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smaxd
Sun Nov 25, 2012 9:19 am
Python Sudoku Module
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This is a module I made for solving Sudoku puzzles. It is a recursive backtracking search that solves most
puzzles pretty quick. I tried to make it as fast as possible and it manages to solve Al Escargot in around 3 seconds on my comp.
In this version Im computing the domains of each empty cell each time i need them. It might be more ideal to keep the domains in a dict so I
might change that.
[code]
from copy import deepcopy, copy
from time import clock
def parseBoard(data):
"""
Takes an iterable (but not string) with string elements.
Parses the data into a 2d list of integers to be processed as Sudoku board.
Returns the board with a list of empty squares.
"""
board = [[int(x) for x in line.strip()] for line in data]
emptySquares = list((x,y) for x in range(9) for y in range(9) if board[x][y]==0)
return (board,emptySquares)
def possibleValues(board, position):
"""
Returns a generator of valid values of the square on the board
at position (row,col).
"""
r,c = position
adjacent = tuple(board[r][y] for y in range(9)) + tuple(board[x][c] for x in range(9)) + tuple(board[x][y] for x in range(int(r/3)*3,int(r/3)*3+3) for y in range(int(c/3)*3,int(c/3)*3+3))
for v in range(1,10):
if v not in adjacent: yield v
def leastConstrainingValue(board,cell,value):
"""
Function used in calculating least constraining value heuristic.
"""
r,c = cell
adjacent = {(r,y) for y in range(9)} | {(x,c) for x in range(9)} | {(x,y) for x in range(int(r/3)*3,int(r/3)*3+3) for y in range(int(c/3)*3,int(c/3)*3+3)}
adjacent.discard(cell)
return sum(1 for near in adjacent if value in possibleValues(board,near))
def solve(board,emptyCells):
"""
Returns a solved version of the initial Sudoku board.
Board must be 9*9 grid of integers
"""
emptyCells.sort(key = lambda cell: len(list(possibleValues(board,cell))))
if len(emptyCells)==0: return board
else: row,col = emptyCells.pop(0)
for value in sorted(possibleValues(board,(row,col)), key = lambda v: leastConstrainingValue(board,(row,col),v)):
newBoard = deepcopy(board)
newBoard[row][col] = value
newBoard = solve(newBoard,copy(emptyCells))
if newBoard: return newBoard
return False
#Used for testing algorithm efficiency.
"""
board, i = parseBoard(['120400300', '300010050', '006000100', '700090000', '040603000', '003002000', '500080700', '007000005', '000000098'])
start = clock()
board = solve(board,i)
end = clock()
for line in board: print(line)
print(end-start)
"""
[/code]