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math combinations

 
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I am suppose to compute the combination function C(n, k)= n!/(k!(n-k)!)
C(n,k) = 1 if k = 0
C(n,k) = 0 if n=0 and k>0
C(n,k) = C(n-1, k)+ C(n-1,k-1)

I have to do it non-recursively. This is what I have so far. Any help would be great.

 
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I would compute C(n,k) using
C(n,k)=n * (n-1) * (n-2) * ... * (n-k+1) / k!

Non-recursive algorithm using the recursive definition would need an array to store intermediate results.
 
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Something like the following pseudocode?

 
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I suggest defining the recursive solution, then translating it to the loops - at least, this works for me. Is this a lesson on writing compilers?
 
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