Dueling with the input

Still thinking about how to keep those combinations (or palindromes, now that we see we can avoid some sorting if we go ahead and generate them) around only as long as necessary. One thing that's kind of tempting is to take advantage of what we know about when we can reuse these values--we can generate them for one of  2 * k and 2  * k + 1 and then reuse them (with some modification) for the other. So, why not generate the trees two at a time?

"Well, you don't know that you'll need both of them," you object. "The Code Jam people could make you waste your time by generating input that only asks about ranges corresponding to Ys with even numbers of digits (or odd, take your pick)." And you're right, they could. Our attempts to speed things up can be subverted... but I think this one is worth a try.

At least initially, I'd be inclined to generate a list of pairs of trees, with the first being for 2 * k digits, the second being for 2 * k + 1. (Yes, one-digit Ys are a special case again.) More news as it happens.

UPDATE: new best time output:

real    0m0.192s
user    0m0.160s
sys     0m0.028s


Total allocation is down to not quite 117 MB, compared with 124 MB before, and "maximum residency" is around 9.6 MB. GC time is down to 41.2% of total execution time. I guess that's better than almost half, but that still seems high. One thing that is gratifying: the first time I used -sstderr to save GC info, it listed almost 160 MB copied during GC and over 16 MB maximum residency. Now the maximum copying during GC is just 63 MB, less than half what it was before.

And that's using spread, which is expensive because it does Integer divides. We'll do that next, and then I really should try to ditch the gratuitous meets of values in the trees that we never search for. That should be pure gravy.

UPDATE: spread is worth it to avoid having to sort again. (Before we weren't taking advantage of that, so spread was overhead.)

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