def solve():
model = Model("Enigma Riddle")
letters = {"E", "N", "I", "G", "M", "A"}
digits = range(1, 10)
x = model.addVars(letters, digits, vtype=GRB.BINARY)
y = model.addVars(letters, vtype=GRB.INTEGER)
# Stay in digit range
for i in letters:
model.addRange(y[i], 1, 9, f"digitRange{i}")
# Final value for first word
b = model.addVar(vtype=GRB.INTEGER)
first_word = "ENIGMA"
second_word = "IGMAEN"
# Constraint for the enigma-igmaen numbers
model.addConstr(quicksum(10 ** (len(first_word) - 1 - i) * y[first_word[i]] for i in range(len(first_word))) == b)
model.addConstr(
quicksum(10 ** (len(second_word) - 1 - i) * y[second_word[i]] for i in range(len(second_word))) == b * 1.2)
# Conflict constraint
model.addConstrs(x[i_1, j] + x[i_2, j] <= 1 for i_1 in letters for i_2 in letters for j in digits if i_1 != i_2)
# Linking constraint
model.addConstrs(j * x[i, j] <= y[i] for i in letters for j in digits)
# Exactly one digit has to be packed
model.addConstrs(quicksum(x[i, j] for j in digits) == 1 for i in letters)
model.optimize()
return model
('sweets', 'calories'): 450,
('sweets', 'protein'): 4,
('sweets', 'calcium'): 22
}
# Using Python looping constructs and m.addVar() to create decision variables:
buy = {}
for f in foods:
buy[f] = m.addVar(0.0, maxPortions[f], name=f)
# The objective is to minimize the costs, using looping constructs:
m.setObjective(sum(buy[f] * cost[f] for f in foods), GRB.MINIMIZE)
# Nutrition constraints to respect minimum daily necessities:
for c in categories:
m.addRange(sum(nutritionValues[f, c] * buy[f] for f in foods),
minNutrition[c], maxNutrition[c], c)
def printSolution():
if m.status == GRB.Status.OPTIMAL:
print('\nCost: %g' % m.objVal)
print('\nBuy:')
buyx = m.getAttr('x', buy)
for f in foods:
if buy[f].x > 0.0001:
print('%s %g' % (f, buyx[f]))
else:
print('No solution')
# Solve
