etc. Given this data and a node (such as C) I would like to construct the complete path that C is found that is A -> B -> C -> D . I tried to do this by using a few dictionaries and recursive loops but I don’t like such a sluggish solution since there are lots of data in db. What is a better way to solve this problem ? In terms of both algorithm and the data structure ? Any ideas or hints are appreciated.

Answer 1

You are looking basically for DFS, but you need to do it twice – one per direction.

First do a a DFS on the reverse ‘graph’, starting from C.

In your example it will give you Path1 = C->B->A

Next, do a DFS on the original graph, again from C.

In your example it will give you Path2= C->D

Now, by reversing Path1, and concatinating Path2 to it you will get:

reverse(Path1)  + Path2 = A->B->C + C->D = A->B->C->D

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Clarification – DFS is just abstraction, what you actually are doing is something similar to (pseudo code):

current <- C
list = []
while (current != null):
   list.addFirst(current)
   current <- u such that (u,current) is in the DataBase
current <- C
list.deleteLast() // last is C
while (current != null):
   list.addLast(current)
   current <- u such that (current,u) is in the DataBase

Note that finding u both cases is a simple dictionary look up, in the first the “Target” is the key, and in the second the “Source” is the key.