solution.py

import itertools

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

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]

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 = [['{}{}'.format(rows[i], cols[i]) for i in range(len(rows))],\
                  ['{}{}'.format(list(reversed(rows))[i], cols[i]) for i in range(len(rows)-1, -1, -1)]]
# Diagonal units are added to the previous unit list
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 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
    # Eliminate the naked twins as possibilities for their peers
    for unit in unitlist:
        # Possible Naked Twins
        possible_naked_twins = [box for box in unit if len(values[box]) == 2]

        naked_twins = []
        for box_1 in possible_naked_twins:
            for box_2 in possible_naked_twins:
                # Determine if the boxes are peers (required to be Naked Twins)
                # and that both boxes contain the same values
                if box_1 in peers[box_2] and values[box_1] == values[box_2]:
                    if (box_1, box_2) not in naked_twins and (box_2, box_1) not in naked_twins:
                        naked_twins.append((box_1, box_2))

        for pair in naked_twins:
            box_1, box_2 = pair
            # Look at all units that the each Naked Twins box is in
            for units_box_1, units_box_2 in zip(units[box_1], units[box_2]):
                # If each box in the the Naked Twins pair shares a common unit,
                # then update the values to remove their common digits from the other units
                if units_box_1 == units_box_2:
                    for box in units_box_1:
                        for i in values[box_1]:
                            if box != box_1 and box != box_2:
                                assign_value(values, box, values[box].replace(i, ''))

    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'.
    """
    grid_dict = dict(zip(boxes, grid))
    for box in grid_dict:
        if grid_dict[box] == '.':
            grid_dict[box] = '123456789'
    return grid_dict

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):
    """
    Eliminate values from peers of each box with a single value.

    Go through all the boxes, and whenever there is a box with a single value,
    eliminate this value from the set of values of all its peers.

    Args:
        values: Sudoku in dictionary form.
    Returns:
        Resulting Sudoku in dictionary form after eliminating values.
    """
    for box in values:
        if len(values[box]) == 1:
            for peer in peers[box]:
                assign_value(values, peer, values[peer].replace(values[box], ''))

    return values

def only_choice(values):
    """
    Finalize all values that are the only choice for a unit.

    Go through all the units, and whenever there is a unit with a value
    that only fits in one box, assign the value to this box.

    Input: Sudoku in dictionary form.
    Output: Resulting Sudoku in dictionary form after filling in only choices.
    """
    for unit in unitlist:
        for digit in '123456789':
            dplaces = [box for box in unit if digit in values[box]]
            if len(dplaces) == 1:
                assign_value(values, dplaces[0], digit)
    return values

def reduce_puzzle(values):
    stalled = False
    while not stalled:
        # Check how many boxes have a determined value
        solved_values_before = len([box for box in values.keys() if len(values[box]) == 1])
        # Use the Eliminate Strategy
        eliminate(values)
        # Use the Only Choice Strategy
        only_choice(values)
        # Use the Naked Twins Strategy
        naked_twins(values)
        # Check how many boxes have a determined value, to compare
        solved_values_after = len([box for box in values.keys() if len(values[box]) == 1])
        # If no new values were added, stop the loop.
        stalled = solved_values_before == solved_values_after
        # Sanity check, return False if there is a box with zero available values:
        if len([box for box in values.keys() if len(values[box]) == 0]):
            return False
    return values

def search(values):
    "Using depth-first search and propagation, try all possible values."
    # First, reduce 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!
    # Choose 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)
    # Now use recurrence to solve each one of the resulting sudokus, and
    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.
    """
    grid_dict = grid_values(grid)
    result = search(grid_dict)
    return result


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.')