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Topic: make 100 by using 1, 7, 7, 7, 7
Replies: 41   Last Post: Nov 15, 2007 6:13 PM

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 Rick Decker Posts: 1,356 Registered: 12/6/04
Re: make 100 by using 1, 7, 7, 7, 7
Posted: Nov 15, 2007 8:06 AM

Michael Press wrote:
>

>> On 2007-11-14 21:08:03 -0500, Michael Press <rubrum@pacbell.net> said:
>>

>>> Here is a Perl script that prints out all balanced strings
>>> of parentheses. The balanced strings of 2n parentheses
>>> can be bijected with the binary trees on n vertices.
>>>
>>> The script works like this:
>>>
>>> P_n is the set of balanced strings of 2n parentheses so
>>> P_{n+1} = (P_{k}) P_{n - k}.
>>>
>>> The script is criminally wasteful of time and
>>> space, but it is easy to code, an easy to understand. :)
>>>
>>> ________________________
>>> #!/usr/bin/perl

>
> [...]
>

>>> ________________________
>> Nice work with the recursion!
>
> Thanks. I should have mentioned that the balanced
> strings are bijectable with the complete binary
> trees on 2n+1 vertices, a more relevant structure.

Not to mention the triangulations of a convex polygon
with n + 2 vertices.
>
> A sane approach to listing the strings
> is by branch and bound, keeping track of
> parentheses depth.
>

Regards,

Rick

Date Subject Author
11/12/07 dangerousgame95@gmail.com
11/12/07 Thomas Nordhaus
11/12/07 amzoti
11/12/07 quasi
11/12/07 dangerousgame95@gmail.com
11/13/07 magidin@math.berkeley.edu
11/12/07 Thomas Nordhaus
11/12/07 quasi
11/12/07 Joshua Cranmer
11/12/07 Raymond Manzoni
11/13/07 William Elliot
11/13/07 amzoti
11/12/07 David R Tribble
11/12/07 Nat Silver
11/12/07 Raymond Manzoni
11/12/07 Raymond Manzoni
11/13/07 benjamin.a.bartsch@gmail.com
11/13/07 amzoti
11/13/07 David W. Cantrell
11/13/07 magidin@math.berkeley.edu
11/13/07 David W. Cantrell
11/13/07 magidin@math.berkeley.edu
11/13/07 briggs@encompasserve.org
11/13/07 Robert Israel
11/13/07 Dave Seaman
11/13/07 benjamin.a.bartsch@gmail.com
11/13/07 amzoti
11/13/07 David W. Cantrell
11/13/07 Jan Kristian Haugland
11/13/07 Robert Israel
11/13/07 Kira Yamato
11/13/07 Kira Yamato
11/13/07 Robert Israel
11/13/07 amzoti
11/14/07 Thomas Nordhaus
11/15/07 Michael Press
11/14/07 Michael Press
11/15/07 Kira Yamato
11/15/07 Michael Press
11/15/07 Rick Decker
11/13/07 Raymond Manzoni