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sudoku_sat.py
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sudoku_sat.py
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#!/usr/bin/env python3
# Copyright 2010-2021 Google LLC
# 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.
"""This model implements a sudoku solver."""
from ortools.sat.python import cp_model
def solve_sudoku():
"""Solves the sudoku problem with the CP-SAT solver."""
# Create the model.
model = cp_model.CpModel()
cell_size = 3
line_size = cell_size**2
line = list(range(0, line_size))
cell = list(range(0, cell_size))
initial_grid = [[0, 6, 0, 0, 5, 0, 0, 2, 0], [0, 0, 0, 3, 0, 0, 0, 9, 0],
[7, 0, 0, 6, 0, 0, 0, 1, 0], [0, 0, 6, 0, 3, 0, 4, 0, 0],
[0, 0, 4, 0, 7, 0, 1, 0, 0], [0, 0, 5, 0, 9, 0, 8, 0, 0],
[0, 4, 0, 0, 0, 1, 0, 0, 6], [0, 3, 0, 0, 0, 8, 0, 0, 0],
[0, 2, 0, 0, 4, 0, 0, 5, 0]]
grid = {}
for i in line:
for j in line:
grid[(i, j)] = model.NewIntVar(1, line_size, 'grid %i %i' % (i, j))
# AllDifferent on rows.
for i in line:
model.AddAllDifferent([grid[(i, j)] for j in line])
# AllDifferent on columns.
for j in line:
model.AddAllDifferent([grid[(i, j)] for i in line])
# AllDifferent on cells.
for i in cell:
for j in cell:
one_cell = []
for di in cell:
for dj in cell:
one_cell.append(grid[(i * cell_size + di,
j * cell_size + dj)])
model.AddAllDifferent(one_cell)
# Initial values.
for i in line:
for j in line:
if initial_grid[i][j]:
model.Add(grid[(i, j)] == initial_grid[i][j])
# Solve and print out the solution.
solver = cp_model.CpSolver()
status = solver.Solve(model)
if status == cp_model.OPTIMAL:
for i in line:
print([int(solver.Value(grid[(i, j)])) for j in line])
solve_sudoku()