nextPermutation and ranges

[John Colvin]

On Friday, 8 February 2013 at 06:59:20 UTC, Marco Leise wrote:
> Am Thu, 7 Feb 2013 13:52:01 -0800
> schrieb "H. S. Teoh" <hsteoh at quickfur.ath.cx>:
>
>> On Thu, Feb 07, 2013 at 09:42:34PM +0100, bearophile wrote:
>> > H. S. Teoh:
>> > 
>> > >Combinatorial puzzles come to mind (Rubik's cube solvers 
>> > >and its ilk,
>> > >for example).  Maybe other combinatorial problems that 
>> > >require some
>> > >kind of exhaustive state space search. Those things easily 
>> > >go past
>> > >20!  once you get beyond the most trivial cases.
>> > 
>> > I know many situations/problems where you have more than 20! 
>> > cases,
>> > but in those problems you don't iterate all permutations, 
>> > because the
>> > program takes ages to do it. In those programs you don't use
>> > nextPermutation, you scan the search space in a different 
>> > and smarter
>> > way.
>> > 
>> > I don't know of any use case for permuting so large sets of 
>> > items.
>> [...]
>> 
>> It depends, sometimes in complex cases you have no choice but 
>> to do
>> exhaustive search. I agree that it's very rare, though.
>> 
>> 
>> T
>> 
>
> So right now we can handle 20! = 2,432,902,008,176,640,000
> permutations. If every check took only 20 clock cycles of a 4
> Ghz CPU, it would take you ~386 years to go through the list.
> For the average human researcher this is plenty of time.

On a modern supercomputer this would take well under 2 months. (I 
calculated it as ~44 days on minerva at Warwick,  UK). 19! would 
take less than 3 days.

In a parallel setting, such large numbers are assailable.