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lib_sudoku.py
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lib_sudoku.py
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#!/usr/bin/python
'''
program: lib_sudoku.py
author: tc
created: 2015-12-06 -- 20 CEST
last-modified: 2015-12-07 -- 21 CEST
'''
# imports for python 2/3 compatibility
from __future__ import print_function
from builtins import range
from builtins import object
import numpy
import random
import math
class Sudoku(object):
'''
Members:
scheme : 9x9 numpy array of integers
energy
beta
Methods:
__init__(input_file, seed=0)
_load_puzzle(filename)
_fill_puzzle()
_get_box(i, j)
_total_energy()
_local_energy(i ,j)
set_beta()
MC_move()
print_puzzle()
'''
def __init__(self, input_file, seed=0):
'''
Initializes an instance of the Sudoku class.
Arguments:
input_file : file with the puzzle
seed* : seed for the random-number generator (if 0, a random
value is chosen as seed)
'''
print('[sudoku] init')
if seed == 0:
seed = random.randrange(99999999)
random.seed(seed)
print('[sudoku] random seed: %i' % seed)
# initialize and fill puzzle
self._load_puzzle(input_file)
self._fill_puzzle()
assert self.puzzle.min() >= 1
assert self.puzzle.max() <= 9
# initialize other members
self.energy = self._total_energy()
self.beta = 1.0e4
def _load_puzzle(self, filename):
''' Reads puzzle from input file.
'''
x = numpy.loadtxt(filename, dtype=numpy.int)
assert x.shape == (9, 9), 'ERROR: wrong-shape puzzle in %s' % filename
assert x.max() <= 9, 'ERROR: puzzle.max() = %i' % x.max()
assert x.min() >= 0, 'ERROR: puzzle.min() = %i' % x.min()
self.puzzle = x[:, :]
number_clues = (x > 0).sum()
print('[sudoku] read puzzle from %s (%i clues)' % (filename,
number_clues))
def _fill_puzzle(self):
''' Replaces zeros with random numbers in [1,..,9].
'''
tot = list(range(1, 10)) * 9
for n in self.puzzle[numpy.nonzero(self.puzzle)].flatten():
tot.pop(tot.index(n))
self.non_clues = []
for i in range(9):
for j in range(9):
if not self.puzzle[i, j]:
self.non_clues.append([i, j])
self.puzzle[i, j] = tot.pop(random.randrange(len(tot)))
assert tot == [], 'ERROR, in _fill_puzzle()'
assert self.puzzle.min() > 0, 'ERROR, in _fill_puzzle()'
def _get_box(self, i, j):
''' Returns entries of the 3x3 box for the cell (i, j).
'''
return self.puzzle[(i // 3) * 3:(i // 3 + 1) * 3,
(j // 3) * 3:(j // 3 + 1) * 3]
def _total_energy(self):
''' Computes the total energy of a puzzle.
'''
E = 0
list_i = list(range(9))
list_j = [0, 3, 6, 1, 4, 7, 2, 5, 8]
for ind in range(9):
E += self._local_energy(list_i[ind], list_j[ind])
return E
def _local_energy(self, i, j):
''' Computes the local energy of the cell (i, j).
'''
E = 0
# check row
row = self.puzzle[i, :]
occupations = numpy.bincount(row)
occupations = occupations[occupations > 1]
E += sum(occupations)
# check column
column = self.puzzle[:, j]
occupations = numpy.bincount(column)
occupations = occupations[occupations > 1]
E += sum(occupations)
# check box
box = self._get_box(i, j).flatten()
occupations = numpy.bincount(box)
occupations = occupations[occupations > 1]
E += sum(occupations)
return E
def set_beta(self, beta):
''' Sets a new value of beta.
'''
self.beta = beta
def MC_move(self):
'''
Proposes to replace one of the non-fixed cells with a random entry, and
accepts/rejects according to Metropolis rule.
'''
i, j = random.choice(self.non_clues)
E_ij_old = self._local_energy(i, j)
n_old = self.puzzle[i, j]
self.puzzle[i, j] = random.randrange(1, 10)
E_ij_new = self._local_energy(i, j)
dE = E_ij_new - E_ij_old
if dE < 0.0 or random.uniform(0.0, 1.0) < math.exp(- self.beta * dE):
self.energy += dE
return
else:
self.puzzle[i, j] = n_old
def print_puzzle(self):
for i in range(9):
for j in range(9):
print(self.puzzle[i, j], end=' ')
print()
if __name__ == '__main__':
S = Sudoku('puzzle.dat', seed=1)
S.print_puzzle()