diff --git a/1851/src/bin/e.rs b/1851/src/bin/e.rs
index 30bcf6f..de0b15c 100644
--- a/1851/src/bin/e.rs
+++ b/1851/src/bin/e.rs
@@ -25,34 +25,59 @@ impl Way {
     }
 }
 
+#[derive(Debug, Clone, Copy, PartialEq, Eq)]
+enum Mark {
+    None,
+    Temporary,
+    Permanent,
+}
+
+fn toposort(ways: &[Way], marks: &mut Vec<Mark>) -> Vec<usize> {
+    fn visit(ways: &[Way], marks: &mut Vec<Mark>, ordering: &mut Vec<usize>, u: usize) {
+        match marks[u] {
+            Mark::None => {
+                marks[u] = Mark::Temporary;
+
+                for v in &ways[u].required {
+                    visit(ways, marks, ordering, v - 1);
+                }
+
+                marks[u] = Mark::Permanent;
+                ordering.push(u);
+            }
+            Mark::Temporary => unreachable!("no loops should be present"),
+            Mark::Permanent => { /* no-op */ }
+        }
+    }
+
+    let mut ordering = vec![];
+
+    for i in 0..marks.len() {
+        visit(ways, marks, &mut ordering, i);
+    }
+
+    ordering
+}
+
 fn find_costs(costs: &mut Vec<u64>, unlimited: Vec<usize>, ways: Vec<Way>) {
-    let mut is_final = vec![false; costs.len()];
+    let mut marks = vec![Mark::None; costs.len()];
 
     // set cost of unlimited
     for i in unlimited {
         costs[i - 1] = 0;
-        is_final[i - 1] = true;
+        marks[i - 1] = Mark::Permanent;
     }
 
     // set cost of inconstructible
-    let mut q: HashSet<usize> = HashSet::new();
     for (i, way) in ways.iter().enumerate() {
         if way.estimated_cost(costs) == u64::MAX {
-            is_final[i] = true;
-        } else {
-            q.insert(i);
+            marks[i] = Mark::Permanent;
         }
     }
 
-    while let Some(i) = q
-        .iter()
-        .filter(|i| !is_final[**i])
-        .min_by_key(|i| ways[**i].estimated_cost(costs))
-        .map(|i| *i)
-    {
+    // do toposort to find the ideal order
+    for i in toposort(&ways, &mut marks) {
         costs[i] = min(costs[i], ways[i].estimated_cost(costs));
-        is_final[i] = true;
-        q.remove(&i);
     }
 }