September 2017 Update

Task/Permutations-Derangements/Julia/permutations-derangements.julia

@@ -0,0 +1,34 @@
+# v0.6
+
+using Combinatorics
+
+derangements(n::Int) = (perm for perm in permutations(1:n)
+                        if all(indx != p for (indx, p) in enumerate(perm)))
+
+function subfact(n::Integer)::Integer
+    if n in (0, 2)
+        return 1
+    elseif n == 1
+        return 0
+    elseif 1 ≤ n ≤ 18
+        return round(Int, factorial(n) / e)
+    elseif n > 0
+        return (n - 1) * ( subfact(n - 1) + subfact(n - 2) )
+    else
+        error()
+    end
+end
+
+println("Derangements of [1, 2, 3, 4]")
+for perm in derangements(4)
+    println(perm)
+end
+
+@printf("\n%5s%13s%13s\n", "n", "derangements", "!n")
+for n in 1:10
+    ders = derangements(n)
+    subf = subfact(n)
+    @printf("%5i%13i%13i\n", n, length(collect(ders)), subf)
+end
+
+println("\n!20 = ", subfact(20))