You may wish to tighten the conditions on the competition,
for example to exclude the following:
L=: *./@:>:@:i."0 i.1000x
f2=: {&L
f2 99
69720375229712477164533808935312303556800
y=: 100 [EMAIL PROTECTED] 1000x
ts 'f2 y'
5.11238e_5 2112
By the way:
lcm 0x
|index error
| y ((([EMAIL PROTECTED]){.){{:@])z2
----- Original Message -----
From: "R.E. Boss" <[EMAIL PROTECTED]>
Date: Monday, December 31, 2007 11:55
Subject: [Jprogramming] FW: (New Year) Competition: most efficient
alternative for ([: *./ >:@i.)"0 y for extended y
To: 'Programming forum' <[email protected]>
>
>
> 5 ts '([:*./ >:@i.)"0 y'[y=:[EMAIL PROTECTED] 1000x
> 0.28845623 188992
>
> is not an optimal solution, see
>
> 5 ts '([:*./&.|. >:@i.)"0 y'
> 0.20137625 189504
>
> (([:*./ >:@i.)"0 -: ([:*./&.|. >:@i.)"0) y
> 1
>
> Nevertheless, the first ([:*./ >:@i.)"0 will serve as the
> benchmark.(You may use any y (of natural numbers) you like.)
>
> Solutions foo0, foo1, ... will be ranked according to
>
> (\:,.]) 2 rsd ({.%"1 ]) 5 ts&'([:*./ >:@i.)"0 y';'foo0 y';'foo1
> y';'....'
> with
>
> ts=: 6!:2 , 7!:[EMAIL PROTECTED]
>
> and with
>
> rsd=: 4 : 0 NB.
> round y to x significant digits
> z0=. (<: x) + -@<.@(10&^.)y
> z1=. 0.5<[EMAIL PROTECTED] y (*10&^) z0
> (10^- z0)* z1
> )
>
> Of course one should have
> (fooX -: ([:*./ >:@i.)"0) y
> 1
>
> (Perhaps, under http://www.jsoftware.com/jwiki/Showcase there
> should be a
> subpage Competitions.)
>
>
> Here is my try:
>
> y=:[EMAIL PROTECTED] 1000x
> (\:,.]) 2 rsd ({.%"1 ]) 5 ts&'([:*./ >:@i.)"0
> y';'([:*./&.|. >:@i.)"0
> y';'lcm y' NB. wrap around!
> 2 1 1
> 1 1.3 1
> 0 90 0.45
> (lcm -: ([:*./ >:@i.)"0) y
> 1
>
> y=:[EMAIL PROTECTED] 10000x
> (\:,.]) 2 rsd ({.%"1 ]) 5 ts&'([:*./ >:@i.)"0
> y';'([:*./&.|. >:@i.)"0
> y';'lcm y' NB. wrap around!
> 2 1 1
> 1 1.6 1
> 0 280 0.11
> (lcm -: ([:*./ >:@i.)"0) y
> 1
>
> lcm is defined by
>
> lcm=: 3 : 0
> z0=. i.&.(_1&p:)1x+m=: >./, y
> NB. primes less than max y
> z1=. |:/:~;(<@([,.~ (^ >:@i.@>:))"0 <.@:^.&m) z0
> NB. prime powers with corresponding primes
> z2=. ({.,: [:*/\.&.|. {:) z1
> NB. prime powers with corresponding ([:*./ >:@i.)
> y(((I.~- [EMAIL PROTECTED]){.){ {:@]) z2
> NB. ([:*./ >:@i.)"0 y
> )
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