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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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Kira Yamato

Posts: 526
Registered: 7/2/05
Re: make 100 by using 1, 7, 7, 7, 7
Posted: Nov 15, 2007 1:40 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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
>
> $count = $ARGV[0];
>
> print join "\n", pren($count), "";
>
> sub pren
> {
> my @list = ();
>
> (my $n) = @_;
> if ($n == 0) {push(@list, "")}
> elsif($n == 1) {push(@list, "()")}
> elsif($n > 1)
> {
> foreach $k (0 .. $n-1)
> {
> foreach $p1 (pren($k))
> {
> foreach $p2 (pren($n - 1 - $k))
> {
> push @list, sprintf "(%s)%s", $p1, $p2;
> }
> }
> }
> }
> return @list;
> }
> ________________________


Nice work with the recursion!

>
>
> $ ./parens.pl 5 | cat -n
> 1 ()()()()()
> 2 ()()()(())
> 3 ()()(())()
> 4 ()()(()())
> 5 ()()((()))
> 6 ()(())()()
> 7 ()(())(())
> 8 ()(()())()
> 9 ()((()))()
> 10 ()(()()())
> 11 ()(()(()))
> 12 ()((())())
> 13 ()((()()))
> 14 ()(((())))
> 15 (())()()()
> 16 (())()(())
> 17 (())(())()
> 18 (())(()())
> 19 (())((()))
> 20 (()())()()
> 21 (()())(())
> 22 ((()))()()
> 23 ((()))(())
> 24 (()()())()
> 25 (()(()))()
> 26 ((())())()
> 27 ((()()))()
> 28 (((())))()
> 29 (()()()())
> 30 (()()(()))
> 31 (()(())())
> 32 (()(()()))
> 33 (()((())))
> 34 ((())()())
> 35 ((())(()))
> 36 ((()())())
> 37 (((()))())
> 38 ((()()()))
> 39 ((()(())))
> 40 (((())()))
> 41 (((()())))
> 42 ((((()))))


--

-kira



Date Subject Author
11/12/07
Read make 100 by using 1, 7, 7, 7, 7
dangerousgame95@gmail.com
11/12/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Thomas Nordhaus
11/12/07
Read Re: make 100 by using 1, 7, 7, 7, 7
amzoti
11/12/07
Read Re: make 100 by using 1, 7, 7, 7, 7
quasi
11/12/07
Read Re: make 100 by using 1, 7, 7, 7, 7
dangerousgame95@gmail.com
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
magidin@math.berkeley.edu
11/12/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Thomas Nordhaus
11/12/07
Read Re: make 100 by using 1, 7, 7, 7, 7
quasi
11/12/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Joshua Cranmer
11/12/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Raymond Manzoni
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
William Elliot
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
amzoti
11/12/07
Read Re: make 100 by using 1, 7, 7, 7, 7
David R Tribble
11/12/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Nat Silver
11/12/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Raymond Manzoni
11/12/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Raymond Manzoni
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Adrian Duma
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
benjamin.a.bartsch@gmail.com
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
amzoti
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
David W. Cantrell
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
magidin@math.berkeley.edu
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
David W. Cantrell
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
magidin@math.berkeley.edu
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
briggs@encompasserve.org
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Robert Israel
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Dave Seaman
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
benjamin.a.bartsch@gmail.com
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
amzoti
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
David W. Cantrell
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Jan Kristian Haugland
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Robert Israel
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Kira Yamato
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Kira Yamato
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Robert Israel
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
amzoti
11/14/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Thomas Nordhaus
11/15/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Michael Press
11/14/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Michael Press
11/15/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Kira Yamato
11/15/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Michael Press
11/15/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Rick Decker
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Raymond Manzoni

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