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day-21.R
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# Create a two-dimensional matrix of the number of parallel universes in which
# a player is at a position <row> with <column - 1> number of points
create_player <- function(init_pos, pos_max, points_win) {
states <- matrix(rep(0, pos_max * (pos_max + points_win)), nrow = pos_max)
rownames(states) <- 1:10
colnames(states) <- seq(0, pos_max + points_win - 1)
states[init_pos, 1] <- 1
states
}
# For each universe with <position>-<score> state (two-dimensional matrix of
# states), expand to a new set of universes in which the three dice rolled all
# possible sums, taking into account that different dice results create
# different number of universes. Return the new universes counts as a new
# matrix.
play <- function(states, dice, pos_max) {
new_states <- states
new_states[] <- 0
# detect which states are present in the matrix
present_states <- which(states > 0, arr.ind = TRUE)
for (i in seq_len(nrow(present_states))) {
# extract at which positions of the game have how many players scored
# how many points
coord <- present_states[i, , drop = FALSE]
pos <- as.integer(coord[, 1])
score <- as.integer(coord[, 2]) - 1
count <- states[coord]
# compute the new positions starting from the current position in
# all parallel universes
new_pos <- (pos + as.integer(names(dice))) %% pos_max
new_pos[new_pos == 0] <- pos_max
# compute the new score for players who move to a given new position
# (knowing the started from the same score before the universes branch out
new_score <- score + new_pos
# compute how many of such players are, given how likely are the sums of the
# three dice rolls
new_count <- count * as.integer(dice)
# update the state matrix -
new_states[cbind(new_pos, new_score + 1)] <-
new_states[cbind(new_pos, new_score + 1)] +
new_count
}
new_states
}
part_2_game <- function(p1_pos, p2_pos, debug = FALSE) {
pos_max <- 10
points_win <- 21
# sum up all possible combinations of three die rolls
comb <- as.matrix(expand.grid(1:3, 1:3, 1:3))
dice <- table(rowSums(comb))
# create initial state matrices for counting all parallel universes -- at the
# beginning, each matrix has only one non-zero value, which is the row
# position corresponding to the initial position and the first column
# (representing zero score)
player1 <- create_player(init_pos = p1_pos, pos_max, points_win)
player2 <- create_player(init_pos = p2_pos, pos_max, points_win)
# which columns of the state matrix represent winning situations (i.e. states
# in which a player at whatever position of the board has at least 21 points)
win_states <- (points_win + 1):ncol(player1)
wins1 <- wins2 <- 0
while (TRUE) {
# player 1
# calculate the number of universes surviving after player 2 played their
# round (at the beginning this is 1)
universes <- sum(player2)
if (debug) {
cat(sprintf("turn %i\n", turn))
cat(sprintf("player 1 universes %s\n", universes))
cat("universes / sum(player1)", universes / sum(player1), "\n")
}
# let the player 1 play the game, taking into account the change in the
# number of universes that happened between their last round and the number
# of universes in which player 2 has not won in their round of the game
player1 <- play(player1 * universes / sum(player1), dice, pos_max)
# count the number of universes in which player 1 won
win_count <- sum(player1[, win_states])
wins1 <- wins1 + win_count
player1[, win_states] <- 0
if (debug) {
cat("player 1 wins in", win_count, "universes\n")
cat("player 1 has", sum(player1[, -win_states]), "universes alive\n")
}
if (all(player1[, -win_states] == 0)) break
# player 2 -- same procedure as the one for player 1 above
universes <- sum(player1)
if (debug) {
cat(sprintf("turn %i\n", turn))
cat(sprintf("player 2 universes %s\n", universes))
cat("universes / sum(player2)", universes / sum(player2), "\n")
}
player2 <- play(player2 * universes / sum(player2), dice, pos_max)
win_count <- sum(player2[, win_states])
wins2 <- wins2 + win_count
player2[, win_states] <- 0
if (debug) {
cat("player 2 wins in", win_count, "universes\n")
cat("player 2 has", sum(player2[, -win_states]), "universes alive\n")
}
if (all(player2[, -win_states] == 0)) break
}
max(wins1, wins2)
}
# Hard-coded ugly solution to game in part 1 -- not worth improving, given that
# part 2 is a completely different beast
part_1_game <- function(pos_p1, pos_p2, debug = FALSE) {
p1 <- p2 <- 0
pos_max <- 10
die <- 1
die_max <- 100
die_counter <- 0
while (TRUE) {
# p1
die_add <- 0
for (i in 1:3) {
if (debug) cat(die, " ")
die_add <- die_add + die
die <- die + 1
if (die > die_max) die <- 1
die_counter <- die_counter + 1
}
p1_shift <- die_add %% pos_max
if (debug) cat("die add ", die_add, "\n")
pos_p1 <- (pos_p1 + p1_shift) %% pos_max
if (pos_p1 == 0) pos_p1 <- 10
p1 <- p1 + pos_p1
if (p1 >= 1000) break
# p2
die_add <- 0
for (i in 1:3) {
if (debug) cat(die, " ")
die_add <- die_add + die
die <- die + 1
if (die > die_max) die <- 1
die_counter <- die_counter + 1
}
p2_shift <- die_add %% pos_max
if (debug) cat("die add ", die_add, "\n")
pos_p2 <- (pos_p2 + p2_shift) %% pos_max
if (pos_p2 == 0) pos_p2 <- 10
p2 <- p2 + pos_p2
if (p2 >= 1000) break
if (debug) cat("p1 ", p1, "-", pos_p1, " ", "p2 ", p2, "-", pos_p2, "\n")
}
if (debug) cat(p1, " vs ", p2, "\n")
min(p1, p2) * die_counter
}