A sudoku solver

Sudoku_solver.py

__author__ = 'Girish Ramnani'
"""

This program takes in a sudoku and solves it ,here 0 means not set so add numbers write them down
requirement - python 3.3 or higher.
"""


board = \
    [[9, 0, 6, 0, 7, 1, 5, 0, 0],
     [5, 0, 0, 0, 9, 0, 3, 0, 0],
     [0, 0, 0, 3, 8, 0, 0, 0, 0],
     [2, 0, 1, 0, 0, 0, 0, 0, 3],
     [0, 0, 9, 0, 0, 0, 4, 0, 0],
     [7, 0, 0, 0, 0, 0, 8, 0, 5],
     [0, 0, 0, 0, 6, 7, 0, 0, 0],
     [0, 0, 2, 0, 4, 0, 0, 0, 9],
     [0, 0, 3, 9, 2, 0, 7, 0, 1]]
'''medium level'''
board2 = \
    [[0, 0, 0, 0, 2, 0, 4, 1, 6],
     [0, 0, 9, 1, 5, 0, 0, 0, 0],
     [0, 0, 0, 0, 0, 0, 3, 5, 0],
     [0, 2, 0, 0, 0, 0, 7, 0, 4],
     [5, 0, 0, 2, 0, 7, 0, 0, 3],
     [1, 0, 8, 0, 0, 0, 0, 6, 0],
     [0, 5, 7, 0, 0, 0, 0, 0, 0],
     [0, 0, 0, 0, 7, 8, 5, 0, 0],
     [8, 6, 2, 0, 3, 0, 0, 0, 0]]
'''evil level, Thats what the websudoku guys say '''
board3 = \
    [[0, 0, 5, 7, 0, 0, 1, 0, 0],
     [9, 0, 0, 0, 0, 2, 6, 0, 0],
     [0, 0, 0, 0, 0, 8, 5, 0, 2],
     [0, 0, 0, 0, 2, 0, 8, 0, 3],
     [6, 0, 0, 0, 0, 0, 0, 0, 1],
     [7, 0, 9, 0, 1, 0, 0, 0, 0],
     [3, 0, 2, 4, 0, 0, 0, 0, 0],
     [0, 0, 7, 5, 0, 0, 0, 0, 9],
     [0, 0, 4, 0, 0, 6, 3, 0, 0]]

def moves(board, row, column):
    """
    used set to i
    :param board:
    :param row:
    :param column:
    :return:list -> list of legal moves that the computer can choose from
    """

    all_taken = set([x for x in board[row]])
    for x in range(len(board)):
        all_taken.add(board[x][column])
    first_row = (row // 3) * 3
    first_column = (column // 3) * 3
    for x in range(first_row, first_row + 3):
        for y in range(first_column, first_column + 3):
            all_taken.add(board[x][y])
    red_moves = set([x for x in range(1, 10)])
    available_moves = red_moves.difference(all_taken)
    return available_moves


def display(board):
    for x in board:
        print(x)


def flatten_count(board, i):
    li = [y for x in board for y in x]
    return li.count(i)


def make_move(board, move, x, y, no):
    board[x][y] = move
    no -= 1
    return no


def undo_move(board, x, y, no_avail):
    board[x][y] = 0
    no_avail += 1
    return no_avail


def _solve(board, no_avail, a):
    if no_avail <= 0:
        return True
    for x in range(a, len(board)):
        for y in range(len(board)):
            if board[x][y] == 0:
                t = moves(board, x, y)
                if len(t) == 0:
                    return False
                for move in t:
                    no_avail = make_move(board, move, x, y, no_avail)
                    if _solve(board, no_avail, x):
                        return True
                    no_avail = undo_move(board, x, y, no_avail)
                return False


display(board)
print()


def solve_game(board):
    """
    the main method from where the running starts

    :param board:
    :return:
    """
    import time

    t = time.time()

    no_available = flatten_count(board, 0)
    _solve(board, no_available, 0)
    for z in board:
        print(z)
    print()
    print(time.time() - t, " seconds to solve")


solve_game(board)
solve_game(board2)
solve_game(board3)

[9, 3, 6, 4, 7, 1, 5, 2, 8]
[5, 1, 8, 6, 9, 2, 3, 4, 7]
[4, 2, 7, 3, 8, 5, 1, 9, 6]
[2, 8, 1, 7, 5, 4, 9, 6, 3]
[3, 5, 9, 8, 1, 6, 4, 7, 2]
[7, 6, 4, 2, 3, 9, 8, 1, 5]
[8, 9, 5, 1, 6, 7, 2, 3, 4]
[1, 7, 2, 5, 4, 3, 6, 8, 9]
[6, 4, 3, 9, 2, 8, 7, 5, 1]

0.7425298690795898 seconds to solve
[7, 3, 5, 8, 2, 9, 4, 1, 6]
[6, 4, 9, 1, 5, 3, 8, 2, 7]
[2, 8, 1, 7, 4, 6, 3, 5, 9]
[3, 2, 6, 5, 8, 1, 7, 9, 4]
[5, 9, 4, 2, 6, 7, 1, 8, 3]
[1, 7, 8, 3, 9, 4, 2, 6, 5]
[4, 5, 7, 9, 1, 2, 6, 3, 8]
[9, 1, 3, 6, 7, 8, 5, 4, 2]
[8, 6, 2, 4, 3, 5, 9, 7, 1]

0.055059194564819336 seconds to solve
[2, 3, 5, 7, 6, 4, 1, 9, 8]
[9, 1, 8, 3, 5, 2, 6, 4, 7]
[4, 7, 6, 1, 9, 8, 5, 3, 2]
[5, 4, 1, 9, 2, 7, 8, 6, 3]
[6, 2, 3, 8, 4, 5, 9, 7, 1]
[7, 8, 9, 6, 1, 3, 2, 5, 4]
[3, 5, 2, 4, 8, 9, 7, 1, 6]
[8, 6, 7, 5, 3, 1, 4, 2, 9]
[1, 9, 4, 2, 7, 6, 3, 8, 5]

0.01198887825012207 seconds to solve
Output of the code ..
Do tell if something is wrong