Question

I am looking for an algorithm to create a linked list from a set of nodes. For example, let’s assume a node is an airline ticket from a source point to destination. (e.g., Chicago to Detroit) and there are several airline tickets. Assuming all these airline tickets are jumbled, what is the best way to determine the entire journey path.
If there are 5 airline tickets like Chicago->Detroit, Denver->Chicago, Detroit->DC, DC->New York, San Jose->Denver, the algorithm should be able to come up with the correct start to end path.

San Jose -> Denver -> Chicago -> Detroit -> DC -> New York

Answer 1

If you are guaranteed that the nodes will form a single path (ie, maximum indegree is 1, maximum outdegree is 1, exactly one node has indegree 0, exactly one node has outdegree 0), then you could do the following:

• Construct two hashes: in_cities and out_cities
• For every node A -> B, add it to in_cities with key A and out_cities with key B
• Pick a node arbitrarily, call it S
• Have curr point to S. While the source city of curr is in out_cities, insert the corresponding node in the beginning of the path. Update curr to point to this node.
• Have curr point to S. While the destination city of curr is in in_cities, add the corresponding node to the end of the path. Update curr to point to this node.

Now you are done, in linear time with respect to the total number of cities.