# Copyright 2010 Hakan Kjellerstrand hakank@bonetmail.com
#
# Licensed under the Apache License, Version 2.0 (the 'License');
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an 'AS IS' BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""
Broken weights problem in Google CP Solver.
From http://www.mathlesstraveled.com/?p=701
'''
Here's a fantastic problem I recently heard. Apparently it was first
posed by Claude Gaspard Bachet de Meziriac in a book of arithmetic problems
published in 1612, and can also be found in Heinrich Dorrie's 100
Great Problems of Elementary Mathematics.
A merchant had a forty pound measuring weight that broke
into four pieces as the result of a fall. When the pieces were
subsequently weighed, it was found that the weight of each piece
was a whole number of pounds and that the four pieces could be
used to weigh every integral weight between 1 and 40 pounds. What
were the weights of the pieces?
Note that since this was a 17th-century merchant, he of course used a
balance scale to weigh things. So, for example, he could use a 1-pound
weight and a 4-pound weight to weigh a 3-pound object, by placing the
3-pound object and 1-pound weight on one side of the scale, and
the 4-pound weight on the other side.
'''
Compare with the following problems:
* MiniZinc: http://www.hakank.org/minizinc/broken_weights.mzn
* ECLiPSE: http://www.hakank.org/eclipse/broken_weights.ecl
* Gecode: http://www.hakank.org/gecode/broken_weights.cpp
* Comet: http://hakank.org/comet/broken_weights.co
This model was created by Hakan Kjellerstrand (hakank@bonetmail.com)
Also see my other Google CP Solver models:
http://www.hakank.org/google_or_tools/
"""
import sys
import string
from ortools.constraint_solver import pywrapcp
def main(m=40, n=4):
# Create the solver.
solver = pywrapcp.Solver('Broken weights')
#
# data
#
print 'total weight (m):', m
print 'number of pieces (n):', n
print
#
# variables
#
weights = [solver.IntVar(1, m, 'weights[%i]' % j) for j in range(n)]
x = {}
for i in range(m):
for j in range(n):
x[i, j] = solver.IntVar(-1, 1, 'x[%i,%i]' % (i, j))
x_flat = [x[i, j] for i in range(m) for j in range(n)]
#
# constraints
#
# symmetry breaking
for j in range(1, n):
solver.Add(weights[j - 1] < weights[j])
solver.Add(solver.SumEquality(weights, m))
# Check that all weights from 1 to 40 can be made.
#
# Since all weights can be on either side
# of the side of the scale we allow either
# -1, 0, or 1 or the weights, assuming that
# -1 is the weights on the left and 1 is on the right.
#
for i in range(m):
solver.Add(i + 1 == solver.Sum([weights[j] * x[i, j]
for j in range(n)]))
# objective
objective = solver.Minimize(weights[n - 1], 1)
#
# search and result
#
db = solver.Phase(weights + x_flat,
solver.CHOOSE_FIRST_UNBOUND,
solver.ASSIGN_MIN_VALUE)
search_log = solver.SearchLog(1)
solver.NewSearch(db, [objective])
num_solutions = 0
while solver.NextSolution():
num_solutions += 1
print 'weights: ',
for w in [weights[j].Value() for j in range(n)]:
print '%3i ' % w,
print
print '-' * 30
for i in range(m):
print 'weight %2i:' % (i + 1),
for j in range(n):
print '%3i ' % x[i, j].Value(),
print
print
print
solver.EndSearch()
print 'num_solutions:', num_solutions
print 'failures :', solver.Failures()
print 'branches :', solver.Branches()
print 'WallTime:', solver.WallTime(), 'ms'
m = 40
n = 4
if __name__ == '__main__':
if len(sys.argv) > 1:
m = string.atoi(sys.argv[1])
if len(sys.argv) > 2:
n = string.atoi(sys.argv[2])
main(m, n)