Created
July 12, 2012 03:39
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Sudoku checker and solver for CS258
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hard = [[1,0,0,0,0,7,0,9,0], | |
[0,3,0,0,2,0,0,0,8], | |
[0,0,9,6,0,0,5,0,0], | |
[0,0,5,3,0,0,9,0,0], | |
[0,1,0,0,8,0,0,0,2], | |
[6,0,0,0,0,4,0,0,0], | |
[3,0,0,0,0,0,0,1,0], | |
[0,4,0,0,0,0,0,0,7], | |
[0,0,7,0,0,0,3,0,0]] | |
def times(A, B): | |
return [(i,j) for i in A for j in B] | |
dims = range(9) | |
subdims = ([0,1,2],[3,4,5],[6,7,8]) | |
squares = times(dims, dims) | |
unitlist = ([times(dims, [c]) for c in dims] + | |
[times([r], dims) for r in dims] + | |
[times(rs, cs) for rs in subdims for cs in subdims]) | |
units = dict((s, [u for u in unitlist if s in u]) | |
for s in squares) | |
peers = dict((s, set(sum(units[s],[]))-set([s])) | |
for s in squares) | |
def copy(board): | |
return map(lambda x: x[:], board) | |
def subgrid(i): | |
return range(i/3*3, i/3*3+3) | |
def check_row(nums): | |
## each number should be between 0 and 9 | |
counts = [0 for i in range(10)] | |
for num in nums: | |
counts[num] += 1 | |
if num > 0 and counts[num] > 1: | |
return False | |
return True | |
def get_constraints(grid, i, j): | |
row = grid[i] | |
col = [grid[k][j] for k in dims] | |
cell = [grid[k][l] for k in subgrid(i) for l in subgrid(j)] | |
if check_row(row) and check_row(col) and check_row(cell): | |
if grid[i][j] > 0 and grid[i][j] < 10: | |
return str(grid[i][j]) | |
else: | |
return ''.join(map(lambda x: str(x), set(range(1, 10)) - set(row) - set(col) - set(cell))) | |
def check_sudoku(grid): | |
if type(grid) is not list or len(grid) != 9: return | |
for row in grid: | |
if type(row) is not list or len(row) != 9: return | |
for num in row: | |
if type(num) is not int or num < 0 or num > 9: return | |
for i in range(9): | |
for j in range(9): | |
if get_constraints(grid, i, j) is None: | |
return False | |
return True | |
def erase(board, i, j, d): | |
if d not in board[i][j]: | |
return board | |
board[i][j] = board[i][j].replace(d, '') | |
if len(board[i][j]) == 0: | |
return False # contradiction | |
elif len(board[i][j]) == 1: | |
d2 = board[i][j] # single option; erase option from peers | |
if not all(erase(board, i1, j1, d2) for (i1,j1) in peers[i,j]): | |
return False | |
for unit in units[i,j]: # number only present once in unit; assign | |
dplaces = [c for c in unit if d in board[c[0]][c[1]]] | |
if len(dplaces) == 0: | |
return False | |
elif len(dplaces) == 1: | |
i1,j1 = dplaces[0] | |
if not assign(board, i1, j1, d): | |
return False | |
return board | |
def assign(board, i, j, d): | |
if all(erase(board, i, j, d2) for d2 in board[i][j].replace(d, '')): | |
return board | |
else: | |
return False | |
def assign_from(board): | |
return [map(lambda x: int(x), row) for row in board] | |
def solve_partial(board): | |
if board is False: return False | |
# most constrained | |
cell_lengths = [(len(board[c[0]][c[1]]), c) for c in squares] | |
if all(lc[0] == 1 for lc in cell_lengths): | |
return board | |
least, (i, j) = min([lc for lc in cell_lengths if lc[0] > 1], key=lambda x: x[0]) | |
for d in board[i][j]: | |
newboard = solve_partial(assign(copy(board), i, j, d)) | |
if newboard: return newboard # found partial solution | |
return False | |
def solve_sudoku (grid): | |
###Your code here. | |
grid_check = check_sudoku(grid) | |
if grid_check == None or grid_check == False: return grid_check | |
board = copy(grid) | |
for i in range(9): | |
for j in range(9): board[i][j] = get_constraints(grid, i, j) | |
soln = solve_partial(board) | |
if soln: | |
grid = assign_from(soln) | |
assert check_sudoku(grid) == True | |
assert sum(map(sum, grid)) == 405 | |
return grid | |
else: | |
return False | |
print solve_sudoku(hard) |
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