day 11: add A*

this is slower than BFS. See Claude for possible reasoning

day11/src/main.rs

@@ -1,10 +1,13 @@
-use std::collections::{BTreeSet, HashSet, VecDeque};
+use std::{
+    cmp::Reverse,
+    collections::{BTreeSet, BinaryHeap, HashSet, VecDeque},
+};
 
 use itertools::Itertools;
 
 fn main() {
     part_1(); // 33
-    part_2();
+    part_2(); // 57
 }
 
 fn part_2() {
@@ -19,7 +22,7 @@ fn part_1() {
     println!("{result}");
 }
 
-#[derive(Clone, Debug, PartialEq, Eq, Hash)]
+#[derive(Clone, Debug, PartialEq, Eq, Hash, PartialOrd, Ord)]
 struct State {
     floors: [BTreeSet<Item>; 4],
     elevator: usize,
@@ -150,6 +153,17 @@ impl State {
 
         result
     }
+
+    fn heuristic(&self) -> usize {
+        self.floors
+            .iter()
+            .take(3)
+            .rev()
+            .zip(1..=3)
+            .map(|(set, distance)| set.len() * distance)
+            .sum::<usize>()
+            / 2
+    }
 }
 
 fn floor_is_valid(floor: &BTreeSet<Item>) -> bool {
@@ -190,3 +204,37 @@ fn bfs(start: State) -> usize {
     }
     panic!("goal state unreachable");
 }
+
+#[allow(dead_code)]
+fn a_star(start: State) -> usize {
+    let mut heap: BinaryHeap<_> = BinaryHeap::new();
+
+    let mut visited = HashSet::new();
+
+    heap.push(Reverse((start.heuristic(), 0_usize, start)));
+
+    while let Some(Reverse((_, distance, current_state))) = heap.pop() {
+        if visited.contains(&current_state) {
+            continue;
+        } else {
+            visited.insert(current_state.clone());
+        }
+
+        if current_state.is_goal_state() {
+            return distance;
+        }
+
+        for state in current_state.neighbors() {
+            if visited.contains(&state) {
+                continue;
+            }
+
+            let heuristic = state.heuristic();
+            let new_distance = distance + 1;
+            // f_score = g_score + h_score
+            //         = distance + heuristic;
+            heap.push(Reverse((distance + heuristic, new_distance, state)));
+        }
+    }
+    panic!("goal state unreachable");
+}