examples/notebook/contrib/fill_a_pix.ipynb
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First, you must install ortools package in this colab.
%pip install ortools
Fill-a-Pix problem in Google CP Solver.
From http://www.conceptispuzzles.com/index.aspx?uri=puzzle/fill-a-pix/basiclogic ''' Each puzzle consists of a grid containing clues in various places. The object is to reveal a hidden picture by painting the squares around each clue so that the number of painted squares, including the square with the clue, matches the value of the clue. '''
http://www.conceptispuzzles.com/index.aspx?uri=puzzle/fill-a-pix/rules ''' Fill-a-Pix is a Minesweeper-like puzzle based on a grid with a pixilated picture hidden inside. Using logic alone, the solver determines which squares are painted and which should remain empty until the hidden picture is completely exposed. '''
Fill-a-pix History: http://www.conceptispuzzles.com/index.aspx?uri=puzzle/fill-a-pix/history
Compare with the following models:
And see the Minesweeper model:
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
# Puzzle 1 from
# http://www.conceptispuzzles.com/index.aspx?uri=puzzle/fill-a-pix/rules
default_n = 10
X = -1
default_puzzle = [
[X, X, X, X, X, X, X, X, 0, X], [X, 8, 8, X, 2, X, 0, X, X, X],
[5, X, 8, X, X, X, X, X, X, X], [X, X, X, X, X, 2, X, X, X, 2],
[1, X, X, X, 4, 5, 6, X, X, X], [X, 0, X, X, X, 7, 9, X, X, 6],
[X, X, X, 6, X, X, 9, X, X, 6], [X, X, 6, 6, 8, 7, 8, 7, X, 5],
[X, 4, X, 6, 6, 6, X, 6, X, 4], [X, X, X, X, X, X, 3, X, X, X]
]
def main(puzzle='', n=''):
# Create the solver.
solver = pywrapcp.Solver('Fill-a-Pix')
#
# data
#
# Set default problem
if puzzle == '':
puzzle = default_puzzle
n = default_n
else:
print('n:', n)
# for the neighbors of 'this' cell
S = [-1, 0, 1]
# print problem instance
print('Problem:')
for i in range(n):
for j in range(n):
if puzzle[i][j] == X:
sys.stdout.write('.')
else:
sys.stdout.write(str(puzzle[i][j]))
print()
print()
#
# declare variables
#
pict = {}
for i in range(n):
for j in range(n):
pict[(i, j)] = solver.IntVar(0, 1, 'pict %i %i' % (i, j))
pict_flat = [pict[i, j] for i in range(n) for j in range(n)]
#
# constraints
#
for i in range(n):
for j in range(n):
if puzzle[i][j] > X:
# this cell is the sum of all the surrounding cells
solver.Add(puzzle[i][j] == solver.Sum([
pict[i + a, j + b]
for a in S
for b in S
if i + a >= 0 and j + b >= 0 and i + a < n and j + b < n
]))
#
# solution and search
#
db = solver.Phase(pict_flat, solver.INT_VAR_DEFAULT, solver.INT_VALUE_DEFAULT)
solver.NewSearch(db)
num_solutions = 0
print('Solution:')
while solver.NextSolution():
num_solutions += 1
for i in range(n):
row = [str(pict[i, j].Value()) for j in range(n)]
for j in range(n):
if row[j] == '0':
row[j] = ' '
else:
row[j] = '#'
print(''.join(row))
print()
print('num_solutions:', num_solutions)
print('failures:', solver.Failures())
print('branches:', solver.Branches())
print('WallTime:', solver.WallTime(), 'ms')
#
# Read a problem instance from a file
#
def read_problem(file):
f = open(file, 'r')
n = int(f.readline())
puzzle = []
for i in range(n):
x = f.readline()
row = [0] * n
for j in range(n):
if x[j] == '.':
tmp = -1
else:
tmp = int(x[j])
row[j] = tmp
puzzle.append(row)
return [puzzle, n]
if len(sys.argv) > 1:
file = sys.argv[1]
print('Problem instance from', file)
[puzzle, n] = read_problem(file)
main(puzzle, n)
else:
main()