examples/notebook/contrib/discrete_tomography.ipynb
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First, you must install ortools package in this colab.
%pip install ortools
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:
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(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(" ", end=" ")
for j in range(cols):
print(col_sums[j], end=" ")
print()
for i in range(rows):
print(row_sums[i], end=" ")
for j in range(cols):
if x[i][j].Value() == 1:
print("#", end=" ")
else:
print(".", end=" ")
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 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()