# 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.
"""
Kakuru puzzle in Google CP Solver.
http://en.wikipedia.org/wiki/Kakuro
'''
The object of the puzzle is to insert a digit from 1 to 9 inclusive
into each white cell such that the sum of the numbers in each entry
matches the clue associated with it and that no digit is duplicated in
any entry. It is that lack of duplication that makes creating Kakuro
puzzles with unique solutions possible, and which means solving a Kakuro
puzzle involves investigating combinations more, compared to Sudoku in
which the focus is on permutations. There is an unwritten rule for
making Kakuro puzzles that each clue must have at least two numbers
that add up to it. This is because including one number is mathematically
trivial when solving Kakuro puzzles; one can simply disregard the
number entirely and subtract it from the clue it indicates.
'''
This model solves the problem at the Wikipedia page.
For a larger picture, see
http://en.wikipedia.org/wiki/File:Kakuro_black_box.svg
The solution:
9 7 0 0 8 7 9
8 9 0 8 9 5 7
6 8 5 9 7 0 0
0 6 1 0 2 6 0
0 0 4 6 1 3 2
8 9 3 1 0 1 4
3 1 2 0 0 2 1
Compare with the following models:
* Comet : http://www.hakank.org/comet/kakuro.co
* MiniZinc: http://www.hakank.org/minizinc/kakuro.mzn
* SICStus : http://www.hakank.org/sicstus/kakuro.pl
* ECLiPSe: http://www.hakank.org/eclipse/kakuro.ecl
* Gecode: http://www.hakank.org/gecode/kenken2.cpp
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
#
# Ensure that the sum of the segments
# in cc == res
#
def calc(cc, x, res):
solver = x.values()[0].solver()
# ensure that the values are positive
for i in cc:
solver.Add(x[i[0] - 1, i[1] - 1] >= 1)
# sum the numbers
solver.Add(solver.Sum([x[i[0] - 1, i[1] - 1] for i in cc]) == res)
def main():
# Create the solver.
solver = pywrapcp.Solver("Kakuro")
#
# data
#
# size of matrix
n = 7
# segments
# [sum, [segments]]
# Note: 1-based
problem = [
[16, [1, 1], [1, 2]],
[24, [1, 5], [1, 6], [1, 7]],
[17, [2, 1], [2, 2]],
[29, [2, 4], [2, 5], [2, 6], [2, 7]],
[35, [3, 1], [3, 2], [3, 3], [3, 4], [3, 5]],
[7, [4, 2], [4, 3]],
[8, [4, 5], [4, 6]],
[16, [5, 3], [5, 4], [5, 5], [5, 6], [5, 7]],
[21, [6, 1], [6, 2], [6, 3], [6, 4]],
[5, [6, 6], [6, 7]],
[6, [7, 1], [7, 2], [7, 3]],
[3, [7, 6], [7, 7]],
[23, [1, 1], [2, 1], [3, 1]],
[30, [1, 2], [2, 2], [3, 2], [4, 2]],
[27, [1, 5], [2, 5], [3, 5], [4, 5], [5, 5]],
[12, [1, 6], [2, 6]],
[16, [1, 7], [2, 7]],
[17, [2, 4], [3, 4]],
[15, [3, 3], [4, 3], [5, 3], [6, 3], [7, 3]],
[12, [4, 6], [5, 6], [6, 6], [7, 6]],
[7, [5, 4], [6, 4]],
[7, [5, 7], [6, 7], [7, 7]],
[11, [6, 1], [7, 1]],
[10, [6, 2], [7, 2]]
]
num_p = len(problem)
# The blanks
# Note: 1-based
blanks = [
[1, 3], [1, 4],
[2, 3],
[3, 6], [3, 7],
[4, 1], [4, 4], [4, 7],
[5, 1], [5, 2],
[6, 5],
[7, 4], [7, 5]
]
num_blanks = len(blanks)
#
# variables
#
# the set
x = {}
for i in range(n):
for j in range(n):
x[i, j] = solver.IntVar(0, 9, "x[%i,%i]" % (i, j))
x_flat = [x[i, j] for i in range(n) for j in range(n)]
#
# constraints
#
# fill the blanks with 0
for i in range(num_blanks):
solver.Add(x[blanks[i][0] - 1, blanks[i][1] - 1] == 0)
for i in range(num_p):
segment = problem[i][1::]
res = problem[i][0]
# sum this segment
calc(segment, x, res)
# all numbers in this segment must be distinct
segment = [x[p[0] - 1, p[1] - 1] for p in segment]
solver.Add(solver.AllDifferent(segment))
#
# 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):
val = x[i, j].Value()
if val > 0:
print val,
else:
print " ",
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()
if __name__ == "__main__":
main()