September 2017 Update

Task/Permutations-Derangements/Phix/permutations-derangements.phix

@@ -0,0 +1,37 @@
+function deranged(sequence s1, sequence s2)
+    for i=1 to length(s1) do
+        if s1[i]==s2[i] then return 0 end if
+    end for
+    return 1
+end function
+
+function derangements(integer n)
+    sequence ts = tagset(n)
+    sequence res = {}
+    for i=1 to factorial(n) do
+        sequence s = permute(i,ts)
+        if deranged(s,ts) then
+            res = append(res,s)
+        end if
+    end for
+    return res
+end function
+
+function subfactorial(integer n)
+    if n<=0 then return 1 end if
+    if n=1 then return 0 end if
+    return (n-1)*(subfactorial(n-1)+subfactorial(n-2))
+end function
+
+?derangements(4)
+for n=0 to 9 do
+    printf(1,"%d: counted:%d, calculated:%d\n",{n,length(derangements(n)),subfactorial(n)})
+end for
+printf(1,"!20=%d (incorrect!)\n",{subfactorial(20)})
+include builtins\bigatom.e
+function ba_subfactorial(integer n)
+    if n<=0 then return 1 end if
+    if n=1 then return 0 end if
+    return ba_multiply(n-1,ba_add(ba_subfactorial(n-1),ba_subfactorial(n-2)))
+end function
+ba_printf(1,"!20=%B (bigatom)\n",ba_subfactorial(20))