1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
| use itertools::Itertools;
use std::cmp::Reverse;
use std::collections::HashMap;
type FlowRates = Vec<u8>;
type FlowRateIndices = Vec<usize>;
type ShortestPathLengths = Vec<Vec<u8>>;
type Input = (FlowRates, ShortestPathLengths, FlowRateIndices, usize);
fn branch_and_bound(
flow_rates: &FlowRates,
sorted_flow_rate_indices: &[usize],
shortest_path_lengths: &ShortestPathLengths,
state: State,
best_for_visited: &mut [u16],
best: &mut u16,
filter_bound: impl Fn(u16, u16) -> bool + Copy,
) {
if let Some(cur_best) = best_for_visited.get_mut(state.visited as usize) {
*cur_best = state.pressure_released.max(*cur_best);
}
*best = state.pressure_released.max(*best);
state
.branch(flow_rates, shortest_path_lengths)
.into_iter()
.map(|state| (state.bound(flow_rates, sorted_flow_rate_indices), state))
.filter(|&(bound, _)| filter_bound(bound, *best))
.sorted_unstable_by_key(|(bound, _)| Reverse(*bound))
.for_each(|(_, branch)| {
branch_and_bound(
flow_rates,
sorted_flow_rate_indices,
shortest_path_lengths,
branch,
best_for_visited,
best,
filter_bound,
)
});
}
#[derive(Default, Debug, Clone, Copy)]
struct State {
visited: u16,
avoid: u16,
pressure_released: u16,
minutes_remaining: u8,
position: u8,
}
impl State {
fn new(position: u8, minutes_remaining: u8) -> Self {
Self {
visited: 0,
avoid: 1 << position,
pressure_released: 0,
minutes_remaining,
position,
}
}
fn can_visit(self, i: usize) -> bool {
(self.visited | self.avoid) & (1 << i) == 0
}
fn bound(self, flow_rates: &FlowRates, sorted_flow_rate_indices: &[usize]) -> u16 {
self.pressure_released
+ (0..=self.minutes_remaining)
.rev()
.step_by(2)
.skip(1)
.zip(
sorted_flow_rate_indices
.iter()
.filter(|&&i| self.can_visit(i))
.map(|&i| flow_rates[i]),
)
.map(|(minutes, flow)| minutes as u16 * flow as u16)
.sum::<u16>()
}
fn branch<'a>(
self,
flow_rates: &'a FlowRates,
shortest_path_lengths: &'a ShortestPathLengths,
) -> impl IntoIterator<Item = Self> + 'a {
shortest_path_lengths[self.position as usize]
.iter()
.enumerate()
.filter(move |&(destination, _distance)| self.can_visit(destination))
.filter_map(move |(destination, distance)| {
let minutes_remaining = self.minutes_remaining.checked_sub(*distance + 1)?;
Some(State {
visited: self.visited | (1 << destination),
avoid: self.avoid,
pressure_released: self.pressure_released
+ minutes_remaining as u16 * flow_rates[destination] as u16,
minutes_remaining,
position: destination as u8,
})
})
}
}
fn floyd_warshall(rows: &[(&str, u8, Vec<&str>)]) -> Vec<Vec<u8>> {
let valve_name_to_idx: HashMap<&str, _> = rows
.iter()
.enumerate()
.map(|(i, &(name, _, _))| (name, i))
.collect();
let mut dist = vec![vec![u8::MAX; rows.len()]; rows.len()];
for (i, (_, _, tunnels)) in rows.iter().enumerate() {
for tunnel in tunnels {
let j = valve_name_to_idx[tunnel];
dist[i][j] = 1;
}
}
(0..dist.len()).for_each(|i| {
dist[i][i] = 0;
});
for k in 0..dist.len() {
for i in 0..dist.len() {
for j in 0..dist.len() {
let (result, overflow) = dist[i][k].overflowing_add(dist[k][j]);
if !overflow && dist[i][j] > result {
dist[i][j] = result;
}
}
}
}
dist
}
fn parse_row(row: &str) -> (&str, u8, Vec<&str>) {
let (a, b) = row.split_once(" has flow rate=").unwrap();
let (b, c) = b.split_once(" to ").expect(b);
let b = match b.strip_suffix("; tunnels lead") {
Some(b) => b,
None => b.strip_suffix("; tunnel leads").expect(b),
};
let c = match c.strip_prefix("valves ") {
Some(c) => c,
None => c.strip_prefix("valve ").unwrap(),
};
(
a.strip_prefix("Valve ").unwrap(),
b.parse().unwrap(),
c.split(", ").collect(),
)
}
fn parse(input: &str) -> Input {
let rows = input.lines().map(parse_row).collect_vec();
let shortest_path_lengths_uncompressed = floyd_warshall(&rows);
let interesting_valve_indices = rows
.iter()
.enumerate()
.filter(|&(_, &(name, flow, _))| name == "AA" || flow > 0)
.map(|(i, _)| i)
.collect_vec();
let flow_rates = interesting_valve_indices
.iter()
.map(|&i| rows[i].1)
.collect_vec();
let shortest_path_lengths = interesting_valve_indices
.iter()
.map(|&i| {
interesting_valve_indices
.iter()
.map(|&j| shortest_path_lengths_uncompressed[i][j])
.collect()
})
.collect();
let starting_node = interesting_valve_indices
.iter()
.position(|&i| rows[i].0 == "AA")
.expect("a valve called AA");
let sorted_flow_rate_indices = flow_rates
.iter()
.enumerate()
.sorted_unstable_by_key(|&(_, &flow)| Reverse(flow))
.map(|(i, _)| i)
.collect_vec();
(
flow_rates,
shortest_path_lengths,
sorted_flow_rate_indices,
starting_node,
)
}
pub fn part_one(
(flow_rates, shortest_paths, sorted_flow_rate_indices, starting_idx): Input,
) -> Option<u16> {
let mut best = 0;
branch_and_bound(
&flow_rates,
&sorted_flow_rate_indices,
&shortest_paths,
State::new(starting_idx as u8, 30),
&mut [],
&mut best,
|bound, best| bound > best,
);
Some(best)
}
pub fn part_two(
(flow_rates, shortest_paths, sorted_flow_rate_indices, starting_idx): Input,
) -> Option<u16> {
let mut best_per_visited = vec![0; u16::MAX as usize];
branch_and_bound(
&flow_rates,
&sorted_flow_rate_indices,
&shortest_paths,
State::new(starting_idx as u8, 26),
&mut best_per_visited,
&mut 0,
|bound, best| bound > best,
);
let mut best = 0;
let best_per_visited_filtered_sorted = best_per_visited
.into_iter()
.enumerate()
.filter(|&(_, best)| best > 0)
.map(|(i, best)| (i as u16, best))
.sorted_unstable_by_key(|&(_, best)| Reverse(best))
.collect_vec();
for (i, &(my_visited, my_best)) in best_per_visited_filtered_sorted.iter().enumerate() {
for &(elephant_visited, elephant_best) in &best_per_visited_filtered_sorted[i + 1..] {
let score = my_best + elephant_best;
if score <= best {
break;
}
if my_visited & elephant_visited == 0 {
best = score;
break;
}
}
}
Some(best)
}
|