solution.py

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


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

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')]
diag_units = [[rows[i]+cols[i] for i in range(0,9)], [rows[i]+cols[8-i] for i in range(0,9)]]
print(diag_units)
unitlist = row_units + column_units + square_units+diag_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 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'.
    """
    return {boxes[i]:cols if grid[i]=='.' else grid[i] for i in range(0,81)}

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)
    print

def eliminate(values):
    """
    Go through all the boxes, and whenever there is a box with a value, eliminate this value from the values of all its peers.
    Input: A sudoku in dictionary form.
    Output: 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 = assign_value(values, peer, values[peer].replace(digit,''))
    return values

def only_choice(values):
    """
    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: A sudoku in dictionary form.
    Output: The resulting sudoku in dictionary form.
    """
    for unit in unitlist:
        for digit in cols:
            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 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
    
    # Go through each unit
    for unit in unitlist:
        # sort boxes in a unit by their values
        # all naked twins should be adjacent in the sorted list
        sorted_unit = sorted(unit, key=lambda box: values[box])
        prev_value = None
        for box in sorted_unit:
            value = values[box]
            # compare to the previous value, if length = 2 and identical, we found the naked twins
            if len(value) == 2 and value == prev_value:
                # remove the naked twins from all other boxes in the unit
                table = str.maketrans('', '', value)
                for rbox in unit:
                    if values[rbox] != value:
                        values = assign_value(values, rbox, values[rbox].translate(table))
            prev_value = value
    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 reduce_puzzle(values):
    """
    Iterate through different reduction methods.
    If at some point, there is a box with no available values, return False.
    If the sudoku is solved, return the sudoku.
    If after a single iteration, the sudoku remains the same, return the sudoku.
    Input: A sudoku in dictionary form.
    Output: The resulting sudoku in dictionary form.
    """
    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):
    "Using depth-first search and propagation, try all possible values."
    # First, reduce the puzzle
    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
    for value in values[s]:
        new_sudoku = values.copy()
        new_sudoku[s] = value
        attempt = search(new_sudoku)
        if attempt:
            assign_value(values, s, value)
            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)
    for box in values:
        assign_value(values, box, values[box])
    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.')