examples/notebook/contrib/strimko2.ipynb
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First, you must install ortools package in this colab.
%pip install ortools
Strimko problem in Google CP Solver.
From 360: A New Twist on Latin Squares http://threesixty360.wordpress.com/2009/08/04/a-new-twist-on-latin-squares/ ''' The idea is simple: each row and column of an nxn grid must contain the number 1, 2, ... n exactly once (that is, the grid must form a Latin square), and each "stream" (connected path in the grid) must also contain the numbers 1, 2, ..., n exactly once. '''
For more information, see:
I have blogged about this (using MiniZinc model) in 'Strimko - Latin squares puzzle with "streams"' http://www.hakank.org/constraint_programming_blog/2009/08/strimko_latin_squares_puzzle_w_1.html
Compare with the following models:
This model was created by Hakan Kjellerstrand ([email protected]) See my other Google CP Solver models: http://www.hakank.org/google_or_tools/
import sys
from ortools.constraint_solver import pywrapcp
def main(streams='', placed=''):
# Create the solver.
solver = pywrapcp.Solver('Strimko')
#
# default problem
#
if streams == '':
streams = [[1, 1, 2, 2, 2, 2, 2], [1, 1, 2, 3, 3, 3, 2],
[1, 4, 1, 3, 3, 5, 5], [4, 4, 3, 1, 3, 5, 5],
[4, 6, 6, 6, 7, 7, 5], [6, 4, 6, 4, 5, 5, 7],
[6, 6, 4, 7, 7, 7, 7]]
# Note: This is 1-based
placed = [[2, 1, 1], [2, 3, 7], [2, 5, 6], [2, 7, 4], [3, 2, 7], [3, 6, 1],
[4, 1, 4], [4, 7, 5], [5, 2, 2], [5, 6, 6]]
n = len(streams)
num_placed = len(placed)
print('n:', n)
#
# variables
#
x = {}
for i in range(n):
for j in range(n):
x[i, j] = solver.IntVar(1, n, 'x[%i,%i]' % (i, j))
x_flat = [x[i, j] for i in range(n) for j in range(n)]
#
# constraints
#
# all rows and columns must be unique, i.e. a Latin Square
for i in range(n):
row = [x[i, j] for j in range(n)]
solver.Add(solver.AllDifferent(row))
col = [x[j, i] for j in range(n)]
solver.Add(solver.AllDifferent(col))
#
# streams
#
for s in range(1, n + 1):
tmp = [x[i, j] for i in range(n) for j in range(n) if streams[i][j] == s]
solver.Add(solver.AllDifferent(tmp))
#
# placed
#
for i in range(num_placed):
# note: also adjust to 0-based
solver.Add(x[placed[i][0] - 1, placed[i][1] - 1] == placed[i][2])
#
# search and solution
#
db = solver.Phase(x_flat, solver.INT_VAR_DEFAULT, solver.INT_VALUE_DEFAULT)
solver.NewSearch(db)
num_solutions = 0
while solver.NextSolution():
for i in range(n):
for j in range(n):
print(x[i, j].Value(), end=' ')
print()
print()
num_solutions += 1
solver.EndSearch()
print()
print('num_solutions:', num_solutions)
print('failures:', solver.Failures())
print('branches:', solver.Branches())
print('WallTime:', solver.WallTime(), 'ms')
if len(sys.argv) > 1:
problem_file = sys.argv[1]
exec(compile(open(problem_file).read(), problem_file, 'exec'))
main(streams, placed)
else:
main()