examples/notebook/contrib/kakuro.ipynb
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First, you must install ortools package in this colab.
%pip install ortools
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:
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
#
# Ensure that the sum of the segments
# in cc == res
#
def calc(cc, x, res):
solver = list(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, end=" ")
else:
print(" ", 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())
main()