Test checked_binomial

Only test for `n <= 500` but only a few values of the last row do not already have overflow on a 64 bits computer.
NOTE: Not faster with an array updated in-place.

src/combinations.rs

@@ -156,6 +156,25 @@ pub(crate) fn checked_binomial(mut n: usize, mut k: usize) -> Option<usize> {
     Some(c)
 }
 
+#[test]
+fn test_checked_binomial() {
+    // With the first row: [1, 0, 0, ...] and the first column full of 1s, we check
+    // row by row the recurrence relation of binomials (which is an equivalent definition).
+    // For n >= 1 and k >= 1 we have:
+    //   binomial(n, k) == binomial(n - 1, k - 1) + binomial(n - 1, k)
+    const LIMIT: usize = 500;
+    let mut row = vec![Some(0); LIMIT + 1];
+    row[0] = Some(1);
+    for n in 0..=LIMIT {
+        for k in 0..=LIMIT {
+            assert_eq!(row[k], checked_binomial(n, k));
+        }
+        row = std::iter::once(Some(1))
+            .chain((1..=LIMIT).map(|k| row[k - 1]?.checked_add(row[k]?)))
+            .collect();
+    }
+}
+
 /// For a given size `n`, return the count of remaining combinations or None if it would overflow.
 fn remaining_for(n: usize, first: bool, indices: &[usize]) -> Option<usize> {
     let k = indices.len();