Day 3: Gear Ratios

 17th December 2023 at 6:13pm

Part 1

This was a tricky exercise. From the get-go I avoided iterating over the matrix with plain for loops, and again tried to stick with functional principles. Thus, I'd analyse a set of three lines at once. I think there are some further optimisations in code quality by making the matrix variable global: look_at_surroundings_of_char only needs the line index and the index in the line; the first two parameters are unnecessary.

The get_number_string_under_index was a bit tricky: it uses some sort of flood-fill kind of logic to get the full number (eg. ....2513..., and the algorithm starts at the 1 char; it would concatenate 25 to 1 to 3).

Tests

TEST_DATA = """
467..114..
...*......
..35..633.
......#...
617*......
.....+.58.
..592.....
......755.
...$.*....
.664.598.."""

class Test202303_01(unittest.TestCase):
    def test_transform_input_into_game_data(self):
        matrix = get_game_data_from_input(TEST_DATA)
        self.assertEqual(matrix,
                         TEST_DATA.strip().splitlines())

    def test_upper_current_lower_lines(self):
        matrix = get_game_data_from_input(TEST_DATA)
        self.assertEqual(get_upper_current_lower_lines(matrix, 0),
                         (None, matrix[0], matrix[1]))
        self.assertEqual(get_upper_current_lower_lines(matrix, 2),
                         (matrix[1], matrix[2], matrix[3]))
        self.assertEqual(get_upper_current_lower_lines(matrix, len(matrix) - 1),
                         (matrix[len(matrix) - 2], matrix[len(matrix) - 1], None))

    def test_number_string_under_index(self):
        self.assertEqual(
                get_number_string_under_index("...123...", 3),
                "123"
                )
        self.assertEqual(
                get_number_string_under_index("...123...", 2),
                ""
                )
        self.assertEqual(
                get_number_string_under_index("...1234", 3),
                "1234"
                )
        self.assertEqual(
                get_number_string_under_index("...4", 3),
                "4"
                )
        self.assertEqual(
                get_number_string_under_index(".124", 3),
                "124"
                )

    def test_look_at_surroundings_of_char(self):
        matrix = get_game_data_from_input(TEST_DATA)
        # match on below right diagonal
        self.assertEqual(
            look_at_surroundings_of_char(None,
                                         matrix[0],
                                         matrix[1],
                                         2),
            True
            )
        # No matches
        self.assertEqual(
            look_at_surroundings_of_char(None,
                                         matrix[0],
                                         matrix[1],
                                         5),
            False
            )
        # No matches on 35 above the three
        self.assertEqual(
            look_at_surroundings_of_char(matrix[1],
                                         matrix[2],
                                         matrix[3],
                                         2),
            False
            )
        # match on 35 above the five
        self.assertEqual(
            look_at_surroundings_of_char(matrix[1],
                                         matrix[2],
                                         matrix[3],
                                         3),
            True
            )
        # match on 655 below the six
        self.assertEqual(
            look_at_surroundings_of_char(matrix[1],
                                         matrix[2],
                                         matrix[3],
                                         6),
            True
            )
        self.assertEqual(
            look_at_surroundings_of_char(matrix[8],
                                         matrix[9],
                                         None,
                                         5),
            True
            )

    def test_accumulate_part_numbers_in_line(self):
        matrix = get_game_data_from_input(TEST_DATA)
        self.assertEqual(
            accumulate_part_numbers_in_line(matrix, len(matrix) - 1),
            [664, 598]
            )
        self.assertEqual(
            accumulate_part_numbers_in_line(matrix, 5),
            []
            )
        # excerpt from part 1 solution
        self.assertEqual(
            accumulate_part_numbers_in_line(["$..733*758..."], 0),
            [733, 758]
            )

    def test_solve_part1(self):
        self.assertEqual(
            solve_part_1(TEST_DATA),
            4361
            )               

Code

from functools import reduce

def get_game_data_from_input(data: str) -> list[str]:
    return data.strip().splitlines()

def char_is_a_symbol(char: str) -> bool:
    return not (char.isdigit() or char == '.')

def get_upper_current_lower_lines(
        matrix: list[str],
        line_nbr: int
        ) -> tuple[str | None, str, str | None]:
    upper = (None if line_nbr == 0
             else matrix[line_nbr - 1])
    lower = (None if line_nbr == len(matrix) - 1
             else matrix[line_nbr + 1])
    return (upper, matrix[line_nbr], lower)

def get_number_string_under_index(
        line: str,
        index: int
        ) -> str:
    def get_chars_behind_or_ahead(
            index: int,
            behind: bool = False) -> str:
        if behind:
            return (line[index] +
                    get_chars_behind_or_ahead(index - 1, True)
                    if index >= 0 and line[index].isdigit()
                    else "")
        else:
            return (line[index] +
                    get_chars_behind_or_ahead(index + 1)
                    if index < len(line) and line[index].isdigit()
                    else "")
    return (get_chars_behind_or_ahead(index - 1, True)[::-1] +
                line[index] +
                get_chars_behind_or_ahead(index + 1)
            if line[index].isdigit()
            else "")

def get_next_non_digit_symbol_index(line: str, index: int) -> int:
    return (get_next_non_digit_symbol_index(line, index + 1)
            if index < len(line) and line[index].isdigit()
            else index)

def look_at_surroundings_of_char(upper: str | None,
                                 line: str, lower: str | None, index: int) -> bool:
   # Check vertically
   if any(map(lambda x: x is not None and char_is_a_symbol(x[index]),
              [upper, lower])):
       return True

   # Check horizontally
   for offset in [-1, 1]:
       new_index = index + offset
       if 0 <= new_index < len(line):
           if (char_is_a_symbol(line[new_index])):
               return True
           # Check diagonally
           if (line[new_index] == '.' and
               any(map(lambda x: x is not None and char_is_a_symbol(x[new_index]),
                       [upper, lower]))):
               return True

   return False


# recursively checks the line
def accumulate_part_numbers_in_line(
        matrix: list[str],
        line_nbr: int,
        index: int = 0,
        result: list[int] = []):
    if index >= len(matrix[line_nbr]):
        return result
    char = matrix[line_nbr][index]
    # if a digit is found, check its surroundings.
    # if there is a symbol nearby, add the number and keep going
    if (char.isdigit() and look_at_surroundings_of_char(
        *get_upper_current_lower_lines(matrix, line_nbr),
        index)):
        # add the number to the result list, and
        number = get_number_string_under_index(matrix[line_nbr], index)
        # make the index jump to the end of that digit
        next_index = get_next_non_digit_symbol_index(matrix[line_nbr], index)
        return accumulate_part_numbers_in_line(
                matrix,
                line_nbr,
                next_index,
                result + [int(number)]
                )
    else:
        return accumulate_part_numbers_in_line(
                matrix,
                line_nbr,
                index + 1,
                result
                )

def solve_part_1(data: str) -> int:
    matrix = get_game_data_from_input(data)
    return sum(reduce(lambda x, y: x + y,
                  map(lambda x: accumulate_part_numbers_in_line(matrix, x),
                      range(len(matrix))),
                  []))

with open('input', 'r') as f:
    data = f.read()
    print(solve_part_1(data))

Part 2

Part two seems to demand a whole different approach. On Part one, I focused mainly on the numbers, checking whether they were adjacent to anything; this time around, we're only paying attention to * chars (stars), and we must retrieve the cases where there are two adjacent numbers.

So I started working from the bigger functions to the smallest, while devising some tests. It seems like a natural adaptation to change the code to the following:

# recursively checks the line
def accumulate_eligible_gears_in_line(
        matrix: list[str],
        line_nbr: int,
        index: int = 0,
        result: list[int] = []):
    if index >= len(matrix[line_nbr]):
        return result
    # if a star is found, check its surroundings.
    char = matrix[line_nbr][index]
    nbrs = look_at_surroundings_of_star(
            *get_upper_current_lower_lines(matrix, line_nbr),
            index)
    # add the number to the result list, and
    # make the index jump to the end of that digit
    return accumulate_eligible_gears_in_line(
            matrix,
            line_nbr,
            get_next_star_symbol_index(matrix[line_nbr], index),
            result + nbrs if len(nbrs) == 2 else result
            )

def solve_part_2(data: str) -> int:
    matrix = get_game_data_from_input(data)
    return sum(reduce(lambda x, y: x + y,
                  map(lambda x: accumulate_part_numbers_in_line(matrix, x),
                      range(len(matrix))),
                  []))

Debugging

After concluding the code and having the example scenario pass, I came to the unfortunate situation of failing the problem result. Thus, one has to step debug, or try to find, like searching for a needle in a haystack, the piece of code that is making the whole thing crumble.

I tried going line by line and manually check for the correct pairs; comparing each line with the result of accumulate_eligible_gears_in_star_position. This absurd procedure went for a little bit more than what I think is sane (sane = 2 lines. Not more).

Then I tried comparing the number of pairs to the number of stars. This should be a nice metric to have around: it's possible that the number of pairs is fewer than the number of stars (situation where a star is adjacent to a different number of gears than two). What I did not expect, though, is to have more pairs than stars, which is a gross mistake.

On the problem input,

..........................126.121......935*......235.815.......*.887........*........34..........294........*............$..............@...
45......$..651....$...............................*.........526.............41......*......302...................530..........@819.......463
.....710......*....26................734.......791......565............625.......%.887........@.......381..741..*...........................

my code finds an additional pair [345, 45]. Not good!

Apparently, I had just missed the condition of the char being a * when calling to accumulate via look_at_surroundings_of_star. The following fixes the problem of having more pairs than stars (which was very much absurd).

def accumulate_eligible_gears_in_star_position(
        matrix: list[str],
        line_nbr: int,
        index: int = 0,
        result: list[int] = []) -> list[list[int] | None]:
    if index >= len(matrix[line_nbr]):
        return result
    # if a star is found, check its surroundings;
    nbrs = (look_at_surroundings_of_star(
            *get_upper_current_lower_lines(matrix, line_nbr),
            index)
            if matrix[line_nbr][index] == '*' else [])
    return accumulate_eligible_gears_in_star_position(
            matrix,
            line_nbr,
            get_next_star_symbol_index(matrix[line_nbr], index + 1),
            (result + [nbrs] if nbrs is not None and len(nbrs) == 2
                           else result)
            )

And yet, the calculation is was still wrong, and I had not got the slighest clue as to why; only that my answer was below the correct one. So I looked into the output, having also noticed that the test data did not have two gear rations in the same line: and thus, my tests were not thorough enough. Below is the definition of my solver function.

def solve_part_2(data: str) -> int:
    matrix = get_game_data_from_input(data)
    all_lines = sum(map(lambda t: t[0][0] * t[0][1],
                    filter(lambda r: r != [],
                            map(lambda x: accumulate_eligible_gears_in_star_position(matrix, x),
                  range(len(matrix))))))
    return all_lines

And, for a taste of the output,

[[[102, 206], [449, 140], [138, 301]], [[723, 877], [687, 380], [692, 263]], [[814, 483], [154, 779]], [[733, 758], [489, 551]], [[674, 405]], [[503, 422], [591, 840], [676, 167], [147, 410]] (...)

I suppose all_lines is just calculating the product of the first two elements of each sublist (each sublist corresponding to the gear ratios of a line). Thus, what I have is a nesting problem, because, in fact, I'm assuming my final answer to be a flattened list.

def solve_part_2(data: str) -> int:
    matrix = get_game_data_from_input(data)
    all_lines = sum(map(lambda t: t[0] * t[1],
                     reduce(lambda x, y: x + y if y is not None else x,
                            map(lambda x: accumulate_eligible_gears_in_star_position(matrix, x),
                                range(len(matrix))),
                            [])))
    return all_lines

The reduce is now flattening the list, while also filtering the empty results.

Tests

class Test202303_02(unittest.TestCase):
    def test_accumulate_eligible_gears_in_line_upperleft_below(self):
        matrix = get_game_data_from_input(TEST_DATA)
        self.assertEqual(
            accumulate_eligible_gears_in_star_position(matrix, 1),
            [[35, 467]]
            )

    def test_accumulate_eligible_gears_in_line_single_result(self):
        matrix = get_game_data_from_input(TEST_DATA)
        self.assertEqual(
            accumulate_eligible_gears_in_star_position(matrix, 4),
            []
            )

    def test_accumulate_eligible_gears_in_line_single_result_upperright_below(self):
        matrix = get_game_data_from_input(TEST_DATA)
        self.assertEqual(
            accumulate_eligible_gears_in_star_position(matrix, 8),
            [[598, 755]]
            )

    def test_accumulate_eligible_gears_in_line_double_result(self):
        TEST_DATA = """467..114..\n...*..*...\n..35..633."""
        matrix = get_game_data_from_input(TEST_DATA)
        self.assertEqual(
            accumulate_eligible_gears_in_star_position(matrix, 1),
            [[35, 467], [114, 633]]
            )

    def test_accumulate_eligible_gears_in_line_extra_gears_on_real_input(self):
        with open("input", "r") as f:
            matrix = get_game_data_from_input(f.read())
        self.assertEqual(
            accumulate_eligible_gears_in_star_position(matrix, 29),
            [[235, 791], [887, 34]]
            )

    def test_can_get_all_adjacent_numbers(self):
        TEST_DATA = """467.11.4..\n...*......\n..35.2.333"""
        matrix = get_game_data_from_input(TEST_DATA)
        self.assertEqual(
            look_at_surroundings_of_star(*matrix, 3),
            [35, 467, 11],
            )
    def test_can_get_all_adjacent_numbers_two(self):
        TEST_DATA = """467.11.4..\n......*...\n..35.2.333"""
        matrix = get_game_data_from_input(TEST_DATA)
        self.assertEqual(
            look_at_surroundings_of_star(*matrix, 6),
            [11, 4, 2, 333]
            )

    def test_solve_part2(self):
        self.assertEqual(
            solve_part_2(TEST_DATA),
            467835
            )               
             
```