[Jprogramming] Permutations of a sort.

[Roger Hui]

nv nv3 nc nct were written to satisfy the specifications 
which were that there was insufficient memory to hold 
all m!n entries at once, or n could be larger than the
number of bits in a machine word.  That is, the next 
string should be computed.  Under such conditions 
nv nv3 nc nct could run where ncb would fail with an 
"out-of-memory".  Moreover, if n > word size, nv nv3 
would give right answers when nc nct ncb would not.




----- Original Message -----
From: "R.E. Boss" <r.e.boss at planet.nl>
Date: Thursday, August 30, 2007 10:46
Subject: RE: [Jprogramming] Permutations of a sort.
To: 'Programming forum' <programming at jsoftware.com>

> To conclude: (NB. beware of line wraps!)
> 
> First, all output is equal
> 
>    2-:&>/\ ".&.> 
> 'nv^:(i.5!28)_28{.5#1';'nv3^:(i.5!28)_28{.5#1';'#:nc^:(i.5!28) 
> 31';'#: nct^:(i.5!28) 31';'#: 5 ncb 28'
> 1 1 1 1
> 
> 
> although some verbs perform better than others:
> 
>      ('nv';'nv3';'nc';'nct';'ncb')rnkng 
> score 'nv^:(i.5!28)_28{.5#1';
> 'nv3^:(i.5!28)_28{.5#1'; '#: nc^:(i.5!28) 31'; '#: nct^:(i.5!28) 31';
>  '#: 5 ncb 28'
> 
> +-----+-------+------+----+-----+
> |place| rlprf | rlt  |rls |verbs|
> +-----+-------+------+----+-----+
> |3    | 861.83|216.89|3.97| nv  |
> +-----+-------+------+----+-----+
> |4    |1029.54|259.10|3.97| nv3 |
> +-----+-------+------+----+-----+
> |2    | 580.08|210.85|2.75| nc  |
> +-----+-------+------+----+-----+
> |1    | 207.48| 75.42|2.75| nct |
> +-----+-------+------+----+-----+
> |0    |   1.00|  1.00|1.00| ncb |
> +-----+-------+------+----+-----+
> 
> 
> where the verbs are
> 
> +----+-----------------------------------------------------------
> ----------+
> | nv |+-+-+--------------------------------
> +                               |
> |    ||3|:| j=. 0 i:~ (>: +./\.) 
> y         |                               |
> |    || | | (j{.y),1,(1+j-
> #y){.1$~_1++/j}.y|                               |
> |    |+-+-+--------------------------------
> +                               |
> +----+-----------------------------------------------------------
> ----------+
> | nv3|+-+-+---------------------------------------
> +                        |
> |    ||3|:| one=.y i: 
> 1                           |                        |
> |    || | | zer=.y i: 
> 0                           |                        |
> |    || | | if. one < zer 
> do.                     |                        |
> |    || | |  zer=. (one {. y) i: 
> 0                |                        |
> |    || | |  1 0 (zer+0 1)} y /: 
> y+2*(2+zer)<.i.#y|                        |
> |    || | | 
> else.                                 |                        |
> |    || | |  1 0 (zer+0 1)} 
> y                     |                        |
> |    || | | 
> end.                                  |                        |
> |    |+-+-+---------------------------------------
> +                        |
> +----+-----------------------------------------------------------
> ----------+
> | nc |+-+-+--------------------------------
> +                               |
> |    ||3|:|  n=. 
> y                         |                               |
> |    || | |  t=. n xor n and n-
> 1           |                               |
> |    || | |  b=. 
> t+n                       |                               |
> |    || | |  b or _2 shift (b xor n) <.@% 
> t|                               |
> |    |+-+-+--------------------------------
> +                               |
> +----+-----------------------------------------------------------
> ----------+
> | nct|(] 23 b. (_2"_) 33 b. -~ <.@%~ ] 22 b. [) (] + ] 22 b. 
> ] 17 b. ]- 1:)|
> +----+-----------------------------------------------------------
> ----------+
> | ncb|[: |.@; [: (+&.> <@;\.)/ [ */&(2 <.@^ |. at i.) >:@-
> ~                   |
> +----+-----------------------------------------------------------
> ----------+