#
from pysmt.shortcuts import Symbol, BV, Real, And, BVToNatural, ToReal
from pysmt.shortcuts import get_model
from pysmt.typing import BV8, REAL, INT, ArrayType
# We create a map from BitVectors to Reals, so that each bitvector
# value (interpreted as unary number) is equal to the Real
# value.
#
# The map is represented by an Array of type BV8 -> Real
map_type = ArrayType(BV8, REAL)
my_map = Symbol("my_map", map_type)
# Fill-up the map, by defining all 256 values:
for i in range(0, 255):
my_map = my_map.Store(BV(i, 8), Real(i))
# We want to find find a value for which our relation does not work.
# In other words, we ask if there is a value for the bitvector
# s.t. the corresponding value in the array is different from the
# unary interpretation of the bitvector.
bv_var = Symbol("bv", BV8)
int_var = Symbol("int", INT)
real_var = Symbol("real", REAL)
f = And(
# Convert the BV into INT
int_var.Equals(BVToNatural(bv_var)),
# Convert the INT into REAL
real_var.Equals(ToReal(int_var)),
# Compare the value stored in the map with the REAL value
def test_infix(self):
a = Symbol("a", ARRAY_INT_INT)
self.assertEqual(a.Select(Int(5)),
Select(a, Int(5)))
self.assertEqual(a.Store(Int(5), Int(6)),
Store(a, Int(5), Int(6)))
def main():
# Given variables =================================================
I = int(input())
J = int(input())
K = int(input())
T_MAX = int(input())
array_1D = Symbol("1D", ArrayType(INT, INT))
array_2D = Symbol("2D", ArrayType(INT, ArrayType(INT, INT)))
# T[j][k]
# Earliest start execution time of service k on server j
'''
T = Symbol("T", ArrayType(INT, ArrayType(INT, INT)))
for j in range(0, J):
T_row = array_1D
k = 0
for val in [int(x) for x in input().split()]:
# print(symbol_name("T", j, k), " -> ", str(val))
T_row = T_row.Store(Int(k), Int(val))
k = k + 1
T = T.Store(Int(j), T_row)
'''
T = Symbol("T", ArrayType(INT, ArrayType(INT, ArrayType(INT, INT))))
for i in range(0, I):
T_mat = array_2D
for j in range(0, J):
T_mat_row = array_1D
k = 0
for val in [int(x) for x in input().split()]:
# print(symbol_name("T", j, k), " -> ", str(val))
T_mat_row = T_mat_row.Store(Int(k), Int(val))
k = k + 1
T_mat = T_mat.Store(Int(j), T_mat_row)
T = T.Store(Int(i), T_mat)
# C[j][k]
# The computation time of service k on server j
C = Symbol("C", ArrayType(INT, ArrayType(INT, INT)))
for j in range(0, J):
C_row = array_1D
k = 0
for val in [int(x) for x in input().split()]:
# print(symbol_name("C", j, k), " -> ", str(val))
C_row = C_row.Store(Int(k), Int(val))
k = k + 1
C = C.Store(Int(j), C_row)
# Tv[j][j'][k]
# the transmission time (delivery) of service k from server j to server j'
Tv = Symbol("Tv", ArrayType(INT, ArrayType(INT, ArrayType(INT, INT))))
for j in range(0, J):
Tv_mat = array_2D
for jj in range(0, J):
Tv_mat_row = array_1D
k = 0
for val in [int(x) for x in input().split()]:
# print(symbol_name("Tv", j, jj, k), " -> ", str(val))
Tv_mat_row = Tv_mat_row.Store(Int(k), Int(val))
k = k + 1
Tv_mat = Tv_mat.Store(Int(jj), Tv_mat_row)
Tv = Tv.Store(Int(j), Tv_mat)
# D[i][k]
# Vehicle i's reception deadline for service k
# valid[i][k] == -1 iff vehicle i doesn't demand service k
D = Symbol("D", ArrayType(INT, ArrayType(INT, INT)))
valid = []
for i in range(0, I):
D_row = array_1D
k = 0
valid.append([])
for val in [int(x) for x in input().split()]:
# print(symbol_name("D", i, k), " -> ", str(val))
D_row = D_row.Store(Int(k), Int(val))
k = k + 1
if (val == -1): valid[-1].append(False)
else: valid[-1].append(True)
D = D.Store(Int(i), D_row)
# F[i][k]
# The required freshness of vehicle i for service k
F = Symbol("F", ArrayType(INT, ArrayType(INT, INT)))
for i in range(0, I):
F_row = array_1D
k = 0
for val in [int(x) for x in input().split()]:
# print(symbol_name("F", i, k), " -> ", str(val))
F_row = F_row.Store(Int(k), Int(val))
k = k + 1
F = F.Store(Int(i), F_row)
# R[i][j][t]
# if vehicle i is in the communication of server j at time t
'''
R = Symbol("R", ArrayType(INT, ArrayType(INT, ArrayType(INT, INT))))
for i in range(0, I):
R_mat = array_2D
for j in range(0, J):
R_mat_row = array_1D
t = 0
for val in [int(x) for x in input().split()]:
# print(symbol_name("R", i, j, t), " -> ", str(val))
R_mat_row = R_mat_row.Store(Int(t), Int(val))
t = t + 1
R_mat = R_mat.Store(Int(j), R_mat_row)
R = R.Store(Int(i), R_mat)
'''
R = Symbol("R", ArrayType(INT, ArrayType(INT, INT)))
for i in range(0, I):
R_mat = array_1D
R_it = input().split(',')
t = 0
for r in R_it:
cum_t = int(r.split()[0])
cur_j = int(r.split()[1])
for _ in range(cum_t):
R_mat = R_mat.Store(Int(t), Int(cur_j))
t += 1
R = R.Store(Int(i), R_mat)
# M[k]
# the required memory size (delivery) of service k
M = [int(x) for x in input().split()]
# M_bar[j]
# the memory size of server j
M_bar = [int(x) for x in input().split()]
start_time = time.time()
# Decision variables =================================================
class DV: # Decision variable
def __init__(self, i, k):
self.i_int = i
self.k_int = k
self.i = Int(i)
self.k = Int(k)
self.e = Symbol(symbol_name("e", i, k), INT)
self.d = Symbol(symbol_name("d", i, k), INT)
self.s = Symbol(symbol_name("s", i, k), INT)
self.t = Symbol(symbol_name("t", i, k), INT)
DV_set = set()
for i in range(0, I):
for k in range(0, K):
if valid[i][k]:
DV_set.add(DV(i, k))
# Constraints =================================================
# Variable domain
domain = And(
[And(GE(dv.e, Int(0)), LT(dv.e, Int(J))) for dv in DV_set] +
[And(GE(dv.d, Int(0)), LT(dv.d, Int(J))) for dv in DV_set] +
[And(GE(dv.s, Int(0)), LT(dv.s, Int(T_MAX))) for dv in DV_set] +
[And(GE(dv.t, Int(0)), LT(dv.t, Int(T_MAX))) for dv in DV_set])
# Execution constraint
eq1 = And([
Or(dv1.s + C.Select(dv1.e).Select(dv1.k) <= dv2.s,
dv1.s >= dv2.s + C.Select(dv2.e).Select(dv2.k),
And(dv1.k.Equals(dv2.k), dv1.s.Equals(dv2.s)))
for (dv1, dv2) in itertools.combinations(DV_set, 2)
])
# Timing constraint
#eq2 = And([T.Select(dv.e).Select(dv.k) <= dv.s for dv in DV_set])
eq2 = And(
[T.Select(dv.i).Select(dv.e).Select(dv.k) <= dv.s for dv in DV_set])
eq3 = And([
dv.s + C.Select(dv.e).Select(dv.k) +
Tv.Select(dv.e).Select(dv.d).Select(dv.k) <= dv.t for dv in DV_set
])
eq4 = And([dv.t <= D.Select(dv.i).Select(dv.k) for dv in DV_set])
eq5 = And([dv.t <= dv.s + F.Select(dv.i).Select(dv.k) for dv in DV_set])
#eq3_1 = And([Tv.Select(dv.e).Select(dv.d).Select(dv.k) >= 0])
# Pinpoint constraint
#eq6 = And([R.Select(dv.i).Select(dv.d).Select(dv.t).Equals(Int(1)) for dv in DV_set])
eq6 = And([R.Select(dv.i).Select(dv.t).Equals(dv.d) for dv in DV_set])
# Memory constraint
eq7 = And(Bool(True))
memory_sums = [] # for objective function
for t in range(0, T_MAX):
memory_sums.append(Int(0))
for j in range(0, J):
memory_sum = Int(0) # for a single server at time t
for dv in DV_set:
indicator = Symbol(
symbol_name("ind", j, t, dv.i_int, dv.k_int), INT)
existence_formula = And(
dv.d.Equals(j), t >= dv.s + C.Select(dv.e).Select(dv.k) +
Tv.Select(dv.e).Select(dv.d).Select(dv.k), t < dv.t)
# print(existence_formula.Iff(indicator.Equals(1)))
eq7 = eq7.And(Not(existence_formula).Iff(indicator.Equals(0)))
eq7 = eq7.And(existence_formula.Iff(indicator.Equals(1)))
memory_sum += M[dv.k_int] * indicator
eq7 = eq7.And(memory_sum <= M_bar[j])
memory_sums[-1] += memory_sum
# print(memory_sum)
# print(eq7)
# print(memory_sums[0])
# memory_sums[t] == the sum of memory usage of all server at time t
# # Decision version
# # Objective constraint
# obj = Max(memory_sums) <= 4
# model = get_model(And(domain, eq1, eq2, eq3, eq4, eq5, eq6, eq7, obj))
# print(model)
# Optimization version
# Minimize the maximum memory used
constraints = And(domain, eq1, eq2, eq3, eq4, eq5, eq6, eq7)
if (not is_sat(And(constraints,
Max(memory_sums) <= sum(M_bar)),
solver_name="z3")):
print("Unsat")
else:
if (is_sat(And(constraints, Max(memory_sums) <= 0), solver_name="z3")):
print(f"Objective value = 0")
#print(get_model(And(constraints, Max(memory_sums) <= 0)))
else:
l = 1
r = sum(M_bar) + 1
while l < r:
# print(f"{l}, {r}")
m = int((l + r) / 2)
if is_sat(And(constraints,
Max(memory_sums) <= m),
solver_name="z3"):
# print(m)
r = m
else:
l = m + 1
print(f"Objective value = {l}")
#print(get_model(And(constraints, Max(memory_sums) <= m)))
# print(is_sat(And(domain, eq1, eq2, eq3, eq4, eq5, eq6, eq7, obj)))
running_time = time.time() - start_time
outfile = open("time.out", "a")
outfile.write(f"{running_time}")
outfile.write("\n")