solution.py

rows = 'ABCDEFGHI'
cols = '123456789'
assignments = []

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.
    """
    for unit in unitlist: # go through each peer
        naked_twins = []
        for box in unit:
            if len(values[box])==2: #are we a potential twin?
                for potential_twin in unit:
                    if potential_twin != box and values[box] == values[potential_twin]:
                        #new entry only, eg ['A1','B1']  == ['B1', 'A1']
                        if [box, potential_twin] not in naked_twins and [potential_twin, box] not in naked_twins:
                            naked_twins.append([box, potential_twin])
        for twins in naked_twins:
            for box in unit: # for all peers
                for digit in values[twins[0]]:
                    if box not in twins: # if not the twins
                        values = assign_value(values, box, values[box].replace(digit, ''))

    return values


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

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'.
    """
    chars = []
    digits = '123456789'
    for c in grid:
        if c in digits:
            chars.append(c)
        if c == '.':
            chars.append(digits)
    assert len(chars) == 81
    return dict(zip(boxes, chars))


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')]
diagonal_units = [[row_units[i][i] for i in range(len(row_units[0]))],[row_units[len(row_units[0])-1-i][i] for i in range(len(row_units[0]))]]
unitlist = row_units + column_units + square_units + diagonal_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 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):
    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 = assign_value(values, peer, values[peer].replace(digit, ''))
    return values

def only_choice(values):
    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):
    stalled = False
    while not stalled:
        solved_values_before = len([box for box in values.keys() if len(values[box]) == 1])
        values = naked_twins(values)
        values = eliminate(values)
        values = only_choice(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):
    values = reduce_puzzle(values)
    if values is False:
        return False  # failed
    if (all(len(values[s]) == 1 for s in boxes)):
        return values  # solved

    # Choose one of the unfilled squares with the fewest possibilities
    square, _ = min([(box, len(values[box])) for box in values.keys() if len(values[box]) != 1], key=lambda b: b[1])
    # Now use recursion to solve each one of the resulting sudokus, and if one returns a value (not False), return that answer!
    for value in values[square]:
        new_puzzle = values.copy()
        new_puzzle[square] = value
        solution = search(new_puzzle)
        if solution:
            return solution

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)
    return search(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.')