06. Strategy 2: Only Choice

Insight: Every unit must contain exactly one occurrence of every number

So, these are the values we obtain when we apply the function eliminate.

Let's actually look more carefully at the top 3x3 square in the center, highlighted in red.

Single possibility quiz

Looking only at the unsolved boxes in the red 3x3 square, which of the below values can we fill in? Select all the values that apply.
SOLUTION:
  • 1

Yes! In this unit, there seems to be only one box which would allow a value of 1 (explained below). Since each digit must appear somewhere in the unit, we conclude that the top right box must contain the digit 1.

Only Choice

So, we have another strategy!

Strategy 2: Only Choice

If there is only one box in a unit which would allow a certain digit, then that box must be assigned that digit.

Time to code it! In the next quiz, finish the code for the function only_choice, which will take as input a puzzle in dictionary form. The function will go through all the units, and if there is a unit with a digit that only fits in one possible box, it will assign that digit to that box.

The above image shows the result of applying the only choice rule.

The above image shows the result of applying the only choice rule.

Start Quiz:

from utils import *

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.
    """
    # TODO: Implement only choice strategy here
    return values

rows = 'ABCDEFGHI'
cols = '123456789'

def cross(a, 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')]
unitlist = row_units + column_units + square_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.
    Input: The sudoku in dictionary form
    Output: None
    """
    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 grid_values(grid):
    """
    Convert grid into a dict of {square: char} with '123456789' for empties.
    Input: A grid in string form.
    Output: 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))

from utils import *

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:
                values[dplaces[0]] = digit
    return values

User's Answer:

(Note: The answer done by the user is not guaranteed to be correct)

from utils import *

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.
    """
    # TODO: Implement only choice strategy here
    for unit in unitlist:
        for digit in '123456789':
            num_hits = 0;
            for box in unit:
                if digit in values[box]:
                    num_hits= num_hits + 1
                    last_box = box
            if num_hits == 1:
                values[last_box] = digit
    return values

rows = 'ABCDEFGHI'
cols = '123456789'

def cross(a, 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')]
unitlist = row_units + column_units + square_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.
    Input: The sudoku in dictionary form
    Output: None
    """
    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 grid_values(grid):
    """
    Convert grid into a dict of {square: char} with '123456789' for empties.
    Input: A grid in string form.
    Output: 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))

from utils import *

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:
                values[dplaces[0]] = digit
    return values

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