def main(problem):
model = cp.CpModel()
# data
n = len(problem[0][0]) # number of digits
# decision variabels
x = [model.NewIntVar(0,9,f"x[{i}]") for i in range(n)]
# constraints
for digits, num_correct_pos, num_correct_number in problem:
check(model, digits, x, num_correct_pos, num_correct_number)
# search and solution
solver = cp.CpSolver()
solution_printer = ListPrinter(x)
status = solver.SearchForAllSolutions(model, solution_printer)
if not status in [cp.OPTIMAL, cp.FEASIBLE]:
print("No solution!")
print()
print("NumSolutions:", solution_printer.SolutionCount())
print("NumConflicts:", solver.NumConflicts())
print("NumBranches:", solver.NumBranches())
print("WallTime:", solver.WallTime())
print()
def main(k=8, num_sol=0):
model = cp.CpModel()
#
# data
#
print("k:", k)
if not (k % 4 == 0 or k % 4 == 3):
print("There is no solution for K unless K mod 4 == 0 or K mod 4 == 3")
return
p = list(range(2 * k))
#
# declare variables
#
position = [model.NewIntVar(0, 2 * k - 1, "position[%i]" % i) for i in p]
solution = [model.NewIntVar(1, k, "position[%i]" % i) for i in p]
#
# constraints
#
model.AddAllDifferent(position)
for i in range(1, k + 1):
model.Add(position[i + k - 1] == position[i - 1] + i + 1)
model.AddElement(position[i - 1], solution, i)
model.AddElement(position[k + i - 1], solution, i)
# symmetry breaking
model.Add(solution[0] < solution[2 * k - 1])
#
# search and result
#
solver = cp.CpSolver()
# Activating these makes it faster for small numbers but
# slower on larger numbers.
# solver.parameters.search_branching = cp.PORTFOLIO_SEARCH
# solver.parameters.cp_model_presolve = False
# solver.parameters.linearization_level = 0
# solver.parameters.cp_model_probing_level = 0
# status = solver.Solve(model)
solution_printer = ListPrinter(solution, num_sol)
# solution_printer = SimpleSolutionCounter(solution) # count sols
status = solver.SearchForAllSolutions(model, solution_printer)
print("status:", solver.StatusName(status))
if status != cp.OPTIMAL and status != cp.FEASIBLE:
print("No solution")
print()
print("NumSolutions:", solution_printer.SolutionCount())
print("NumConflicts:", solver.NumConflicts())
print("NumBranches:", solver.NumBranches())
print("WallTime:", solver.WallTime())
def main():
model = cp.CpModel()
#
# data
#
family = [1, 1, 1, 1, 2, 3, 3, 3, 3, 3, 4, 4]
n = len(family)
#
# declare variables
#
x = [model.NewIntVar(0, n - 1, 'x[%i]' % i) for i in range(n)]
#
# constraints
#
model.AddAllDifferent(x)
# Can't be one own's Secret Santa
# Ensure that there are no fix-point in the array
for i in range(n):
model.Add(x[i] != i)
# No Secret Santa to a person in the same family
for i in range(n):
val = model.NewIntVar(min(family), max(family), "val")
model.AddElement(x[i], family, val)
model.Add(val != family[i])
#
# solution and search
#
solver = cp.CpSolver()
# solver.parameters.search_branching = cp.PORTFOLIO_SEARCH
# solver.parameters.cp_model_presolve = False
# solver.parameters.linearization_level = 0
# solver.parameters.cp_model_probing_level = 0
solution_printer = ListPrinter(x)
# solution_printer = SimpleSolutionCounter(x)
status = solver.SearchForAllSolutions(model, solution_printer)
if not (status == cp.OPTIMAL or status == cp.FEASIBLE):
print("No solution!")
print('NumSolutions:', solution_printer.SolutionCount())
print('NumConflicts:', solver.NumConflicts())
print('NumBranches:', solver.NumBranches())
print('WallTime:', solver.WallTime())
def main():
model = cp.CpModel()
#
# data
#
Belgium = 0
Denmark = 1
France = 2
Germany = 3
Netherlands = 4
Luxembourg = 5
n = 6
max_num_colors = 4
# declare variables
color = [model.NewIntVar(1, max_num_colors, "x%i" % i) for i in range(n)]
#
# constraints
#
model.Add(color[Belgium] == 1) # Symmetry breaking
model.Add(color[France] != color[Belgium])
model.Add(color[France] != color[Luxembourg])
model.Add(color[France] != color[Germany])
model.Add(color[Luxembourg] != color[Germany])
model.Add(color[Luxembourg] != color[Belgium])
model.Add(color[Belgium] != color[Netherlands])
model.Add(color[Belgium] != color[Germany])
model.Add(color[Germany] != color[Netherlands])
model.Add(color[Germany] != color[Denmark])
#
# solution and search
#
solver = cp.CpSolver()
solution_printer = ListPrinter(color)
status = solver.SearchForAllSolutions(model, solution_printer)
if not (status == cp.OPTIMAL or status == cp.FEASIBLE):
print("No solutions found")
print()
print("NumSolutions:", solution_printer.SolutionCount())
print("NumConflicts:", solver.NumConflicts())
print("NumBranches:", solver.NumBranches())
print("WallTime:", solver.WallTime())
def main():
model = cp.CpModel()
# data
m = 32
n = 8
# Note: this is 1-based for compatibility (and lazyness)
graph = [[1, 2], [1, 3], [1, 4], [2, 1], [2, 3], [2, 5], [2, 6], [3, 2],
[3, 4], [3, 6], [3, 7], [4, 1], [4, 3], [4, 6], [4, 7], [5, 2],
[5, 3], [5, 6], [5, 8], [6, 2], [6, 3], [6, 4], [6, 5], [6, 7],
[6, 8], [7, 3], [7, 4], [7, 6], [7, 8], [8, 5], [8, 6], [8, 7]]
# declare variables
x = [model.NewIntVar(1, n, "x%i" % i) for i in range(n)]
#
# constraints
#
model.AddAllDifferent(x)
for i in range(m):
# Note: make 0-based
# model.Add(abs(x[graph[i][0] - 1] - x[graph[i][1] - 1]) > 1)
diff = model.NewIntVar(-n, n, "d")
model.Add(diff == x[graph[i][0] - 1] - x[graph[i][1] - 1])
diff_abs = model.NewIntVar(-n, n, "d")
model.AddAbsEquality(diff_abs, diff)
model.Add(diff_abs > 1)
# symmetry breaking
model.Add(x[0] < x[n - 1])
#
# solution and search
#
solver = cp.CpSolver()
solution_printer = ListPrinter(x)
status = solver.SearchForAllSolutions(model, solution_printer)
if not (status == cp.FEASIBLE or status == cp.OPTIMAL):
print("No solution!")
print()
print("NumSolutions:", solution_printer.SolutionCount())
print("NumConflicts:", solver.NumConflicts())
print("NumBranches:", solver.NumBranches())
print("WallTime:", solver.WallTime())
print()
def main(n=7):
model = cp.CpModel()
x = [model.NewIntVar(0, n-1, 'x%i' % i) for i in range(n)]
alldifferent_except_0(model, x)
# Require that there should be exactly 2 0s.
# z = model.NewIntVar(0,n-1,'z')
# count_vars(model,x, 0, z)
# model.Add(z == 2)
# Simpler:
count_vars(model,x, 0, 2)
# model.AddDecisionStrategy(x,
# cp.CHOOSE_MIN_DOMAIN_SIZE,
# # cp.CHOOSE_FIRST,
# cp.SELECT_LOWER_HALF
# # cp.SELECT_MIN_VALUE
# )
solver = cp.CpSolver()
# solver.parameters.search_branching = cp.FIXED_SEARCH
# solver.parameters.search_branching = cp.AUTOMATIC_SEARCH
# These speeds things up:
solver.parameters.search_branching = cp.PORTFOLIO_SEARCH
solver.parameters.cp_model_presolve=False
# solver.parameters.linearization_level = 0
# solver.parameters.cp_model_probing_level = 0
# flat = x
# flat.append(z)
solution_printer = ListPrinter(x)
# solution_printer = SimpleSolutionCounter(x)
status = solver.SearchForAllSolutions(model, solution_printer)
print('Solutions found : %i' % solution_printer.SolutionCount())
# status = solver.Solve(model)
# if status == cp.FEASIBLE or status == cp.OPTIMAL:
# print([int(solver.Value(x[i])) for i in range(n)])
print('Statistics:')
print(' - conflicts : %i' % solver.NumConflicts())
print(' - branches : %i' % solver.NumBranches())
print(' - wall time : %f s' % solver.WallTime())
def main(base=10):
model = cp.CpModel()
# data
print('base:', base)
# declare variables
s = model.NewIntVar(0, base - 1, 's')
e = model.NewIntVar(0, base - 1, 'e')
n = model.NewIntVar(0, base - 1, 'n')
d = model.NewIntVar(0, base - 1, 'd')
m = model.NewIntVar(0, base - 1, 'm')
o = model.NewIntVar(0, base - 1, 'o')
r = model.NewIntVar(0, base - 1, 'r')
y = model.NewIntVar(0, base - 1, 'y')
x = [s, e, n, d, m, o, r, y]
#
# constraints
#
model.AddAllDifferent(x)
model.Add(
s * base**3 + e * base**2 + n * base + d + m * base**3 + o * base**2 +
r * base + e == m * base**4 + o * base**3 + n * base**2 + e * base +
y, )
model.Add(s > 0)
model.Add(m > 0)
#
# solution and search
#
solver = cp.CpSolver()
solution_printer = ListPrinter(x)
status = solver.SearchForAllSolutions(model, solution_printer)
if status != cp.OPTIMAL:
print("No solution!")
print()
print('NumSolutions:', solution_printer.SolutionCount())
print('NumConflicts:', solver.NumConflicts())
print('NumBranches:', solver.NumBranches())
print('WallTime:', solver.WallTime())
print()
def main():
model = cp.CpModel()
#
# data
#
n = 10
#
# declare variables
#
Vars = [model.NewIntVar(1, n, 'Vars[%i]' % i) for i in range(n)]
X1, X2, X3, X4, X5, X6, X7, X8, X9, X10 = Vars
#
# constraints
#
model.AddAllDifferent(Vars)
model.Add(X1 == 3)
minus(model, X2, X3, X1)
minus(model, X4, X5, X2)
minus(model, X5, X6, X3)
minus(model, X7, X8, X4)
minus(model, X8, X9, X5)
minus(model, X9, X10, X6)
#
# solution and search
#
solver = cp.CpSolver()
solution_printer = ListPrinter(Vars)
_status = solver.SearchForAllSolutions(model, solution_printer)
# if status == cp.OPTIMAL:
# print('Vars:', [solver.Value(Vars[i]) for i in range(n)])
print()
print('NumSolutions:', solution_printer.SolutionCount())
print('NumConflicts:', solver.NumConflicts())
print('NumBranches:', solver.NumBranches())
print('WallTime:', solver.WallTime())
def main(n, use_all_diff=1, print_sols=1):
model = cp.CpModel()
queens = [model.NewIntVar(0, n - 1, f'x{i}') for i in range(n)]
model.AddAllDifferent(queens)
if use_all_diff == 1:
print("Use All Different")
for i in range(n):
diag1 = []
diag2 = []
for j in range(n):
q1 = model.NewIntVar(0, 2 * n, f'diag1_{i}')
diag1.append(q1)
model.Add(q1 == queens[j] + j)
q2 = model.NewIntVar(-n, n, f'diag2_{i}')
diag2.append(q2)
model.Add(q2 == queens[j] - j)
model.AddAllDifferent(diag1)
model.AddAllDifferent(diag2)
else:
# Alternative (naive) model (see nqueens.py)
print("Use Naive")
for i in range(n):
for j in range(i):
model.Add(queens[i] != queens[j])
model.Add(queens[i] + i != queens[j] + j)
model.Add(queens[i] - i != queens[j] - j)
# print("model:", model) # Show the model
solver = cp.CpSolver()
# solution_printer = DiagramPrinter(queens) # Nicer output
solution_printer = ListPrinter(queens) # List of integers
if print_sols != 1:
solution_printer = SimpleSolutionCounter(
queens) # Just count solutions
_ = solver.SearchForAllSolutions(model, solution_printer)
print()
print('Solutions found : %i' % solution_printer.SolutionCount())
print()
# print(solver.ResponseStats())
print("WallTime:", solver.WallTime())
def main():
model = cp.CpModel()
# data
n = 4
base = 10
# declare variables
x = [model.NewIntVar(0, n - 1, "x%i" % i) for i in range(n)]
y = model.NewIntVar(0, 10**n - 1, "y")
#
# constraints
#
# solver.Add(solver.AllDifferent([x[i] for i in range(n)]))
model.AddAllDifferent(x)
# solver.Add(x[0] > 0) # just for fun
toNum(model, x, y, base)
#
# solution and search
#
solver = cp.CpSolver()
all = x
all.append(y)
# solution_printer = SimpleSolutionPrinter(all)
solution_printer = ListPrinter(all)
status = solver.SearchForAllSolutions(model, solution_printer)
if status != cp.OPTIMAL:
print("No solution!")
print()
print("NumSolutions", solution_printer.SolutionCount())
print("NumConflicts:", solver.NumConflicts())
print("NumBranches:", solver.NumBranches())
print("WallTime:", solver.WallTime())
def main(n=5):
model = cp.CpModel()
# data
print("n:", n)
# declare variables
# Note: domain should be 0..n-1
x = [model.NewIntVar(0, n - 1, "x%i" % i) for i in range(n)]
#
# constraints
#
circuit(model, x)
#
# solution and search
#
solver = cp.CpSolver()
solver.parameters.search_branching = cp.PORTFOLIO_SEARCH
solver.parameters.cp_model_presolve = False
solver.parameters.linearization_level = 0
solver.parameters.cp_model_probing_level = 0
# status = solver.Solve(model)
solution_printer = ListPrinter(x)
_status = solver.SearchForAllSolutions(model, solution_printer)
# if status == cp.OPTIMAL:
# print("x:", [solver.Value(x[i]) for i in range(len(x))])
print()
print("NumSolutions:", solution_printer.SolutionCount())
print("NumConflicts:", solver.NumConflicts())
print("NumBanches:", solver.NumBranches())
print("WallTime:", solver.WallTime())
print()
def main(base=10):
model = cp.CpModel()
# data
# declare variables
x = [model.NewIntVar(0, base - 1, f"x[{i}") for i in range(8)]
s, e, n, d, m, o, r, y = x
xx = [s, e, n, d, m, o, r, e, m, o, n, e, y]
coeffs = [
1000,
100,
10,
1, # S E N D +
1000,
100,
10,
1, # M O R E
-10000,
-1000,
-100,
-10,
-1 # == M O N E Y
]
#
# constraints
#
model.AddAllDifferent(x)
model.Add(0 == cp.LinearExpr.ScalProd(xx, coeffs))
model.Add(s > 0)
model.Add(m > 0)
#
# solution and search
#
solver = cp.CpSolver()
solution_printer = ListPrinter(x)
status = solver.SearchForAllSolutions(model, solution_printer)
if status != cp.OPTIMAL:
print("No solution!")
print()
print("NumConflicts:", solver.NumConflicts())
print("NumBranches:", solver.NumBranches())
print("WallTime:", solver.WallTime())
print()
def main(MONEY=0):
model = cp.CpModel()
# data
# declare variables
s = model.NewIntVar(0, 9, 's')
e = model.NewIntVar(0, 9, 'e')
n = model.NewIntVar(0, 9, 'n')
d = model.NewIntVar(0, 9, 'd')
m = model.NewIntVar(0, 9, 'm')
o = model.NewIntVar(0, 9, 'o')
t = model.NewIntVar(0, 9, 't')
y = model.NewIntVar(0, 9, 'y')
money = model.NewIntVar(0, 100000, 'money')
x = [s, e, n, d, m, o, t, y]
#
# constraints
#
if MONEY > 0:
model.Add(money == MONEY)
model.AddAllDifferent(x)
model.Add(money == m * 10000 + o * 1000 + n * 100 + e * 10 + y)
model.Add(money > 0)
model.Add(1000 * s + 100 * e + 10 * n + d + 1000 * m + 100 * o + 10 * s +
t == money)
model.Add(s > 0)
model.Add(m > 0)
if MONEY == 0:
model.Maximize(money)
#
# solution and search
#
solver = cp.CpSolver()
if MONEY == 0:
status = solver.Solve(model)
else:
solution_printer = ListPrinter(x)
status = solver.SearchForAllSolutions(model, solution_printer)
money_val = 0
if MONEY == 0 and status == cp.OPTIMAL:
money_val = solver.Value(money)
print("Optimal value of money:", money_val)
else:
print()
print('NumSolutions:', solution_printer.SolutionCount())
print('NumConflicts:', solver.NumConflicts())
print('NumBranches:', solver.NumBranches())
print('WallTime:', solver.WallTime())
if MONEY == 0:
return money_val
def main(opt=0):
model = cp.CpModel()
#
# data
#
persons = ["Betty", "Chris", "Donald", "Fred", "Gary", "Mary", "Paul"]
n = len(persons)
preferences = [
# 0 1 2 3 4 5 6
# B C D F G M P
[0, 0, 0, 0, 1, 1, 0], # Betty 0
[1, 0, 0, 0, 1, 0, 0], # Chris 1
[0, 0, 0, 0, 0, 0, 0], # Donald 2
[0, 0, 1, 0, 0, 1, 0], # Fred 3
[0, 0, 0, 0, 0, 0, 0], # Gary 4
[0, 0, 0, 0, 0, 0, 0], # Mary 5
[0, 0, 1, 1, 0, 0, 0] # Paul 6
]
if opt == 0:
print("""Preferences:
1. Betty wants to stand next to Gary and Mary.
2. Chris wants to stand next to Betty and Gary.
3. Fred wants to stand next to Mary and Donald.
4. Paul wants to stand next to Fred and Donald.
""")
#
# declare variables
#
positions = [
model.NewIntVar(0, n - 1, "positions[%i]" % i) for i in range(n)
]
# successful preferences
# z = model.NewIntVar(0, n * n, "z")
z = model.NewIntVar(0, sum(flatten(preferences)), "z")
#
# constraints
#
model.AddAllDifferent(positions)
# calculate all the successful preferences
# b = [model.NewBoolVar("") for i in range(n) for j in range(n)]
bb = []
for i in range(n):
for j in range(n):
if preferences[i][j] == 1:
b = model.NewBoolVar("b")
p = model.NewIntVar(-n, n, "p")
model.Add(p == positions[i] - positions[j])
d = model.NewIntVar(-n, n, "d")
# This don't work:
# model.AddAbsEquality(d,p).OnlyEnforce(b)
model.AddAbsEquality(d, p)
model.Add(d == 1).OnlyEnforceIf(b)
bb.append(b)
model.Add(z == sum(bb))
#
# Symmetry breaking (from the Oz page):
# Fred is somewhere left of Betty
model.Add(positions[3] < positions[0])
# objective
if opt == 0:
model.Maximize(z)
else:
model.Add(z == opt)
#
# search and result
#
solver = cp.CpSolver()
if opt == 0:
status = solver.Solve(model)
else:
solution_printer = ListPrinter(positions)
status = solver.SearchForAllSolutions(model, solution_printer)
print("status:", solver.StatusName(status))
if opt == 0 and (status == cp.OPTIMAL or status == cp.FEASIBLE):
print("z:", solver.Value(z))
p = [solver.Value(positions[i]) for i in range(n)]
print("p:", p)
print(" ".join(
[persons[j] for i in range(n) for j in range(n) if p[j] == i]))
print("Successful preferences:")
for i in range(n):
for j in range(n):
if preferences[i][j] == 1 and abs(p[i] - p[j]) == 1:
print("\t", persons[i], persons[j])
print()
print("NumConflicts:", solver.NumConflicts())
print("NumBranches:", solver.NumBranches())
print("WallTime:", solver.WallTime())
print()
return solver.Value(z)