Slightly more efficient search

2022/src/day19.rs

@@ -1,7 +1,6 @@
+use std::array;
 use std::cmp::Ordering;
 use std::collections::BinaryHeap;
-use std::ops::Add;
-use std::ops::Sub;
 
 use anyhow::Result;
 use nom::bytes::complete::tag;
@@ -45,81 +44,146 @@ impl TryFrom<&'_ [u8]> for Mineral {
     }
 }
 
-#[derive(Debug, Clone, Copy, PartialEq, Eq, Default)]
-struct Resources([u8; 4]);
-
-impl Resources {
-    fn enough_for(self, other: Self) -> bool {
-        self.0.iter().zip(&other.0).all(|(a, b)| a >= b)
-    }
-}
-
-impl Sub for Resources {
-    type Output = Self;
-
-    fn sub(self, rhs: Self) -> Self::Output {
-        Self(std::array::from_fn(|i| self.0[i] - rhs.0[i]))
-    }
-}
-
-impl Add<[u8; 4]> for Resources {
-    type Output = Self;
-
-    fn add(self, rhs: [u8; 4]) -> Self::Output {
-        Self(std::array::from_fn(|i| self.0[i] + rhs[i]))
-    }
-}
-
 #[derive(Debug)]
 struct BluePrint {
     id: u32,
-    costs: [Resources; 4],
+    costs: [[u8; 3]; 4],
 }
 
 impl BluePrint {
-    pub fn max_geodes(&self, time: u32) -> u32 {
-        self.max_geodes_recursive(time, 0, [1, 0, 0, 0], Resources::default()) as u32
-    }
-
-    fn max_geodes_recursive(
-        &self,
-        time_left: u32,
-        // forbidden is a bitset for convenience
-        forbidden: u8,
-        machines: [u8; 4],
-        resources: Resources,
-    ) -> u8 {
-        if time_left <= 1 || forbidden.count_ones() == 4 {
-            return resources.0[3] + machines[3] * (time_left as u8);
-        }
-
-        let resources_after = resources + machines;
-
-        let mut best = 0;
-
-        let mut can_buy = 0;
-
-        for (i, &cost) in self.costs.iter().enumerate() {
-            if ((1 << i) & forbidden) == 0 && resources.enough_for(cost) {
-                can_buy |= 1 << i;
-                let mut new_machines = machines;
-                new_machines[i] += 1;
-
-                best = best.max(self.max_geodes_recursive(
-                    time_left - 1,
-                    0,
-                    new_machines,
-                    resources_after - cost,
-                ))
+    pub fn max_geodes(&self, time: u8) -> u8 {
+        /// How much would we produce if all we did was produce geode robots for the remaining time
+        fn ideal(remaining: u32) -> u32 {
+            if remaining <= 1 {
+                0
+            } else {
+                (remaining - 1) * remaining / 2
             }
         }
 
-        best.max(self.max_geodes_recursive(
-            time_left - 1,
-            forbidden | can_buy,
+        #[derive(Eq, PartialEq)]
+        struct State {
+            missed: u32,
+            got: u8,
+            time_left: u8,
+            resources: [u8; 3],
+            machines: [u8; 3],
+        }
+
+        impl Ord for State {
+            fn cmp(&self, other: &Self) -> Ordering {
+                Ordering::Equal
+                    .then(other.missed.cmp(&self.missed))
+                    .then(self.got.cmp(&other.got))
+                    .then(self.time_left.cmp(&other.time_left))
+                    .then(self.machines.cmp(&other.machines))
+            }
+        }
+
+        impl PartialOrd for State {
+            fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
+                Some(self.cmp(other))
+            }
+        }
+
+        let max_needed = self.max_needed();
+        let mut todo = BinaryHeap::new();
+        let mut best = 0;
+
+        todo.push(State {
+            missed: 0,
+            got: 0,
+            time_left: time,
+            resources: [0; 3],
+            machines: [1, 0, 0],
+        });
+
+        while let Some(State {
+            missed,
+            got,
+            time_left,
+            resources,
             machines,
-            resources_after,
-        ))
+        }) = todo.pop()
+        {
+            let ideal_from_now = ideal(time_left as u32);
+            if u32::from(best - got) > ideal_from_now {
+                continue;
+            }
+            if todo.len() > 1_000_000 {
+                panic!(
+                    "Safety: got a todo list of len {}, best: {best}",
+                    todo.len()
+                );
+            }
+            'element: for element in 0..4 {
+                let mut min_to_build = 0;
+                for ((&cost, &avail), &machine) in
+                    self.costs[element].iter().zip(&resources).zip(&machines)
+                {
+                    if cost > avail {
+                        if machine == 0 {
+                            continue 'element;
+                        } else {
+                            min_to_build = min_to_build.max((cost - avail + machine - 1) / machine);
+                        }
+                    }
+                }
+
+                // +1 because we need a turn to build
+                let built_after = min_to_build + 1;
+                if built_after >= time_left {
+                    continue;
+                }
+
+                let resources_after = array::from_fn(|i| {
+                    resources[i] + machines[i] * built_after - self.costs[element][i]
+                });
+                let time_after = time_left - built_after;
+
+                if element == Mineral::Geode as usize {
+                    let new_got = got + time_after;
+                    todo.push(State {
+                        missed,
+                        got: new_got,
+                        time_left: time_after,
+                        resources: resources_after,
+                        machines,
+                    });
+
+                    best = best.max(new_got);
+                } else {
+                    if machines[element] >= max_needed[element] {
+                        continue;
+                    }
+
+                    let mut new_machines = machines;
+                    new_machines[element] += 1;
+                    let new_missed = ideal_from_now - ideal(time_after as u32);
+                    todo.push(State {
+                        missed: new_missed,
+                        got,
+                        time_left: time_after,
+                        resources: resources_after,
+                        machines: new_machines,
+                    })
+                }
+            }
+        }
+
+        best
+    }
+
+    fn max_needed(&self) -> [u8; 3] {
+        let mut max_needed = [0; 3];
+
+        for cost in &self.costs {
+            for (max, &new) in max_needed.iter_mut().zip(cost) {
+                *max = (*max).max(new);
+            }
+        }
+
+        max_needed
     }
 }
 
@@ -137,7 +201,7 @@ fn parse_blueprint(input: &[u8]) -> IResult<&[u8], BluePrint> {
     let (mut input, id) =
         terminated(delimited(tag("Blueprint "), u32, tag(":")), multispace1)(input)?;
 
-    let mut costs: [Resources; 4] = Default::default();
+    let mut costs: [[u8; 3]; 4] = Default::default();
 
     let mut parse_robot = terminated(
         tuple((
@@ -152,10 +216,10 @@ fn parse_blueprint(input: &[u8]) -> IResult<&[u8], BluePrint> {
         let (remaining, (element, (amount1, req1), cost2)) = parse_robot(input)?;
         input = remaining;
 
-        costs[element as usize].0[req1 as usize] = amount1;
+        costs[element as usize][req1 as usize] = amount1;
 
         if let Some((amount2, req2)) = cost2 {
-            costs[element as usize].0[req2 as usize] = amount2;
+            costs[element as usize][req2 as usize] = amount2;
         }
     }
 
@@ -190,8 +254,25 @@ mod tests {
 
     const SAMPLE: &[u8] = include_bytes!("./samples/19.txt");
 
+    fn get_samples() -> Vec<BluePrint> {
+        parse_input(SAMPLE, many1(parse_blueprint)).unwrap()
+    }
+
     #[test]
     fn sample_part1() {
+        let samples = get_samples();
+
+        assert_eq!(samples[0].max_geodes(24), 9);
+        assert_eq!(samples[1].max_geodes(24), 12);
+
         assert_eq!(part1(SAMPLE).unwrap(), "33");
     }
+
+    #[test]
+    fn sample_part2() {
+        let samples = get_samples();
+
+        assert_eq!(samples[0].max_geodes(32), 56);
+        assert_eq!(samples[1].max_geodes(32), 62);
+    }
 }