examples/notebook/contrib/coins3.ipynb
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First, you must install ortools package in this colab.
%pip install ortools
Coin application in Google CP Solver.
From 'Constraint Logic Programming using ECLiPSe' pages 99f and 234 ff. The solution in ECLiPSe is at page 236.
''' What is the minimum number of coins that allows one to pay exactly any amount smaller than one Euro? Recall that there are six different euro cents, of denomination 1, 2, 5, 10, 20, 50 '''
Compare with the following models:
This model was created by Hakan Kjellerstrand ([email protected]) Also see my other Google CP Solver models: http://www.hakank.org/google_or_tools/
import sys
from ortools.constraint_solver import pywrapcp
def main():
# Create the solver.
solver = pywrapcp.Solver("Coins")
#
# data
#
n = 6 # number of different coins
variables = [1, 2, 5, 10, 25, 50]
# declare variables
x = [solver.IntVar(0, 99, "x%i" % i) for i in range(n)]
num_coins = solver.IntVar(0, 99, "num_coins")
#
# constraints
#
# number of used coins, to be minimized
solver.Add(num_coins == solver.Sum(x))
# Check that all changes from 1 to 99 can be made.
for j in range(1, 100):
tmp = [solver.IntVar(0, 99, "b%i" % i) for i in range(n)]
solver.Add(solver.ScalProd(tmp, variables) == j)
[solver.Add(tmp[i] <= x[i]) for i in range(n)]
# objective
objective = solver.Minimize(num_coins, 1)
#
# solution and search
#
solution = solver.Assignment()
solution.Add(x)
solution.Add(num_coins)
solution.AddObjective(num_coins)
db = solver.Phase(x, solver.CHOOSE_MIN_SIZE_LOWEST_MAX,
solver.ASSIGN_MIN_VALUE)
solver.NewSearch(db, [objective])
num_solutions = 0
while solver.NextSolution():
print("x: ", [x[i].Value() for i in range(n)])
print("num_coins:", num_coins.Value())
print()
num_solutions += 1
solver.EndSearch()
print()
print("num_solutions:", num_solutions)
print("failures:", solver.Failures())
print("branches:", solver.Branches())
print("WallTime:", solver.WallTime())
main()