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Coding challenge

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23 pointsColinWright14 comments

This problem is not about a Golomb ruler. When dealing with Golomb rulers you care about uniqueness of lengths across all pairs, while in this problem you do not.

If you had 4 oranges and 5 bowls, you could place them as follows:

1 1 0 1 1

This arrangement is not a Golomb ruler because the lengths 1 and 3 both occur more than once, but it is a valid solution to a smaller version of the problem in the OP.

I made a python program to check every possible combination. It should run for 1 more hour and then should spit "no solution found".

Is there any smarter way to do it (in software) without brute forcing?

The answer to this problem is not zero.

To the best of my knowledge all of the smarter ways to do it are just smarter ways to brute force it.

You are right, I mistakenly thought that it was about a Golomb ruler, which it is not.

EDIT: Found 7555794 solutions, took my 2GHz P4 30 minutes.

Got the same answer with a slightly improved brute force search, in about 3 minutes. I spent more time than that trying to find a "clever" way to do it, lol.

  barnabas:btch pota$ time python btch.py 
  found: 7555794

  real	1m18.464s
  user	1m18.417s
  sys	0m0.031s

(i5 2500k)

Nice! Would you show us the source?

It might be similar to mine: http://pastie.org/2007710

Run on 2.4Ghz Core 2 Duo:

  $time python oranges.py 
  7555794

  real	1m24.252s
  user	1m23.841s
  sys	0m0.144s

You can still get this to be much faster if you stuff this information into bitmasks, especially if you do it in one of the other languages. You can also get a lot of speedup out of more clever pruning if you're willing to precompute a bunch of stuff.

Edit: It seems like a lot of the function calls this program makes are unnecessary. This version runs about 37 seconds faster without any of the trickery I mentioned: http://pastie.org/2007699

Ah, Golomb's Ruler. Did Golom find this in a cave? HEEERRRRP.

correct me if im making a stupid mistake here, but isnt this just proving that the optimal golomb ruler for order 9 has a length of 44 ?

Looks like Golomb ruler to me.

Exactly.

I would just feed this to a counting SAT, or constraint, solver.

If I wrote the constraint solver, does that count as an acceptable answer?

There are some fancy ways of doing this, involving lots of bitshifting, which are quite fun.

Edit: Remove mis-remembered bitshifting.

I bet on 5631408

What would you like to wager?

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