Created
July 3, 2019 22:00
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Water Jugs puzzle with Python-Z3
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from z3 import * | |
Jug, (Big, Small) = EnumSort( | |
'Jug', ['Big', 'Small']) | |
Act, (FillBig, FillSmall, EmptyBig, EmptySmall, BigToSmall, SmallToBig) = EnumSort( | |
'Act', ['FillBig', 'FillSmall', 'EmptyBig', 'EmptySmall', 'BigToSmall', 'SmallToBig']) | |
#m = 10 | |
for n in range(5, 10): | |
print("n = {}".format(n)) | |
# create variables for jugs' volume and actions taken, at each time step | |
big = [] | |
small = [] | |
actions = [] | |
for t in range(n): | |
big.append(Int('big{}'.format(t))) | |
small.append(Int('small{}'.format(t))) | |
actions.append(Const('act{}'.format(t), Act)) | |
s = Solver() | |
# empty at t = 0 | |
s.add(big[0] == 0) | |
s.add(small[0] == 0) | |
s.add(actions[0] == EmptyBig) | |
# 6 constraints, from 6 actions, at each step t < n | |
for t in range(1, n): | |
s.add(Or( | |
actions[t] == BigToSmall, | |
actions[t] == SmallToBig, | |
actions[t] == FillBig, | |
actions[t] == FillSmall, | |
actions[t] == EmptyBig, | |
actions[t] == EmptySmall)) | |
s.add( | |
Or( | |
And(actions[t] == FillBig, | |
big[t] == 5, small[t] == small[t-1]), | |
And(actions[t] == FillSmall, | |
small[t] == 3, big[t] == big[t-1]), | |
And(actions[t] == EmptyBig, | |
big[t] == 0, small[t] == small[t-1]), | |
And(actions[t] == EmptySmall, | |
small[t] == 0, big[t] == big[t-1]), | |
And(actions[t] == BigToSmall, | |
If(big[t-1] + small[t-1] > 3, | |
And(small[t] == 3, | |
big[t] == big[t-1] + small[t-1] - 3), | |
And(small[t] == big[t-1] + small[t-1], big[t] == 0)) | |
), | |
And(actions[t] == SmallToBig, | |
If(big[t-1] + small[t-1] > 5, | |
And(big[t] == 5, small[t] | |
== big[t-1] + small[t-1] - 5), | |
And(big[t] == big[t-1] + small[t-1], small[t] == 0)) | |
))) | |
# can we end up with 4 litres in big jug ? | |
s.add(big[t] == 4) | |
if s.check() == sat: | |
print("SAT") | |
m = s.model() | |
for i in range(n): | |
print("{}: {} {}".format(m.evaluate( | |
actions[i]), m.evaluate(small[i]), m.evaluate(big[i]))) | |
exit(0) | |
else: | |
print("UNSAT") |
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