Nested interval tree encoding

However, I'm running into a snag when I try to decode the materialzed path of certain nodes using the Euclidean algorithm. The first child node of any parent does not decode properly; for instance: 3.12.5.21.1 which is correctly encoded as the continued fraction of 4173/1354 is decoded as 3.12.5.22:

4173 = 1354 * 3 + 111
1354 = 111 * 12 + 22
111 = 22 * 5 + 1
22 = 1 * 22 + 0

Other nodes like 3.12.5.21, 3.12.5.22, and 3.12.5.21.2 are correctly decoded; so this looking like a special case involving the first child node.

Is there any way to detect and handle this without looking-up the parent node? Would using reversed continued fractions avoid this?

-Eric Received on Thu Jul 03 2008 - 19:04:17 CEST