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Task/Permutations-Derangements/EchoLisp/permutations-derangements-1.echolisp

@@ -0,0 +1,19 @@
+(lib 'list) ;; in-permutations
+(lib 'bigint)
+
+;; generates derangements by filtering out permutations
+(define (derangement? nums) ;; predicate
+    (for/and ((n nums) (i (length nums))) (!= n i)))
+
+(define (derangements n)
+    (for/list ((p (in-permutations n))) #:when (derangement? p) p))
+
+(define (count-derangements n)
+    (for/sum ((p (in-permutations n))) #:when (derangement? p) 1))
+
+;;
+;;  !n = (n - 1) (!(n-1) + !(n-2))
+
+(define (!n n)
+	(* (1- n) (+ (!n (1- n)) (!n (- n 2)))))
+(remember '!n #(1 0))

Task/Permutations-Derangements/EchoLisp/permutations-derangements-2.echolisp

@@ -0,0 +1,20 @@
+(derangements 4)
+    → ((3 0 1 2) (2 0 3 1) (2 3 0 1) (3 2 0 1) (3 2 1 0) (2 3 1 0) (1 2 3 0) (1 3 0 2) (1 0 3 2))
+
+;; generated versus computed
+
+(for ((i 10)) (writeln i '| (count-derangements i) (!n i)))
+
+0     |     1     1
+1     |     0     0
+2     |     1     1
+3     |     2     2
+4     |     9     9
+5     |     44     44
+6     |     265     265
+7     |     1854     1854
+8     |     14833     14833
+9     |     133496     133496
+
+(!n 20)
+    → 895014631192902121