Source: Hex Ed¹

Part 1: Work on a hex grid:

\ n / nw +–+ ne /
-+ +- \ / sw +–+ se / s \

> Given a series of steps (`n`, `se`, `ne`) etc, how many steps away from the origin do you end up?




This problem mostly comes down to representation. [This post from Red Blob games](https://www.redblobgames.com/grids/hexagons/) has the best write up of how to use hex coordinate systems I've ever seen. Since it handles distances better, I'm going to use a cube coordinate system, where each hex actually has an `x`, `y`, and `z` coordinate. Now that is decided, we can write up a map to translate directions into offsets, a way to add points together, and a distance function:

```python
neighbors = {
    'n' : (0, 1, -1),
    'ne': (1, 0, -1),
    'se': (1, -1, 0),
    's' : (0, -1, 1),
    'sw': (-1, 0, 1),
    'nw': (-1, 1, 0),
}

def add(p1, p2):
    x1, y1, z1 = p1
    x2, y2, z2 = p2
    return (x1 + x2, y1 + y2, z1 + z2)

def move(p, d):
    return add(p, neighbors[d.strip()])

def distance(p1, p2):
    x1, y1, z1 = p1
    x2, y2, z2 = p2
    return max(abs(x1 - x2), abs(y1 - y2), abs(z1 - z2))

That makes code for the actual question nice and clean:

origin = (0, 0, 0)

for line in lib.input():
    point = origin

    for direction in line.split(','):
        point = move(point, direction)

    distance_to_origin = distance(origin, point)
    print(f'ended at {point} ({distance_to_origin} from origin)')

Part 2: What is the furthest point from the origin visited?

Similar to day 8, we just need to track the maximum value seen thus far as we go:

for line in lib.input():
    point = origin
    furthest_distance = 0
    furthest_point = None

    for direction in line.split(','):
        point = move(point, direction)

        distance_to_origin = distance(origin, point)
        if distance_to_origin > furthest_distance:
            furthest_distance = distance_to_origin
            furthest_point = point

    print(f'ended at {point} ({distance_to_origin} from origin); furthest was {furthest_point} ({furthest_distance} from origin)')

That’s a pretty interesting problem as well.

$ python3 run-all.py day-11

day-11  python3 its-full-of-hexagons.py input.txt       0.0798640251159668      ended at (650, -313, -337) (650 from origin); furthest was (1465, -1070, -395) (1465 from origin)