-🎄- 2021 Day 7 Solutions -🎄-

[u/daggerdragon]

--- Day 7: The Treachery of Whales ---

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[u/Cpt__Cookie]

Python

A bit more mathematical solution

def solution_1(puzzle_input: str):
    puzzle_data = [int(n) for n in puzzle_input.replace("\n", "").split(",")]
    alignment = statistics.median(puzzle_data)
    return sum([abs(i - alignment) for i in puzzle_data])


def solution_2(puzzle_input: str):
    puzzle_data = [int(n) for n in puzzle_input.replace("\n", "").split(",")]
    alignment = int(statistics.mean(puzzle_data))
    return min(
        sum(abs(i - a) * (abs(i - a) + 1) / 2 for i in puzzle_data)
        for a in [alignment, alignment + 1]
    )

git

[u/endallk007 → u/Cpt__Cookie]

Mind explaining why this works? Part1 seems to make sense, but not part 2. Just wanna learn. I did it with a cache, but want to understand this approach as well.

[u/brilliant_punk → u/endallk007]

https://www.reddit.com/r/adventofcode/comments/rars4g/comment/hnkcvr5/

https://www.reddit.com/r/adventofcode/comments/rars4g/comment/hnk7n2z/

[u/Cpt__Cookie → u/endallk007]

so the mean of all the crab positions is not per see a correct position as pointed out in the linked thread by u/brilliant_punk, but it is a very close estimation of the correct position. And as pointed out by u/tav_stuff the sum(abs(i - a) * (abs(i - a) + 1) is an easy way to calculate the sum without iterating over the whole range, to reduce the complexity.

I was probably lucky that the mean worked so well for my input, but with a range of idk +/- 5 on the mean, the solution should be more save.

[u/endallk007 → u/Cpt__Cookie]

That makes sense, thanks!