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day23.rs
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day23.rs
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use crate::util::grid::*;
use crate::util::hash::*;
use crate::util::point::*;
use std::collections::VecDeque;
pub struct Input {
extra: u32,
horizontal: [[u32; 6]; 6],
vertical: [[u32; 6]; 6],
}
struct State {
letter: u8,
skipped: bool,
grid: [[u8; 6]; 7],
convert: [u8; 32],
result: u32,
}
pub fn parse(input: &str) -> Input {
let mut grid = Grid::parse(input);
let width = grid.width;
let height = grid.height;
// Modify edge of grid to remove the need for boundary checks.
grid[Point::new(1, 0)] = b'#';
grid[Point::new(width - 2, height - 1)] = b'#';
// Move start and end away from edge.
let start = Point::new(1, 1);
let end = Point::new(width - 2, height - 2);
// Points of interest are start, end and junctions.
grid[start] = b'P';
grid[end] = b'P';
let mut poi = Vec::new();
poi.push(start);
poi.push(end);
for y in 1..height - 1 {
for x in 1..width - 1 {
let position = Point::new(x, y);
if grid[position] != b'#' {
let neighbors =
ORTHOGONAL.iter().map(|&o| position + o).filter(|&n| grid[n] != b'#').count();
if neighbors > 2 {
grid[position] = b'P';
poi.push(position);
}
}
}
}
// BFS to find distances between POIs.
let mut todo = VecDeque::new();
let mut edges = FastMap::new();
let mut weight = FastMap::new();
for from in poi {
todo.push_back((from, 0));
grid[from] = b'#';
weight.insert((from, from), 0);
while let Some((position, cost)) = todo.pop_front() {
for direction in ORTHOGONAL {
let to = position + direction;
match grid[to] {
b'#' => (),
b'P' => {
edges.entry(from).or_insert(FastSet::new()).insert(to);
edges.entry(to).or_insert(FastSet::new()).insert(from);
weight.insert((from, to), cost + 1);
weight.insert((to, from), cost + 1);
}
_ => {
todo.push_back((to, cost + 1));
grid[to] = b'#';
}
}
}
}
}
// Convert reduced graph to a 6x6 square grid.
graph_to_grid(start, end, &edges, &weight)
}
/// The graph is directed so the only allowed steps are down or to the right. The maximum value
/// for any cell is the maximum of either the cell to the left or above.
pub fn part1(input: &Input) -> u32 {
let mut total = [[0; 6]; 6];
for y in 0..6 {
for x in 0..6 {
let left = if x == 0 { 0 } else { total[y][x - 1] + input.horizontal[y][x - 1] };
let above = if y == 0 { 0 } else { total[y - 1][x] + input.vertical[y - 1][x] };
total[y][x] = left.max(above);
}
}
input.extra + total[5][5]
}
/// Graph is undirected so we can also move up or to the right.
pub fn part2(input: &Input) -> u32 {
let mut state =
State { letter: 2, skipped: false, grid: [[0; 6]; 7], convert: [0; 32], result: 0 };
state.grid[0][0] = 1;
for i in 0..32 {
state.convert[i] = i as u8;
}
dfs(input, &mut state, 0, 0, 0);
input.extra + state.result
}
#[allow(clippy::needless_range_loop)]
fn graph_to_grid(
start: Point,
end: Point,
edges: &FastMap<Point, FastSet<Point>>,
weight: &FastMap<(Point, Point), u32>,
) -> Input {
let mut extra = 2;
extra += edges[&start].iter().map(|&e| weight[&(start, e)]).sum::<u32>();
extra += edges[&end].iter().map(|&e| weight[&(e, end)]).sum::<u32>();
let mut places = [[ORIGIN; 6]; 6];
let mut horizontal = [[0; 6]; 6];
let mut vertical = [[0; 6]; 6];
let mut point = *edges[&start].iter().next().unwrap();
let mut seen = FastSet::new();
let mut next_perimeter = |point: Point| {
seen.insert(point);
*edges[&point]
.iter()
.find(|&next| edges[next].len() == 3 && !seen.contains(next))
.unwrap_or(&ORIGIN)
};
for y in 0..5 {
places[y][0] = point;
point = next_perimeter(point);
}
for x in 1..6 {
places[5][x] = point;
point = next_perimeter(point);
}
for y in (1..5).rev() {
places[y][5] = point;
point = next_perimeter(point);
}
for x in (1..5).rev() {
places[0][x] = point;
point = next_perimeter(point);
}
for y in 1..5 {
for x in 1..5 {
let above = places[y - 1][x];
let left = places[y][x - 1];
let (&point, _) = edges
.iter()
.find(|(k, v)| !seen.contains(k) && v.contains(&above) && v.contains(&left))
.unwrap();
places[y][x] = point;
seen.insert(point);
}
}
places[0][5] = places[0][4];
places[5][0] = places[5][1];
for y in 0..6 {
for x in 0..5 {
let key = (places[y][x], places[y][x + 1]);
horizontal[y][x] = *weight.get(&key).unwrap_or(&0);
}
}
for y in 0..5 {
for x in 0..6 {
let key = (places[y][x], places[y + 1][x]);
vertical[y][x] = *weight.get(&key).unwrap_or(&0);
}
}
Input { extra, horizontal, vertical }
}
/// Modified depth first search that only allows paths that skip one node.
///
/// For a 6x6 grid there are 1262816 total possible rook walks
/// (given by [OEIS A007764](https://oeis.org/A007764)).
///
/// However since we want the longest path it only makes sense to consider the paths that visit the
/// most possible nodes. There are only 10180 of these paths making it much faster.
fn dfs(input: &Input, state: &mut State, mut row: usize, mut col: usize, mut steps: u32) {
// Wrap around at end of each row.
if col == 6 {
// We've reached the bottom right corner.
if row == 5 {
state.result = state.result.max(steps);
return;
}
row += 1;
col = 0;
}
if state.grid[row][col] == 0 {
// Skip only 1 node in each path.
if !(state.skipped || (row == 5 && col == 5)) {
state.skipped = true;
state.grid[row + 1][col] = 0;
dfs(input, state, row, col + 1, steps);
state.skipped = false;
}
// Create new paths (except on the final row).
if row < 5 {
let id = state.letter;
steps += input.vertical[row][col];
for end in (col + 1)..6 {
state.grid[row + 1][end - 1] = 0;
steps += input.horizontal[row][end - 1];
if state.grid[row][end] == 0 {
state.grid[row + 1][col] = id;
state.grid[row + 1][end] = id;
let extra = input.vertical[row][end];
state.letter += 1;
dfs(input, state, row, end + 1, steps + extra);
state.letter -= 1;
} else {
state.grid[row + 1][col] = state.convert[state.grid[row][end] as usize];
state.grid[row + 1][end] = 0;
dfs(input, state, row, end + 1, steps);
break;
}
}
}
} else {
let index = state.grid[row][col] as usize;
let id = state.convert[index];
// Straight down
if row < 5 || col == 5 {
state.grid[row + 1][col] = id;
let extra = input.vertical[row][col];
dfs(input, state, row, col + 1, steps + extra);
}
for end in (col + 1)..6 {
state.grid[row + 1][end - 1] = 0;
steps += input.horizontal[row][end - 1];
if state.grid[row][end] == 0 {
// Move down only if not final row (except final corner).
if row < 5 || end == 5 {
state.grid[row + 1][end] = id;
let extra = input.vertical[row][end];
dfs(input, state, row, end + 1, steps + extra);
}
} else {
// Join two path together as long as they are different.
// (prevent disjoint loops)
let other = state.convert[state.grid[row][end] as usize];
if id != other {
state.grid[row + 1][end] = 0;
state.convert[index] = other;
dfs(input, state, row, end + 1, steps);
state.convert[index] = id;
}
break;
}
}
}
}