# 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.
"""
Futoshiki problem in Google CP Solver.
From http://en.wikipedia.org/wiki/Futoshiki
'''
The puzzle is played on a square grid, such as 5 x 5. The objective
is to place the numbers 1 to 5 (or whatever the dimensions are)
such that each row, and column contains each of the digits 1 to 5.
Some digits may be given at the start. In addition, inequality
constraints are also initially specifed between some of the squares,
such that one must be higher or lower than its neighbour. These
constraints must be honoured as the grid is filled out.
'''
Also see
http://www.guardian.co.uk/world/2006/sep/30/japan.estheraddley
This Google CP Solver model is inspired by the Minion/Tailor
example futoshiki.eprime.
Compare with the following models:
* MiniZinc: http://hakank.org/minizinc/futoshiki.mzn
* ECLiPSe: http://hakank.org/eclipse/futoshiki.ecl
* Gecode: http://hakank.org/gecode/futoshiki.cpp
* SICStus: http://hakank.org/sicstus/futoshiki.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/
"""
from ortools.constraint_solver import pywrapcp
def main(values, lt):
# Create the solver.
solver = pywrapcp.Solver("Futoshiki problem")
#
# data
#
size = len(values)
RANGE = range(size)
NUMQD = range(len(lt))
#
# variables
#
field = {}
for i in RANGE:
for j in RANGE:
field[i, j] = solver.IntVar(1, size, "field[%i,%i]" % (i, j))
field_flat = [field[i, j] for i in RANGE for j in RANGE]
#
# constraints
#
# set initial values
for row in RANGE:
for col in RANGE:
if values[row][col] > 0:
solver.Add(field[row, col] == values[row][col])
# all rows have to be different
for row in RANGE:
solver.Add(solver.AllDifferent([field[row, col] for col in RANGE]))
# all columns have to be different
for col in RANGE:
solver.Add(solver.AllDifferent([field[row, col] for row in RANGE]))
# all < constraints are satisfied
# Also: make 0-based
for i in NUMQD:
solver.Add(field[lt[i][0] - 1, lt[i][1] - 1] <
field[lt[i][2] - 1, lt[i][3] - 1])
#
# search and result
#
db = solver.Phase(field_flat,
solver.CHOOSE_FIRST_UNBOUND,
solver.ASSIGN_MIN_VALUE)
solver.NewSearch(db)
num_solutions = 0
while solver.NextSolution():
num_solutions += 1
for i in RANGE:
for j in RANGE:
print field[i, j].Value(),
print
print
solver.EndSearch()
print "num_solutions:", num_solutions
print "failures:", solver.Failures()
print "branches:", solver.Branches()
print "WallTime:", solver.WallTime()
#
# Example from Tailor model futoshiki.param/futoshiki.param
# Solution:
# 5 1 3 2 4
# 1 4 2 5 3
# 2 3 1 4 5
# 3 5 4 1 2
# 4 2 5 3 1
#
# Futoshiki instance, by Andras Salamon
# specify the numbers in the grid
#
values1 = [
[0, 0, 3, 2, 0],
[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0]]
# [i1,j1, i2,j2] requires that values[i1,j1] < values[i2,j2]
# Note: 1-based
lt1 = [
[1, 2, 1, 1],
[1, 4, 1, 5],
[2, 3, 1, 3],
[3, 3, 2, 3],
[3, 4, 2, 4],
[2, 5, 3, 5],
[3, 2, 4, 2],
[4, 4, 4, 3],
[5, 2, 5, 1],
[5, 4, 5, 3],
[5, 5, 4, 5]]
#
# Example from http://en.wikipedia.org/wiki/Futoshiki
# Solution:
# 5 4 3 2 1
# 4 3 1 5 2
# 2 1 4 3 5
# 3 5 2 1 4
# 1 2 5 4 3
#
values2 = [
[0, 0, 0, 0, 0],
[4, 0, 0, 0, 2],
[0, 0, 4, 0, 0],
[0, 0, 0, 0, 4],
[0, 0, 0, 0, 0]]
# Note: 1-based
lt2 = [
[1, 2, 1, 1],
[1, 4, 1, 3],
[1, 5, 1, 4],
[4, 4, 4, 5],
[5, 1, 5, 2],
[5, 2, 5, 3]
]
if __name__ == "__main__":
print "Problem 1"
main(values1, lt1)
print "\nProblem 2"
main(values2, lt2)