aka the Hockey Stick Theorem.
Henry Rich
On 6/6/2013 12:18 PM, Bo Jacoby wrote:
The theorem that 2!y is equal to +/i.y is a special case of the more general
theorem that (>:x)!y is equal to +/x!i.y
- Bo
________________________________
Fra: Roger Hui <[email protected]>
Til: Programming forum <[email protected]>
Sendt: 16:41 torsdag den 6. juni 2013
Emne: Re: [Jprogramming] Finding repeated substrings
There is a proof of a very similar theorem in section 1.4 of *Notation as a
Tool of Thought <http://www.jsoftware.com/papers/tot.htm>*. (The
difference is that index origin is 1 in the paper.)
On Thu, Jun 6, 2013 at 6:44 AM, Raul Miller <[email protected]> wrote:
Caution: this code can give an incomplete result. For example, I do
not believe it will find 'aabaab'. Rather than fix this, I'll defer to
other solutions in this thread (which I imagine properly address this
issue).
If anyone wants to take this code and fix it, the first instance of 2
-~/\ ] should be replaced with a mechanism that treats all
combinations of 2 (and not just adjacent pairs).
(And on that note, I Tracy Harms recently directed my attention to a
page with a beautiful proof that 2&! is +/@i. - that concept would be
useful, here, I think. I wish I had recorded the url of that page. But
the gist of my thought is that it should be possible to go from y and
a member of i.2!y to a unique pair of two numbers in the range i.y,
and that might be a nice way of implementing this "combinations of 2"
function.)
FYI,
--
Raul
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