Recursion question

[YuK]

Hi All. I try to find recursion function for C(n,m,p1,p2) for number of sums n=sum(x(i)), p1<=x(i)<=p2, i=1..m. But simple test give me mistake.

YuK

[AlvaroDíaz]

Hi YuK. I think that the problem is in the if structure.

Regards. Alvaro.

[TomGutman]

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� � � � Tom Gutman

[YuK]

Many Thanks.

Recursion is falls for big number. I try to find C(70,10,1,12) - and I have timeproblem.

YuK

[AlvaroDíaz]

Do you need the exact value?

Regards. Alvaro.

[YuK]

Yes I wont to find exact value

1) Firht idea. We can use array (70,11)-size and we can find the exact value. C(70,10,1,70)=C(60,10,0,60)=combin(60+10-1,10-1)=56 672 074 888. Only array - without recursion. Here is't big number C(60,10,0,12)< 56 672 074 888.

2) Second idea. We can use Inclusion-ExclusionPrinciple

http://mathworld.wolfram.com/Inclusion-ExclusionPrinciple.html

YuK

[ptc-1368288]

On 4/23/2009 8:58:09 AM, adiaz wrote:
>Do you need the exact value?
>
>Regards. Alvaro.
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I didn't attempt understanding what it supposed to produce as a custom project. But clearly it is a recursive problem that is of same nature as Fibonacci. Get inspired for one column from fib(m) below Marlett, which fib(m) is the "Mathcad Speedy Gonzalez" for that kind of recursion.

I didn't understand your "genfit", genfit for what on recursive ? Interpolate between values, OK , but you will have to use a more general interpolating function rather than a model function ... like a polynomial or better rational on a range of data points around the desired interpolated values. I'm saying that as the project will issue all sorts of data points, therefore predicting failure of models, unless a large amount of time would be spent and conditionally to a reasonable project.

Efficient programming is quite a challenge in Mathcad. It does not necessarily result from logical-immediate thinking. fib(m) is either from the Mathcad Treasury or the Advisor. It has been posted several times in this collab.

jmG

[YuK]

Here my solution of problem. Check please.



YuK