Data update

Task/Evaluate-binomial-coefficients/DuckDB/evaluate-binomial-coefficients.duckdb

@@ -0,0 +1,23 @@
+# Compute nCr naively using UHUGEINT
+# The caller should ensure 2r < n
+create or replace function nCr_(n, r) as
+    (with recursive cte as
+      (SELECT 1::UHUGEINT as c, n as numerator, 1::UHUGEINT as m
+       UNION ALL
+       SELECT (c * numerator / m) as c,
+       (numerator - 1) as numerator,
+       (m + 1) as m
+       FROM cte
+       WHERE m <= r)
+    SELECT last(c order by m)
+    FROM cte
+);
+
+create or replace function nCr(n,r) as (
+  if( n<r,      error('nCr expects r <= n'),
+  if( 2*r <= n, nCr_(n,r),
+                nCr_(n, n-r) ) )
+);
+
+## Example:
+select nCr(140,50);