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

Have you wonder why a highway is designed like this? Let's say you are driving from a large city A to a large city B. Between them is a mid size city K. Now city A and B are major economic center and travel destinations. City K is none of that. It is yet another non-descript city. Everyone seems to heading to city B. There seems little reason for anyone to stop in city K.

The traffic on the highway was free flowing. Yet as you approach city K, local traffic starts to fill up the highways. the It gets to a point when everything comes to a crawl. You curse at the traffic. Then you wonder why must the intercity highway go through city K at all? Why doesn't it just bypass it so that travelers between A and B can have a smoother trip?

I have wondered about this for a long time. Now I have a theory. Roads are built for people. Where there are more people traveling, more investment will be made to build roads. This should make pretty good sense.

Now which kind of traffic have higher volume? Intercity traffic between A and B or local traffic in K? Despite your intuition that everyone seems to travel between A and B, there are actually more local traffic in city K. This is demonstrated by the fact that traffic is free flowing between A and B but clogged within city K. Therefore more funding will be allocated to build roads for residents of city K and not a bypass. Since intercity travelers are the minority, they will not be better off than the local residents of city K.

2010.07.10 [travel, engineering] - comments