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TedPride,
Good catch! I didn't have time to track it down myself this morning as I was supposed to be getting ready for work. For the purposes of the original thread, it appears that 0 was being allowed as a triangular number. With that allowance, all numbers can indeed be the sum of 3 triangles.

As far as speed, you are right that this is quite fast. If it was not fast enough in a real problem you would likely use C as tachyon, the cheater, did ;-)
I have no idea about how to figure out the big O of either solution, but I did want to mention that my solution is more than a constant factor faster in case you decided to spend the time optimizing. At 5_000 random targets between 1 and 5_000_000 it was twice as fast, but for 10_000 random targets between 1 and 987_654_321 it was three times as fast. I didn't want to come off as offensive - I just like silly challenges like this.


Cheers - L~R


In reply to Re^2: Triangle Numbers Revisited by Limbic~Region
in thread Triangle Numbers Revisited by Limbic~Region

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    [LanX]: well, me was kidding!
    [marto]: One of the main train stations is right across the road, so handy from that perspective, and there are some nice hotels in the area, but it's not great after dark, or sometimes during the day to be honest
    [LanX]: not easy to find good and affordable venues ...
    [marto]: hmm, there are several universities and colleges handy that I'd have thought would offer such services, given this is out of term time, I've no experience of paying for venues :)
    [LanX]: OK ...
    [LanX]: I have no idea how Mark scouted, giving that he lives in London ... but I think he mentioned his wife being Scottish
    [marto]: ah, so this is payback :P
    [LanX]: problem with booking venues is that you only know the number of participants a week in advance. ..
    [marto]: I guess most cities have areas similar to this, I tend not to mind personally, but would not go out of my way to head down that way
    [marto]: it'll probably be fine.

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