# 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.
"""
Discrete tomography in Google CP Solver.
Problem from http://eclipse.crosscoreop.com/examples/tomo.ecl.txt
'''
This is a little 'tomography' problem, taken from an old issue
of Scientific American.
A matrix which contains zeroes and ones gets "x-rayed" vertically and
horizontally, giving the total number of ones in each row and column.
The problem is to reconstruct the contents of the matrix from this
information. Sample run:
?- go.
0 0 7 1 6 3 4 5 2 7 0 0
0
0
8 * * * * * * * *
2 * *
6 * * * * * *
4 * * * *
5 * * * * *
3 * * *
7 * * * * * * *
0
0
Eclipse solution by Joachim Schimpf, IC-Parc
'''
Compare with the following models:
* Comet: http://www.hakank.org/comet/discrete_tomography.co
* Gecode: http://www.hakank.org/gecode/discrete_tomography.cpp
* MiniZinc: http://www.hakank.org/minizinc/tomography.mzn
* Tailor/Essence': http://www.hakank.org/tailor/tomography.eprime
* SICStus: http://hakank.org/sicstus/discrete_tomography.pl
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
from ortools.constraint_solver import pywrapcp
def main(row_sums="", col_sums=""):
# Create the solver.
solver = pywrapcp.Solver("n-queens")
#
# data
#
if row_sums == "":
print "Using default problem instance"
row_sums = [0, 0, 8, 2, 6, 4, 5, 3, 7, 0, 0]
col_sums = [0, 0, 7, 1, 6, 3, 4, 5, 2, 7, 0, 0]
r = len(row_sums)
c = len(col_sums)
# declare variables
x = []
for i in range(r):
t = []
for j in range(c):
t.append(solver.IntVar(0, 1, "x[%i,%i]" % (i, j)))
x.append(t)
x_flat = [x[i][j] for i in range(r) for j in range(c)]
#
# constraints
#
[solver.Add(solver.Sum([x[i][j] for j in range(c)]) == row_sums[i])
for i in range(r)]
[solver.Add(solver.Sum([x[i][j] for i in range(r)]) == col_sums[j])
for j in range(c)]
#
# solution and search
#
solution = solver.Assignment()
solution.Add(x_flat)
# db: DecisionBuilder
db = solver.Phase(x_flat,
solver.INT_VAR_SIMPLE,
solver.ASSIGN_MIN_VALUE)
solver.NewSearch(db)
num_solutions = 0
while solver.NextSolution():
print_solution(x, r, c, row_sums, col_sums)
print
num_solutions += 1
solver.EndSearch()
print
print "num_solutions:", num_solutions
print "failures:", solver.Failures()
print "branches:", solver.Branches()
print "WallTime:", solver.WallTime()
#
# Print solution
#
def print_solution(x, rows, cols, row_sums, col_sums):
print " ",
for j in range(cols):
print col_sums[j],
print
for i in range(rows):
print row_sums[i],
for j in range(cols):
if x[i][j].Value() == 1:
print "#",
else:
print ".",
print ""
#
# Read a problem instance from a file
#
def read_problem(file):
f = open(file, "r")
row_sums = f.readline()
col_sums = f.readline()
row_sums = [int(r) for r in (row_sums.rstrip()).split(",")]
col_sums = [int(c) for c in (col_sums.rstrip()).split(",")]
return [row_sums, col_sums]
if __name__ == "__main__":
if len(sys.argv) > 1:
file = sys.argv[1]
print "Problem instance from", file
[row_sums, col_sums] = read_problem(file)
main(row_sums, col_sums)
else:
main()