solution.py

assignments = []

def cross(A, B):
    "Cross product of elements in A and elements in B."
    return [x + y for x in A for y in B]

"""
Variables for Sudoku Board
"""
rows = 'ABCDEFGHI'
cols = '123456789'
cols_rev = cols[::-1]
boxes = cross(rows, cols)
row_units = [cross(r, cols) for r in rows]
column_units = [cross(rows, c) for c in cols]
square_units = [cross(rs, cs) for rs in ('ABC','DEF','GHI') for cs in ('123','456','789')]
d1_units = [[rows[i]+cols[i] for i in range(len(rows))]]
d2_units = [[rows[i]+cols_rev[i] for i in range(len(rows))]]

unitlist = row_units + column_units + square_units + d1_units + d2_units
units = dict((s, [u for u in unitlist if s in u]) for s in boxes)
peers = dict((s, set(sum(units[s],[]))-set([s])) for s in boxes)

def assign_value(values, box, value):
    """
    Please use this function to update your values dictionary!
    Assigns a value to a given box. If it updates the board record it.
    """

    # Don't waste memory appending actions that don't actually change any values
    if values[box] == value:
        return values

    values[box] = value
    if len(value) == 1:
        assignments.append(values.copy())
    return values

def naked_twins(values):
    """Eliminate values using the naked twins strategy.
    Args:
        values(dict): a dictionary of the form {'box_name': '123456789', ...}

    Returns:
        the values dictionary with the naked twins eliminated from peers.
    """

    # Find all instances of naked twins
    candidate_twins = [box for box in values.keys() if len(values[box]) == 2]
    twins = [[box1, box2] for box1 in candidate_twins for box2 in peers[box1] if set(values[box1]) == set(values[box2])]
    # Eliminate the naked twins as possibilities for their peers
    for twin in twins:
        box1 = twin[0]
        box2 = twin[1]
        peers1 = set(peers[box1])
        peers2 = set(peers[box2])
        common_peers = peers1 & peers2
        for single_peer in common_peers:
            if len(values[single_peer]) > 1:
                for discard_value in values[box1]:
                    values = assign_value(values, single_peer, values[single_peer].replace(discard_value,''))
    return values


def grid_values(grid):
    """
    Convert grid into a dict of {square: char} with '123456789' for empties.
    Args:
        grid(string) - A grid in string form.
    Returns:
        A grid in dictionary form
            Keys: The boxes, e.g., 'A1'
            Values: The value in each box, e.g., '8'. If the box has no value, then the value will be '123456789'.
    """
    values = []
    default_value = '123456789'
    for i in grid:
        if i == ".":
            values.append(default_value)
        elif i in default_value:
            values.append(i)
    assert len(values) == 81
    return dict(zip(boxes, values))

def display(values):
    """
    Display the values as a 2-D grid.
    Args:
        values(dict): The sudoku in dictionary form
    """
    width = 1+max(len(values[s]) for s in boxes)
    line = '+'.join(['-'*(width*3)]*3)
    for r in rows:
        print(''.join(values[r+c].center(width)+('|' if c in '36' else '')
                      for c in cols))
        if r in 'CF': print(line)
    return


def eliminate(values):
    """
    Goes through all the boxes, and whenever there is a box with a value, eliminates that value from the values of all its peers.
    :param values: The sudoku in dictionary form
    :return: The resulting sudoku in dictionary form.
    """
    solved_values = [box for box in values.keys() if len(values[box]) == 1]
    for box in solved_values:
        digit = values[box]
        for peer in peers[box]:
            values[peer] = values[peer].replace(digit,'')
    return values


def only_choice(values):
    """
    Goes through all the units, and whenever there is a unit with a value that only fits in one box, assigns the value to that box.
    :param values: The sudoku in dictionary form
    :return: The resulting sudoku in dictionary form.
    """
    for unit in unitlist:
        for digit in '123456789':
            dplaces = [box for box in unit if digit in values[box]]
            if len(dplaces) == 1:
                values = assign_value(values, dplaces[0], digit)
    return values


def reduce_puzzle(values):
    solved_values = [box for box in values.keys() if len(values[box]) == 1]
    stalled = False
    while not stalled:
        solved_values_before = len([box for box in values.keys() if len(values[box]) == 1])
        values = eliminate(values)
        values = only_choice(values)
        values = naked_twins(values)

        solved_values_after = len([box for box in values.keys() if len(values[box]) == 1])
        stalled = solved_values_before == solved_values_after
        if len([box for box in values.keys() if len(values[box]) == 0]):
            return False
    return values

def search(values):
    "Uses depth-first search and propagation, creates a search tree and solves the sudoku."
    # First, reduces the puzzle using the previous function
    values = reduce_puzzle(values)
    if values is False:
        return False  ## Failed earlier
    if all(len(values[s]) == 1 for s in boxes):
        return values  ## Solved!

    # Chooses one of the unfilled squares with the fewest possibilities
    n, s = min((len(values[s]), s) for s in boxes if len(values[s]) > 1)

    # Uses recursion to solve each one of the resulting sudokus, and if one returns a value (not False), returns the answer!
    for value in values[s]:
        new_sudoku = values.copy()
        new_sudoku[s] = value
        attempt = search(new_sudoku)
        if attempt:
            return attempt


def solve(grid):
    """
    Find the solution to a Sudoku grid.
    Args:
        grid(string): a string representing a sudoku grid.
            Example: '2.............62....1....7...6..8...3...9...7...6..4...4....8....52.............3'
    Returns:
        The dictionary representation of the final sudoku grid. False if no solution exists.
    """
    values = grid_values(grid)
    values = search(values)

    return values

if __name__ == '__main__':
    diag_sudoku_grid = '2.............62....1....7...6..8...3...9...7...6..4...4....8....52.............3'
    display(solve(diag_sudoku_grid))

    try:
        from visualize import visualize_assignments
        visualize_assignments(assignments)

    except SystemExit:
        pass
    except:
        print('We could not visualize your board due to a pygame issue. Not a problem! It is not a requirement.')