# 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")