Data commit

Task/Lah-numbers/Scheme/lah-numbers.ss

@@ -0,0 +1,35 @@
+; Compute the Unsigned Lah number L(n, k).
+(define lah
+  (lambda (n k)
+    (/ (/ (* (fact n) (fact (1- n))) (* (fact k) (fact (1- k)))) (fact (- n k)))))
+
+; Procedure to compute factorial.
+(define fact
+  (lambda (n)
+    (if (<= n 0)
+      1
+      (* n (fact (1- n))))))
+
+; Generate a table of the Unsigned Lah numbers L(n, k) up to L(12, 12).
+(printf "The Unsigned Lah numbers L(n, k) up to L(12, 12):~%")
+(printf "n\\k~10d" 1)
+(do ((k 2 (1+ k)))
+    ((> k 12))
+  (printf " ~10d" k))
+(newline)
+(do ((n 1 (1+ n)))
+    ((> n 12))
+  (printf "~2d" n)
+  (do ((k 1 (1+ k)))
+      ((> k n))
+    (printf " ~10d" (lah n k)))
+  (newline))
+
+; Find the maximum value of L(n, k) where n = 100.
+(printf "~%The maximum value of L(n, k) where n = 100:~%")
+(let ((max 0))
+  (do ((k 1 (1+ k)))
+      ((> k 100))
+    (let ((val (lah 100 k)))
+      (when (> val max) (set! max val))))
+  (printf "~d~%" max))