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

[Donald Alan Morrison]

I've verified the function works correctly for all 10,000 terms in the
b-file (domain: 1 < n < 43465 ):

http://www2.research.att.com/~njas/sequences/b083207.txt

Computation took 1 hour, 26 minutes, 5.17 seconds =)

Was that fast or slow?

On Mon, Aug 2, 2010 at 6:19 PM, Donald Alan Morrison
<donmorrison at gmail.com> wrote:
> 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
>>
>