Here's an interesting little puzzle. I have a set of files named after book ISBNs. These can be from five to nine characters long. There are thousands of these, and I don't want to put them all in one directory because that will hurt file system performance. I was planning to split them all up by zero-padding them all to nine characters and then slicing their numbers into directory names. For example, 123456789.gif would be stored at /12/34/56/123456789.gif.

Now, if I make too many directories I'll be hurting file system performance rather than helping. So, the challenge is to come up with a short algorithm for determining the optimal way to break up these files so that we have no more than n (probably 100) files or subdirectories in any one directory, and the minimum number of directories in total. This would be simple if the data was a uniform distribution, but in this case it isn't. It's possible for 99% of the data to have the same first five digits.

I was attacking this through brute force by simulating the directories with hashes and counting the number of files that fell into each one, but I feel like there must be some simple mathematical solution for this that I'm not seeing. Also, my approach makes it a pain to experiment with alternatives like /12345/67/12345689.gif, which might be the best solution with a given set of data.

I know this is kind of dumb to obsess over, and I could just stop fooling around and split them up on every two digits, but it turned into kind of an interesting brainteaser. Anyone?

In reply to brainteaser: splitting up a namespace evenly by perrin

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