This is the fourth and probably my last post about solving Facebook programming puzzle. The Find Sophie problem is a buffet (hardest) level puzzle. It is basically a variation of the traveling salesman problem. Traveling salesman is of course, a NP-complete problem. But before you throw up your hand, consider the puzzle refers to locations in your home where you may find a cat. Just how many locations are there. Let's say living room, dining room, bedroom, on the bed, under the desk, behind the curtain, ... etc. If Facebook is not very wicked, this puzzle should be bounded to a low hundreds of locations. This mean it is still possible to solve using some relatively simple search algorithm.

Here is the outline of my solution:

1. Prepare to enumerate all paths.
2. Prefer the local optimal during the search. Remember the best solution encountered so far.
3. Prune the search tree. For example if the current best solution has a score of 50. When you are considering another path, as soon as its score exceed 50, you should abandon it.
4. Improve the pruning by taking the additional score to complete the path into account. For example, if the current score of a partial path is S, the minimum score to complete the remaining walk is Rmin. Then if S+Rmin > best score, prune it.

Actually I have submitted the solution a few months ago. Only today do I find out I have not posted my solution in my blog. So I'm really speaking from my memory. I hope my plan is still accurate. Again my un-tidied code is available.

The other 3 facebook puzzles I have solved was posted below:

• Peak Traffic Solution
• Refrigerator Madness solution
• smallworld solution

2010.07.22 [programming] - comments