if unsat(a) or sat(f): return f,a
minj = f.index(min(f,key=len)) # clause with fewest literals
if len(f[minj])==0:
a[0] = UNSAT
return f,a
if len(f[minj])==1:
fixliteral(f[minj][0], f, a)
return backsat(f,a)
#split: 2 possible bool. vals for literal f[minj][0]
#print "split A:", f[minj][0]
fcopy, acopy = mycopy(f,a)
fixliteral(f[minj][0], f, a) # f[minj][0] True
f,a = backsat(f,a)
if sat(f): return f, a
f,a = fcopy, acopy
#print "split B:", -f[minj][0]
fixliteral(-f[minj][0], f, a) # f[minj][0] False
return backsat(f, a)
#myf=[[-5,-6],[-3,5],[-2,5],[1,-6],[1,-4],[1,-3],[2,3],[2,6],[3,-5],[3,4],[4,-5],[5,-6]]
#myf=[[-4,-5,6],[-4,5,-6],[-2,4,-5],[-2,5,-6],[-1,-3,-4],[-1,-3,4],[-1,4,-6],[1,-4,5],[1,-3,-5],[1,-3,4],[1,5,-6],[2,5,6],[3,-5,-6],[4,-5,6],[4,5,-6],[4,5,6]]
n,m = 20,90 #max m is n choose k times 2^k, where k=2or3
myf = formula(n,3,m)
print "\nrandom formula",n,"vars",m,"clauses"
showf(myf)
print ''
asn = [UNKNOWN]*n
f,a = backsat(myf,asn)
showfa(f,a)
else:
print('formula unsatisfiable')
return f, a #
else: # f is not the empty list, a is not the empty string
ndx = ind_short(f)
lenj = len(f[ndx])
if lenj == 1: # fix literal
f, a = fix_literal(f[ndx][0], f, a)
elif lenj >= 2: #try both possible values
fcopy, acopy = deepcopy(f), a
f, a = fix_literal(f[ndx][0], f, a) # try now
newf, newa = fix_literal(-fcopy[ndx][0], fcopy, acopy)
candidates.append((newf, newa)) # try later
def backsolve(n, myf):
asn = UNKNOWN * n
backsat(myf, asn)
n, k, m = 22, 3, 100
f = formula(n, k, m)
#f = [[1, 2, 3], [1, 2, -3], [1, 2, -4], [1, -2, 3], [1, -2, -4], [1, 3, 4], [1, 3, -4], [-1, 2, -3], [-1, 2, -4], [-1, -2, -3], [-1, -2, 4], [-1, -2, -4], [-1, 3, 4], [2, -3, -4], [-2, 3, 4], [-2, -3, -4]]
f2 = deepcopy(f)
print('formula with', n, 'vars', m, 'clauses')
print('')
backsolve(n, f)
print('\nverify with bfsolve')
bfsolve(n, f2, True)
fcopy, acopy = mycopy(f,a) fixliteral(f[minj][0], f, a) # f[minj][0] True f,a = backsat(f,a) if sat(f): return f, a f,a = fcopy, acopy #print "split B:", -f[minj][0] fixliteral(-f[minj][0], f, a) # f[minj][0] False return backsat(f, a) def backsolve(n,myf): asn = [UNKNOWN]*n f,a = backsat(myf,asn) showfa(f,a) #n,myf=6,[[-5,-6],[-3,5],[-2,5],[1,-6],[1,-4],[1,-3],[2,3],[2,6],[3,-5],[3,4],[4,-5],[5,-6]] #n,myf=6,[[-4,-5,6],[-4,5,-6],[-2,4,-5],[-2,5,-6],[-1,-3,-4],[-1,-3,4],[-1,4,-6],[1,-4,5],[1,-3,-5],[1,-3,4],[1,5,-6],[2,5,6],[3,-5,-6],[4,-5,6],[4,5,-6],[4,5,6]] #max m: (n choose k)(2^k) #n, k, m = 20, 5, 400 # good example n, k, m = 30, 5, 600 # backtrack yes, bf too slow myf = formula(n,k,m) n,myf = 5, [[1,-5],[-2,-3],[3,4],[-4,-5],[2,5],[-1,-5]] n,myf = 5, [[1,-2],[1,3],[-2,-3],[2,4],[-3,-4],[3,-5],[3,5]] myf2 = deepcopy(myf) #print "\nrandom formula",n,"vars",m,"clauses" #showf(myf) #print '' backsolve(n,myf) bfsolve(n,myf2,TRUE)