Address code review feedback

- Replace #[allow] with #[expect] for clippy lints
- Fix floyd_partial to handle pure cycle case (mu=0) correctly
- Remove hardcoded upper bound checks for brent_partial in tests
- Update floyd_partial doctest to reflect correct behavior

Co-authored-by: samueltardieu <44656+samueltardieu@users.noreply.github.com>

Author: Copilot

src/directed/cycle_detection.rs

@@ -19,13 +19,13 @@
 ///
 /// let (lam, _elem, mu_tilde) = floyd_partial(1, |x| (x * 2) % 7);
 /// assert_eq!(lam, 3); // Cycle length
-/// assert!(mu_tilde >= 1); // Upper bound on mu
+/// assert!(mu_tilde == 0); // Upper bound on mu (start is in cycle, so mu = 0)
 /// ```
 ///
 /// # Warning
 ///
 /// If no cycle exist, this function loops forever.
-#[allow(clippy::needless_pass_by_value)]
+#[expect(clippy::needless_pass_by_value)]
 pub fn floyd_partial<T, FS>(start: T, successor: FS) -> (usize, T, usize)
 where
     T: Clone + PartialEq,
@@ -39,14 +39,19 @@ where
         tortoise_steps += 1;
     }
     // tortoise and hare met at position tortoise_steps
-    // By Floyd's algorithm analysis: mu <= tortoise_steps < mu + lam
     let mut lam = 1;
     hare = successor(tortoise.clone());
     while tortoise != hare {
         (hare, lam) = (successor(hare), lam + 1);
     }
-    // tortoise_steps is a valid upper bound satisfying mu <= mu_tilde < mu + lam
-    let mu_tilde = tortoise_steps;
+    // Handle edge case where they meet at the start position (pure cycle, mu = 0)
+    // In this case, tortoise_steps equals lam, and to satisfy mu_tilde < mu + lam,
+    // we must return 0.
+    let mu_tilde = if tortoise == start {
+        0
+    } else {
+        tortoise_steps
+    };
     (lam, tortoise, mu_tilde)
 }
 
@@ -106,7 +111,7 @@ where
 /// # Warning
 ///
 /// If no cycle exist, this function loops forever.
-#[allow(clippy::needless_pass_by_value)]
+#[expect(clippy::needless_pass_by_value)]
 pub fn brent_partial<T, FS>(start: T, successor: FS) -> (usize, T, usize)
 where
     T: Clone + PartialEq,

tests/cycle_detection.rs

@@ -32,9 +32,7 @@ fn brent_partial_works() {
     assert!([4, 6, 8].contains(&elem));
     // Check that mu_tilde is an upper bound: mu <= mu_tilde
     // We know mu = 2 from the full algorithm
-    // Brent's partial may have a looser bound than mu + lam
     assert!(2 <= mu_tilde);
-    assert!(mu_tilde <= 2 + 2 * 3);
 }
 
 #[test]
@@ -66,8 +64,6 @@ fn partial_functions_match_full_functions() {
     assert!(mu_floyd <= mu_tilde_floyd);
     assert!(mu_tilde_floyd < mu_floyd + lam_floyd);
     assert!(mu_brent <= mu_tilde_brent);
-    // Brent's partial may have a looser bound due to power-of-2 stepping
-    assert!(mu_tilde_brent <= mu_brent + 2 * lam_brent);
 }
 
 #[test]
@@ -101,7 +97,6 @@ fn test_longer_cycle() {
     assert!(mu_floyd <= mu_tilde_floyd);
     assert!(mu_tilde_floyd <= mu_floyd + lam_floyd);
     assert!(mu_brent <= mu_tilde_brent);
-    assert!(mu_tilde_brent <= mu_brent + 3 * lam_brent);
 }
 
 #[test]
@@ -138,6 +133,4 @@ fn test_short_cycle_large_mu() {
     assert!(mu_floyd <= mu_tilde_floyd);
     assert!(mu_tilde_floyd <= mu_floyd + lam_floyd);
     assert!(mu_brent <= mu_tilde_brent);
-    // Brent's partial may have a looser bound
-    assert!(mu_tilde_brent <= mu_brent + 4 * lam_brent);
 }