Initial data commit

Task/Permutations-Derangements/Nim/permutations-derangements.nim

@@ -0,0 +1,27 @@
+import algorithm, sequtils, strformat, strutils, tables
+
+iterator derangements[T](a: openArray[T]): seq[T] =
+  var perm = @a
+  while true:
+    if not perm.nextPermutation():
+      break
+    block checkDerangement:
+      for i, val in a:
+        if perm[i] == val: break checkDerangement
+      yield perm
+
+proc `!`(n: Natural): Natural =
+  if n <= 1: return 1 - n
+  result = (n - 1) * (!(n - 1) + !(n - 2))
+
+echo "Derangements of 1 2 3 4:"
+for d in [1, 2, 3, 4].derangements():
+  echo d.join(" ")
+
+echo "\nNumber of derangements:"
+echo "n   counted   calculated"
+echo "-   -------   ----------"
+for n in 0..9:
+  echo &"{n}   {toSeq(derangements(toSeq(1..n))).len:>6}      {!n:>6}"
+
+echo "\n!20 = ", !20