[seqfan] Re: A083207 On an observation of Frank Buss.

[Donald Alan Morrison]

Ok, my first mistake :) Not counting the sigma and divisors call in
the running time(!)

On Mon, Aug 2, 2010 at 6:16 PM, Donald Alan Morrison
<donmorrison at gmail.com> wrote:
> SeqFans,
>
> I ported a c version of subset sum to sage/python and converted it to
> a zumkeller verification function.  I verified its correctness for the
> first 1137 terms ( 1 < n < 5001 ) in 76.04 seconds.  Recall it's the
> dynamic programming method where the number of divisors and sigma(n)/2
> determines the memory cost (exponentially), and the cpu running time
> is supposed to be polynomial, together "pseudo-polynomial".  If you
> see a bug, please make fun of me promptly!
>
> def is_zk(a):
>    sa = sigma(a)
>    if mod(sa,2):
>        return False
>    hs = sa/2  # "C" in ssNew.c is sigma(a)/2
>    d = divisors(a)
>    n = len(d)
>    S = (n + 1) * [None]
>    A = (hs + 1) * [None]
>    A[0] = 0
>    S[0] = 0
>    for i in xrange(1,hs+1):
>        A[i] = -1
>    for i in xrange(1,n+1):
>        S[i] = d[i-1]
>    for i in xrange(hs):
>        if A[i] != -1:
>            for j in xrange(A[i]+1,n+1):
>                k = i + S[j]
>                if k > hs:
>                    continue
>                if (A[k] == -1) or (A[k]>j):
>                    A[k] = j
>    if hs < 51:
>        if any(filter(lambda b:b==-1,A[1:hs+1])):
>            return False
>    if A[hs] == -1:
>        return False
>    else:
>        return a
>