200 lines
5.8 KiB
Python
200 lines
5.8 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.
|
|
|
|
"""
|
|
|
|
A programming puzzle from Einav in Google CP Solver.
|
|
|
|
From
|
|
'A programming puzzle from Einav'
|
|
http://gcanyon.wordpress.com/2009/10/28/a-programming-puzzle-from-einav/
|
|
'''
|
|
My friend Einav gave me this programming puzzle to work on. Given
|
|
this array of positive and negative numbers:
|
|
33 30 -10 -6 18 7 -11 -23 6
|
|
...
|
|
-25 4 16 30 33 -23 -4 4 -23
|
|
|
|
You can flip the sign of entire rows and columns, as many of them
|
|
as you like. The goal is to make all the rows and columns sum to positive
|
|
numbers (or zero), and then to find the solution (there are more than one)
|
|
that has the smallest overall sum. So for example, for this array:
|
|
33 30 -10
|
|
-16 19 9
|
|
-17 -12 -14
|
|
You could flip the sign for the bottom row to get this array:
|
|
33 30 -10
|
|
-16 19 9
|
|
17 12 14
|
|
Now all the rows and columns have positive sums, and the overall total is
|
|
108.
|
|
But you could instead flip the second and third columns, and the second
|
|
row, to get this array:
|
|
33 -30 10
|
|
16 19 9
|
|
-17 12 14
|
|
All the rows and columns still total positive, and the overall sum is just
|
|
66. So this solution is better (I don't know if it's the best)
|
|
A pure brute force solution would have to try over 30 billion solutions.
|
|
I wrote code to solve this in J. I'll post that separately.
|
|
'''
|
|
|
|
Compare with the following models:
|
|
* MiniZinc http://www.hakank.org/minizinc/einav_puzzle.mzn
|
|
* SICStus: http://hakank.org/sicstus/einav_puzzle.pl
|
|
|
|
Note:
|
|
This is a Larent Perrons's variant of einav_puzzle.py.
|
|
He removed some of the decision variables and made it more efficient.
|
|
Thanks!
|
|
|
|
|
|
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/
|
|
"""
|
|
|
|
from constraint_solver import pywrapcp
|
|
|
|
|
|
def main():
|
|
|
|
# Create the solver.
|
|
solver = pywrapcp.Solver('Einav puzzle')
|
|
|
|
#
|
|
# data
|
|
#
|
|
|
|
|
|
# small problem
|
|
# rows = 3;
|
|
# cols = 3;
|
|
# data = [
|
|
# [ 33, 30, -10],
|
|
# [-16, 19, 9],
|
|
# [-17, -12, -14]
|
|
# ]
|
|
|
|
# Full problem
|
|
rows = 27
|
|
cols = 9
|
|
data = [
|
|
[33,30,10,-6,18,-7,-11,23,-6],
|
|
[16,-19,9,-26,-8,-19,-8,-21,-14],
|
|
[17,12,-14,31,-30,13,-13,19,16],
|
|
[-6,-11,1,17,-12,-4,-7,14,-21],
|
|
[18,-31,34,-22,17,-19,20,24,6],
|
|
[33,-18,17,-15,31,-5,3,27,-3],
|
|
[-18,-20,-18,31,6,4,-2,-12,24],
|
|
[27,14,4,-29,-3,5,-29,8,-12],
|
|
[-15,-7,-23,23,-9,-8,6,8,-12],
|
|
[33,-23,-19,-4,-8,-7,11,-12,31],
|
|
[-20,19,-15,-30,11,32,7,14,-5],
|
|
[-23,18,-32,-2,-31,-7,8,24,16],
|
|
[32,-4,-10,-14,-6,-1,0,23,23],
|
|
[25,0,-23,22,12,28,-27,15,4],
|
|
[-30,-13,-16,-3,-3,-32,-3,27,-31],
|
|
[22,1,26,4,-2,-13,26,17,14],
|
|
[-9,-18,3,-20,-27,-32,-11,27,13],
|
|
[-17,33,-7,19,-32,13,-31,-2,-24],
|
|
[-31,27,-31,-29,15,2,29,-15,33],
|
|
[-18,-23,15,28,0,30,-4,12,-32],
|
|
[-3,34,27,-25,-18,26,1,34,26],
|
|
[-21,-31,-10,-13,-30,-17,-12,-26,31],
|
|
[23,-31,-19,21,-17,-10,2,-23,23],
|
|
[-3,6,0,-3,-32,0,-10,-25,14],
|
|
[-19,9,14,-27,20,15,-5,-27,18],
|
|
[11,-6,24,7,-17,26,20,-31,-25],
|
|
[-25,4,-16,30,33,23,-4,-4,23]
|
|
]
|
|
|
|
|
|
#
|
|
# variables
|
|
#
|
|
x = {}
|
|
for i in range(rows):
|
|
for j in range(cols):
|
|
x[i,j] = solver.IntVar(-100, 100, "x[%i,%i]" % (i,j))
|
|
|
|
x_flat = [x[i,j] for i in range(rows) for j in range(cols)]
|
|
|
|
row_signs = [solver.IntVar([-1, 1], "row_signs(%i)" % i)
|
|
for i in range(rows)]
|
|
col_signs = [solver.IntVar([-1, 1], "col_signs(%i)" % j)
|
|
for j in range(cols)]
|
|
|
|
#
|
|
# constraints
|
|
#
|
|
for i in range(rows):
|
|
for j in range(cols):
|
|
solver.Add(x[i, j] == data[i][j] * row_signs[i] * col_signs[j])
|
|
|
|
total_sum = solver.Sum([x[i, j] for i in range(rows) for j in range(cols)])
|
|
|
|
#
|
|
# Note: In einav_puzzle.py row_sums and col_sums are decision variables.
|
|
#
|
|
|
|
# row sums
|
|
row_sums = [solver.Sum([x[i, j] for j in range(cols)]).Var()
|
|
for i in range(rows)]
|
|
# >= 0
|
|
for i in range(rows):
|
|
row_sums[i].SetMin(0)
|
|
|
|
# column sums
|
|
col_sums = [solver.Sum([x[i, j] for i in range(rows)]).Var()
|
|
for j in range(cols)]
|
|
for j in range(cols):
|
|
col_sums[j].SetMin(0)
|
|
|
|
|
|
# objective
|
|
objective = solver.Minimize(total_sum, 1)
|
|
|
|
#
|
|
# search and result
|
|
#
|
|
db = solver.Phase(col_signs + row_signs,
|
|
solver.CHOOSE_MIN_SIZE_LOWEST_MIN,
|
|
solver.ASSIGN_MAX_VALUE)
|
|
|
|
solver.NewSearch(db, [objective])
|
|
|
|
num_solutions = 0
|
|
while solver.NextSolution():
|
|
num_solutions += 1
|
|
print "Sum =", objective.best()
|
|
print "row_sums:", [row_sums[i].Value() for i in range(rows)]
|
|
print "col_sums:", [col_sums[j].Value() for j in range(cols)]
|
|
for i in range(rows):
|
|
for j in range(cols):
|
|
print "%3i" % x[i,j].Value(),
|
|
print
|
|
print
|
|
|
|
solver.EndSearch()
|
|
|
|
print
|
|
print "num_solutions:", num_solutions
|
|
print "failures:", solver.failures()
|
|
print "branches:", solver.branches()
|
|
print "wall_time:", solver.wall_time()
|
|
|
|
|
|
if __name__ == '__main__':
|
|
main()
|