Does anybody know if the following sorts of constraints can be solved to
give the subsets of nonnegative integers that satisfy them:
i+j=2
k+l=4
m+n=3
i*k+l+m=3
j*k+l+n=8
The only thing I know to do is just check all possibilities:
def tallies(n, *syms):
for p in partitions(n, len(syms)):
take = sum([v for v in p.values()])
vals = flatten([[k]*v for k, v in p.iteritems()])
for s in subsets(syms, take):
d = defaultdict(int)
for i, si in enumerate(s):
d[si] = vals[i]
yield d
for dd in cartes(tallies(2,i,j), tallies(4,k,l), tallies(3,m,n)):
d = defaultdict(int)
for di in dd:
d.update(di)
if d[i]*d[k]+d[l]+d[m]==3 and d[j]*d[k]+d[l]+d[n]==8:
print dict(d)
{k: 2, m: 1, j: 2, l: 2, n: 2, i: 0}
I suppose that it might be better to work backward from the more
complicated constraints (like the i*k+l+m == 3).
Does anyone have other suggestions/algorithms?
/c
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