def maximize_distance(bots):
o = Optimize()
z3_abs = lambda k: If(k >= 0, k, -k)
z3_in_ranges = [Int('in_range_of_bot_' + str(i)) for i in xrange(len(bots))]
z3_x, z3_y, z3_z = (Int('x'), Int('y'), Int('z'))
z3_sum = Int('sum')
z3_dist = Int('dist')
for i, (x, y, z, r) in enumerate(bots):
o.add(z3_in_ranges[i] == If(distance((z3_x, z3_y, z3_z), (x, y, z), z3_abs) <= r, 1, 0))
o.add(z3_sum == sum(z3_in_ranges))
o.add(z3_dist == distance((z3_x, z3_y, z3_z), (0, 0, 0), z3_abs))
h1, h2 = o.maximize(z3_sum), o.minimize(z3_dist)
o.check()
# o.lower(h1), o.upper(h1)
lower, upper = o.lower(h2), o.upper(h2)
# o.model()[z3_x], o.model()[z3_y], o.model()[z3_z]
if str(lower) != str(upper): raise Exception('lower ({}) != upper ({})'.format(lower, upper))
return (lower, upper)
for (r, c) in board()
]).reshape(H, W)
no_scout_threatens_another_scout = [
Implies(
is_scout[r][c],
And([
Not(is_scout[dr][dc])
for (dr, dc) in scout_moves_from[r, c]
])
)
for (r, c) in board() if (r, c) not in lakes()
]
# Clauses
s = Optimize()
s.add(no_scouts_in_lakes)
s.add(at_most_one_scout_per_segment)
s.add(no_scout_threatens_another_scout)
# Objective
num_scouts = Sum([ If(is_scout[r][c], 1, 0) for (r, c) in board() ])
max_scouts = s.maximize(num_scouts)
if s.check() == sat:
#assert s.upper(max_scouts) == 14
print("The maximum number of scouts satisfying the constraints == %s." % s.upper(max_scouts))
print(diagram(s.model()))
else:
print("Z3 failed to find a solution.")
