144 lines
4.3 KiB
Python
144 lines
4.3 KiB
Python
# 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)
|