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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

Task/Permutations-Derangements/jq/permutations-derangements-1.jq

@@ -0,0 +1,24 @@
+def derangements:
+
+  # In order to reference the original array conveniently, define _derangements(ary):
+  def _derangements(ary):
+    # We cannot put the i-th element in the i-th place:
+    def deranged:  # state: [i, available]
+      .[0] as $i | .[1] as $in
+      | if $i == (ary|length) then []
+        else
+        ($in[] | select (. != ary[$i])) as $j
+        |  [$j] + ([$i+1, ($in - [$j])] | deranged)
+        end
+      ;
+    [0,ary]|deranged;
+    . as $in | _derangements($in);
+
+def subfact:
+  if . == 0 then 1
+  elif . == 1 then 0
+  else (.-1) * (((.-1)|subfact) + ((.-2)|subfact))
+  end;
+
+# Avoid creating an array just to count the items in a stream:
+def count(g): reduce g as $i (0; . + 1);

Task/Permutations-Derangements/jq/permutations-derangements-2.jq

@@ -0,0 +1,7 @@
+ "Derangements:",
+ ([range(1;5)] | derangements),
+ "",
+ "Counted vs Computed Derangments:",
+ (range(1;10) as $i | "\($i): \(count( [range(0;$i)] | derangements)) vs \($i|subfact)"),
+ "",
+ "Computed approximation to !20 (15 significant digits): \(20|subfact)"

Task/Permutations-Derangements/jq/permutations-derangements-3.jq

@@ -0,0 +1,26 @@
+$ jq -n -c -r -f derangements.jq
+jq -n -c -r -f derangements.jq
+
+Derangements:
+[2,1,4,3]
+[2,3,4,1]
+[2,4,1,3]
+[3,1,4,2]
+[3,4,1,2]
+[3,4,2,1]
+[4,1,2,3]
+[4,3,1,2]
+[4,3,2,1]
+
+Counted vs Computed Derangments:
+1: 0 vs 0
+2: 1 vs 1
+3: 2 vs 2
+4: 9 vs 9
+5: 44 vs 44
+6: 265 vs 265
+7: 1854 vs 1854
+8: 14833 vs 14833
+9: 133496 vs 133496
+
+Computed approximation to !20 (15 significant digits): 895014631192902000