Change A* heuristic to be a proper estimate

This makes it:
- Actually find the path with the fewest number of moves, and
- Not be so prone to getting stuck exploring space that seems "close to
  a solution" but is actually a dead end.

src/main.rs

@@ -322,22 +322,8 @@ impl<const TOWER_HEIGHT: usize> Game<TOWER_HEIGHT> {
             hasher.finish()
         };
 
-        #[derive(PartialEq)]
-        struct Ordf32(f32);
-        impl Eq for Ordf32 {}
-        impl PartialOrd for Ordf32 {
-            fn partial_cmp(&self, other: &Self) -> Option<std::cmp::Ordering> {
-                Some(self.cmp(other))
-            }
-        }
-        impl Ord for Ordf32 {
-            fn cmp(&self, other: &Self) -> std::cmp::Ordering {
-                self.0.total_cmp(&other.0)
-            }
-        }
-
         let mut states = Vec::new();
-        let mut todo = BinaryHeap::<(Ordf32, usize, usize)>::new();
+        let mut todo = BinaryHeap::<((i64, i64), i64, usize)>::new();
         let mut had = HashSet::new();
         let mut ctr = 0;
 
@@ -346,7 +332,7 @@ impl<const TOWER_HEIGHT: usize> Game<TOWER_HEIGHT> {
             parent_index: 0,
             m: Move::new(0, 0),
         });
-        todo.push((Ordf32(0.0), 1000000000, 0));
+        todo.push(((0, 0), 1000000000, 0));
 
         while let Some((score, depth, state_index)) = todo.pop() {
             ctr += 1;
@@ -387,8 +373,36 @@ impl<const TOWER_HEIGHT: usize> Game<TOWER_HEIGHT> {
                 working_instance.towers = state.towers.clone();
                 working_instance.make_move(m).unwrap();
 
-                let num_solved = working_instance.num_solved();
-                let brs = working_instance.burried_ring_score();
+                let brs: i64 = {
+                    let this = &working_instance;
+                    let mut seen_bottom_rings = HashSet::new();
+                    this.towers
+                        .iter()
+                        .map(|i| {
+                            let this = &i;
+                            let mut ring_type = None;
+                            let mut burried_score = 0;
+
+                            for ring in this.rings.iter().rev().flatten() {
+                                if let Some(existing_ring_type) = ring_type
+                                    && existing_ring_type != *ring
+                                {
+                                    burried_score += 1;
+                                }
+                                ring_type = Some(*ring);
+                            }
+                            if let Some(Some(ring)) = this.rings.last() {
+                                if seen_bottom_rings.contains(ring) {
+                                    burried_score += 1;
+                                } else {
+                                    seen_bottom_rings.insert(ring);
+                                }
+                            }
+
+                            burried_score
+                        })
+                        .sum()
+                };
 
                 let new_state_hash = hash_state(&working_instance.towers);
                 if had.contains(&new_state_hash) {
@@ -402,9 +416,8 @@ impl<const TOWER_HEIGHT: usize> Game<TOWER_HEIGHT> {
                     m,
                 });
 
-                let score = (num_solved as f32 * 10.0) + (-(brs as f32) * 100.0);
-
-                todo.push((Ordf32(score), depth - 1, new_state_index));
+                let score = (depth) - (brs);
+                todo.push(((score, -depth), depth - 1, new_state_index));
             }
         }