LOGO-L> Re: factorials

[George Mills <mills@softronix.com>]

Note that it does not help that much improving the compute_facts
because it is now dominated by the compare and fact lookups
once the cache was added.

Interestingly the code actually looks cleaner with this optimization.
It certainly helps performance but not as much as you might of
hoped for.

Also note the one line of code I changed below for the purist.
Although some purists might like it the way you had it.

Yehuda Katz wrote:
> 
> Hi,
> 
> The problem was, to remind, to find all 3-digit numbers thar equal the
> sum of their factorials.
> 
> Giving a second thought, you might find that there's a waste in
> calculating all those factorials, for the following reason:
> In calculating 6! - for example - you have to calculate 5! from the
> beginning, AFTER it has already been calculated and even added to the
> array!
> 
> So, you can build directly the array by using the fact that 0!=1, and
> that the Nth element of the array in N*(the N-1 element).
> 
> This leads to something like the following program:
> 
> ===================================================
> to main
> compute_facts
> solve
> end
> 
> to compute_facts
> make "fact_array(array 10 0)
> setitem 0 :fact_array 1
> for[i 1 9][
>     setitem :i :fact_array :i*item :i-1 :fact_array]

     setitem :i :fact_array :i*fact :i-1]

> end
> 
> to solve
> for[num 100 666][
> if equalp :num(sum fact item 1 :num
>                    fact item 2 :num
>                    fact item 3 :num)
>    [pr :num]]
> end
> 
> to fact :n
> op item :n :fact_array
> end
> ===================================================
> 
> What makes me wonder is: Could memory allocation to arrays in Logo be
> dynamic?
> 
> Regards...
> 
> [[Yehuda]]

-- 
===============================================================
George Mills
email: mills@softronix.com
http://www.softronix.com
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