examples/notebook/contrib/broken_weights.ipynb
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First, you must install ortools package in this colab.
%pip install ortools
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:
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(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: ', end=' ')
for w in [weights[j].Value() for j in range(n)]:
print('%3i ' % w, end=' ')
print()
print('-' * 30)
for i in range(m):
print('weight %2i:' % (i + 1), end=' ')
for j in range(n):
print('%3i ' % x[i, j].Value(), end=' ')
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 len(sys.argv) > 1:
m = int(sys.argv[1])
if len(sys.argv) > 2:
n = int(sys.argv[2])
main(m, n)