Day 12

Advent of Code: Worked Solutions

Setup

# Libraries
library(tidyverse)
library(igraph)

# Read input from file into a data frame
input <- read_table("../input/day12.txt", col_names = "chr") |> 
  mutate(
    row = row_number(),
    chr = str_split(chr, "")
  ) |> 
  unnest(chr) |> 
  mutate(col = row_number(), .by = row) |> 
  mutate(idx = row_number(), .before = everything())

Part 1

Format the input as a graph, with edges connecting neighbors of the same type:

# Flag neighboring characters of the same value that border one other
edges_wide <- input |> 
  mutate(v = case_when(row + 1 == lead(row) ~ lead(idx)), .by = c(chr, col)) |> 
  mutate(h = case_when(col + 1 == lead(col) ~ lead(idx)), .by = c(chr, row))

edges_long <- edges_wide |> 
  pivot_longer(
    c(v, h), 
    names_to = NULL, 
    values_to = "target", 
    values_drop_na = TRUE
  )

# Format neighbors as a list of edges and add to add a graph
g <- edges_long |> 
  transmute(
    edge_id = row_number(),
    src = idx, 
    target
  ) |> 
  pivot_longer(c(src, target)) |> 
  arrange(edge_id, value) |> 
  pull(value) |> 
  make_graph(n = nrow(input), directed = FALSE)

V(g)$name <- 1:nrow(input)

# Separate out the resulting graph into sub-graphs of innerconnected regions
dg <- decompose(g)

Compute the perimeter, area, and cost of each subgraph then sum the total:

dg |> 
  map_int(\(subgraph) {
    perim <- sum(4 - degree(subgraph))
    area  <- gorder(subgraph)
    perim * area
  }) |> 
  sum()

[1] 1433460

Part 2

Used a hint from reddit: the number of corners is equal to the number of sides.

A plot can have a convex corner or a concave corner.

• A cell has a convex corner for each pair of adjacent borders
• A cell has a concave corner if it has two adjacent cells of its same group, but its diagonal cell between the two has a different group.

# Get original row/column input and join on the group output from the graph
groups <- left_join(
  input,
  imap_dfr(dg, \(g, grp_idx) tibble(grp = grp_idx, idx = V(g)$name)),
  join_by(idx)
) |> 
  select(idx, grp, row, col)

# For each of a cell's neighbors, flag if they're in the same group
neighbors <- groups |> 
  # Get group number of each adjacent cell (N/S/E/W)
  left_join(transmute(groups, n = grp, row = row + 1, col), join_by(row, col)) |> 
  left_join(transmute(groups, w = grp, col = col + 1, row), join_by(row, col)) |> 
  left_join(transmute(groups, s = grp, row = row - 1, col), join_by(row, col)) |> 
  left_join(transmute(groups, e = grp, col = col - 1, row), join_by(row, col)) |> 
  # Get group number of each diagonal cell (NW/NE/SW/SE)
  left_join(transmute(groups, nw = grp, row = row + 1, col = col + 1), join_by(row, col)) |> 
  left_join(transmute(groups, ne = grp, row = row + 1, col = col - 1), join_by(row, col)) |> 
  left_join(transmute(groups, sw = grp, row = row - 1, col = col + 1), join_by(row, col)) |> 
  left_join(transmute(groups, se = grp, row = row - 1, col = col - 1), join_by(row, col)) |> 
  select(-c(row, col)) |> 
  # Compare group numbers of adjacent/diagonal cells to the current cell
  mutate(across(c(n, w, s, e, nw, ne, sw, se), ~ replace_na(.x == grp, FALSE)))

# Compute total number of concave/convex corners for each cell
corners <- neighbors |> 
  mutate(
    convex = (!n & !w) + (!s & !w) + (!s & !e) + (!n & !e),
    concave = (n & w & !nw) + (s & w & !sw) + (s & e & !se) + (n & e & !ne)
  )

Total the number of corners per group and multiply by the group’s area to get the total cost:

corners |> 
  summarize(
    area = n(),
    num_sides = sum(convex + concave), 
    .by = grp
  ) |> 
  mutate(cost = area * num_sides) |> 
  pull(cost) |> 
  sum()

[1] 855082