Day 6

Advent of Code: Worked Solutions

Setup

# Libraries
library(tidyverse)
library(unglue)

# Read input from file
input <- read_lines("../input/day06.txt", skip_empty_rows = FALSE)

Part 1

Convert input text into a set of time/distance vectors for each race:

races <- c("time" = 1, "distance" = 2) |> 
  imap(\(i, name) {
    input[[i]] |>
      str_remove(regex(str_c(name, ":\\s+"), ignore_case = T)) |>
      str_split_1("\\s+") |>
      as.numeric()
  }) |> 
  pmap(\(time, distance) list(time = time, record = distance))

Define a function to compute your traveled distance in each race, given the amount of time you hold the button:

race_dist <- function(time_race, time_hold) {
  (time_race - time_hold) * time_hold
}

For each race, count the number of record-beating ways to win:

races |> 
  map_int(\(race) sum(race_dist(race$time, 0:race$time) > race$record)) |> 
  prod()

Part 2

Combine the individual race numbers into one single race:

race <- races |> 
  enframe(name = "pos") |> 
  unnest_wider(value) |> 
  summarize(across(c(time, record), ~ as.numeric(str_c(.x, collapse = "")))) |> 
  pivot_longer(everything()) |> 
  deframe() |> 
  as.list()

Compute roots of the race distance function using the quadratic equation to determine the range of record-winning hold times:

winning_methods <- function(time_race, record) {
  root1 <- (time_race + sqrt(time_race^2 - 4 * record)) / 2
  root2 <- (time_race - sqrt(time_race^2 - 4 * record)) / 2
  
  bnd_l <- ceiling(max(min(root1, root2), 0))
  bnd_r <- floor(min(max(root1, root2), time_race))
  
  bnd_l <- if_else(race_dist(time_race, bnd_l) == record, bnd_l + 1, bnd_l)
  bnd_r <- if_else(race_dist(time_race, bnd_r) == record, bnd_r - 1, bnd_r)
  
  bnd_r - bnd_l + 1
}

Run on puzzle input:

winning_methods(race$time, race$record)