• Topcoder 250-Point problem from SRM 486, Division 1
• James S. Plank
• Sun Nov 4 10:47:46 EST 2012

Like many topcoder problems, this is an unweighted shortest path problem, with a couple of twists. I'm not going to hold your hand through this one, though. You are going to build a graph. You can build it before doing the BFS or while you do the BFS. Each edge is labeled with an operation. Whenever you reach a node that is greater than t, you can stop processing that node.

Here is an example of the graph that you would build when s is 7 and t is 392, were you to build the graph before doing the BFS. Whenever I create a node whose value is greater than 392, I stop processing that node.

It should be pretty easy to see how this graph generates "+*+". It should also be clear how it generates "/+***" in example 1. There are some details, however, that you'll have to iron out:

• You only go to node 1 once.
• The + and * edges from node 2 both go to 4. You can use the Unix sort program to figure out the lexicographic order of the operators.
• 10⁹ is an irritating constraint. Think about integer overflow and how to handle it.
• The graph can have cycles if s is a power of two. Think about it.