examples/notebook/contrib/killer_sudoku.ipynb
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First, you must install ortools package in this colab.
%pip install ortools
Killer Sudoku in Google CP Solver.
http://en.wikipedia.org/wiki/Killer_Sudoku ''' Killer sudoku (also killer su doku, sumdoku, sum doku, addoku, or samunamupure) is a puzzle that combines elements of sudoku and kakuro. Despite the name, the simpler killer sudokus can be easier to solve than regular sudokus, depending on the solver's skill at mental arithmetic; the hardest ones, however, can take hours to crack.
...
The objective is to fill the grid with numbers from 1 to 9 in a way that the following conditions are met:
* Each row, column, and nonet contains each number exactly once.
* The sum of all numbers in a cage must match the small number printed
in its corner.
* No number appears more than once in a cage. (This is the standard rule
for killer sudokus, and implies that no cage can include more
than 9 cells.)
In 'Killer X', an additional rule is that each of the long diagonals contains each number once. '''
Here we solve the problem from the Wikipedia page, also shown here http://en.wikipedia.org/wiki/File:Killersudoku_color.svg
The output is: 2 1 5 6 4 7 3 9 8 3 6 8 9 5 2 1 7 4 7 9 4 3 8 1 6 5 2 5 8 6 2 7 4 9 3 1 1 4 2 5 9 3 8 6 7 9 7 3 8 1 6 4 2 5 8 2 1 7 3 9 5 4 6 6 5 9 4 2 8 7 1 3 4 3 7 1 6 5 2 8 9
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()
# sum the numbers
cage = [x[i[0] - 1, i[1] - 1] for i in cc]
solver.Add(solver.Sum(cage) == res)
solver.Add(solver.AllDifferent(cage))
def main():
# Create the solver.
solver = pywrapcp.Solver("Killer Sudoku")
#
# data
#
# size of matrix
n = 9
# For a better view of the problem, see
# http://en.wikipedia.org/wiki/File:Killersudoku_color.svg
# hints
# [sum, [segments]]
# Note: 1-based
problem = [[3, [[1, 1], [1, 2]]], [15, [[1, 3], [1, 4], [1, 5]]],
[22, [[1, 6], [2, 5], [2, 6], [3, 5]]], [4, [[1, 7], [2, 7]]],
[16, [[1, 8], [2, 8]]], [15, [[1, 9], [2, 9], [3, 9], [4, 9]]],
[25, [[2, 1], [2, 2], [3, 1], [3, 2]]], [17, [[2, 3], [2, 4]]],
[9, [[3, 3], [3, 4], [4, 4]]], [8, [[3, 6], [4, 6], [5, 6]]],
[20, [[3, 7], [3, 8], [4, 7]]], [6, [[4, 1], [5, 1]]],
[14, [[4, 2], [4, 3]]], [17, [[4, 5], [5, 5], [6, 5]]],
[17, [[4, 8], [5, 7], [5, 8]]], [13, [[5, 2], [5, 3], [6, 2]]],
[20, [[5, 4], [6, 4], [7, 4]]], [12, [[5, 9], [6, 9]]],
[27, [[6, 1], [7, 1], [8, 1], [9, 1]]],
[6, [[6, 3], [7, 2], [7, 3]]], [20, [[6, 6], [7, 6], [7, 7]]],
[6, [[6, 7], [6, 8]]], [10, [[7, 5], [8, 4], [8, 5], [9, 4]]],
[14, [[7, 8], [7, 9], [8, 8], [8, 9]]], [8, [[8, 2], [9, 2]]],
[16, [[8, 3], [9, 3]]], [15, [[8, 6], [8, 7]]],
[13, [[9, 5], [9, 6], [9, 7]]], [17, [[9, 8], [9, 9]]]]
#
# variables
#
# the set
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
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))
# cells
for i in range(2):
for j in range(2):
cell = [
x[r, c]
for r in range(i * 3, i * 3 + 3)
for c in range(j * 3, j * 3 + 3)
]
solver.Add(solver.AllDifferent(cell))
# calculate the segments
for (res, segment) in problem:
calc(segment, x, res)
#
# 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())
main()