Day 3: Binary Diagnostic - Part 1

00100
11110
10110
10111
10101
01111
00111
11100
10000
11001
00010
01010

Day 3: Binary Diagnostic - Part 1

Read in the bits as a numeric matrix:

input <- read.fwf('input.txt', widths = rep(1, 12))

Get mean of each column and round it:

gamma <- round(colMeans(input) + 1) - 1

Convert result from binary to decimal:

binary_to_int <- function(x) sum(x * 2 ^ rev(seq_along(x) - 1))
binary_to_int(gamma) * binary_to_int(!gamma)

Day 3: Binary Diagnostic - Part 2

Successively filter rows with most (least) common bit:

00100
11110  1110
10110  0110  110  10  0
10111  0111  111  11  1  1  # Oxygen scrubber rating
10101  0101  101  01
01111
00111
11100  1100
10000  0000  000
11001  1001
00010
01010

Day 3: Binary Diagnostic - Part 2

Loop over columns, filtering rows:

most_common <- function(x) round(colMeans(x) + 1) - 1
oxygen <- co2 <- input
for (j in 1:ncol(input)) {
  if (nrow(oxygen) > 1) {
    common <- most_common(oxygen)
    oxygen <- oxygen[oxygen[, j] == common[j], ]
  }
  if (nrow(co2) > 1) {
    common <- most_common(co2)
    co2 <- co2[co2[, j] != common[j], ]
  }
}
binary_to_int(oxygen) * binary_to_int(co2)

Day 9: Smoke Basin - Part 1

Add up the levels of the lowest points (+1):

2199943210      21   43210       1       0
3987894921      3 878 4 21      
9856789892       85678 8 2        5
8767896789      87678 678       
9899965678       8   65678            5

Day 9: Smoke Basin - Part 1

Read in the values as a numeric matrix (again):

heights <- read.matrix('input.txt')  # custom function!

Vectorized way of comparing points with neighbours:

lowest <- function(h) {
  h < cbind(h, Inf)[, -1] &        # right
  h < rbind(h, Inf)[-1, ] &        # down
  h < cbind(Inf, h[, -ncol(h)]) &  # left
  h < rbind(Inf, h[-nrow(h), ])    # up
}

Add up the levels:

sum(heights[lowest_points(heights)] + 1)

Day 9: Smoke Basin - Part 2

Multiply the sizes of the three largest basins:

2199943210      21   43210
3987894921      3 878 4 21
9856789892       85678 8 2
8767896789      87678 678 
9899965678       8   65678

Day 9: Smoke Basin - Part 2

l <- lowest(h)
h[] <- ifelse(h < 9, NA, Inf)
h[l] <- 1:sum(l)
while (anyNA(h)) {
  h <- h %c%
    cbind(h, NA)[, -1] %c%        # right
    rbind(h, NA)[-1, ] %c%        # down
    cbind(NA, h[, -ncol(h)]) %c%  # left
    rbind(NA, h[-nrow(h), ])      # up
}
sizes <- table(h[is.finite(h)])
sort(sizes, decreasing = TRUE) |> head(3) |> prod()

"%c%" <- function(x, y) {
  ifelse(is.infinite(x), x,
         ifelse(!is.na(x), x,
                ifelse(!is.infinite(y), y, x)))
}

Day 21: Dirac Dice - Part 1

Deterministic dice rolls: 1+2+3, 4+5+6, 7+8+9, ...

Circular game track: 1, 2, ... 10, 1, ...

Players' scores increase by spaces they landed on.

How many rolls till someone gets a score ≥1000?

Day 21: Dirac Dice - Part 1

deterministic_dice <- function(player1, player2) {
  score1 <- score2 <- nrolls <- 0
  dice <- 1:3
  repeat {
    player1 <- (player1 + sum(dice) - 1) %% 10 + 1
    score1 <- score1 + player1
    nrolls <- nrolls + 3
    if (score1 >= 1000) break
    player2 <- (player2 + sum(dice + 3) - 1) %% 10 + 1
    score2 <- score2 + player2
    nrolls <- nrolls + 3
    if (score2 >= 1000) break
    dice <- (dice + 6 - 1) %% 100 + 1
  }
  prod(nrolls, min(score1, score2))
}

Day 21: Dirac Dice - Part 2

Three-sided die.

On each roll, universe splits into three: one for each possible outcome.

Game ends when a player's score reaches ≥21.

Which player wins in more universes? How many?

Day 21: Dirac Dice - Part 2

First notice that there are only seven possible sums of 3 rolls:

3 4 5 6 7 8 9 # sum of the three dice
1 3 6 7 6 3 1 # number of combinations

Store in a list called rolls.

Day 21: Dirac Dice - Part 2

dirac_dice <- function(player1, player2) {
  count_wins <- memoise::memoise(
    function(player1, player2, score1, score2) {
      Reduce(
        \(wins, roll) {
          player1 <- (player1 + roll['sum'] - 1) %% 10 + 1
          score1 <- score1 + player1
          if (score1 >= 21) {
            return(wins + c(roll['n'], 0))
          } else
            wins + roll['n'] *
            rev(count_wins(player2, player1, score2, score1))
        },
        rolls,
        init = c(w1 = 0, w2 = 0))
    })
  max(count_wins(player1, player2, 0, 0))
}