Day 7

Advent of Code: Worked Solutions

Setup

Import libraries:

library(tidyverse)

Read input from file:

input <- scan("../input/day07.txt", sep = ",", quiet = TRUE)

Part 1

We define the cost function as the sum of the absolute differences between our given point and all crabs:

cost <- \(x) sum(abs(x - input))

We define the set of candidates for the optimal alignment location:

candidates <- min(input):max(input)

The total fuel cost is computed by minimizing the cost function over all candidates:

candidates |> 
  map_dbl(cost) |> 
  min()

Part 2

Instead of the basic absolute difference function, our new distance function for each crab \(c_i\) is given by the binomial coefficient:

\[ 1 + 2 + \cdots + |x - c_i| = \sum_{k = 1}^{|x - c_i|}k = \binom{|x - c_i| + 1}{2} \]

cost <- \(x) sum(choose(abs(x - input) + 1, 2))

Repeating the computation with our new cost function, we get:

candidates |> 
  map_dbl(cost) |> 
  min()