examples/notebook/contrib/subset_sum.ipynb
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First, you must install ortools package in this colab.
%pip install ortools
Subset sum problem in Google CP Solver.
From Katta G. Murty: 'Optimization Models for Decision Making', page 340 http://ioe.engin.umich.edu/people/fac/books/murty/opti_model/junior-7.pdf ''' Example 7.8.1
A bank van had several bags of coins, each containing either 16, 17, 23, 24, 39, or 40 coins. While the van was parked on the street, thieves stole some bags. A total of 100 coins were lost. It is required to find how many bags were stolen. '''
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 subset_sum(solver, values, total):
n = len(values)
x = [solver.IntVar(0, n) for i in range(n)]
ss = solver.IntVar(0, n)
solver.Add(ss == solver.Sum(x))
solver.Add(total == solver.ScalProd(x, values))
return x, ss
def main(coins, total):
# Create the solver.
solver = pywrapcp.Solver("n-queens")
#
# data
#
print("coins:", coins)
print("total:", total)
print()
#
# declare variables
#
#
# constraints
#
x, ss = subset_sum(solver, coins, total)
#
# solution and search
#
solution = solver.Assignment()
solution.Add(x)
solution.Add(ss)
# db: DecisionBuilder
db = solver.Phase(x, solver.CHOOSE_FIRST_UNBOUND, solver.ASSIGN_MIN_VALUE)
solver.NewSearch(db)
num_solutions = 0
while solver.NextSolution():
print("ss:", ss.Value())
print("x: ", [x[i].Value() for i in range(len(x))])
print()
num_solutions += 1
solver.EndSearch()
print()
print("num_solutions:", num_solutions)
print("failures:", solver.Failures())
print("branches:", solver.Branches())
print("WallTime:", solver.WallTime())
coins = [16, 17, 23, 24, 39, 40]
total = 100
if len(sys.argv) > 1:
total = int(sys.argv[1])
main(coins, total)