September 2017 Update

Task/Permutations-Derangements/Zkl/permutations-derangements-1.zkl

@@ -0,0 +1,19 @@
+fcn subFact(n){
+   if(n==0) return(1);
+   if(n==1) return(0);
+   (n-1)*(self.fcn(n-1) + self.fcn(n-2));
+}
+
+fcn derangements(n){
+   // All deranged permutations of the integers 0..n-1 inclusive
+   enum:=[0..n-1].pump(List);
+   Utils.Helpers.permuteW(enum).filter('wrap(perm){
+      perm.zipWith('==,enum).sum(0) == 0
+   });
+}
+fcn derangers(n){  // just count # of derangements
+   enum:=[0..n-1].pump(List);
+   Utils.Helpers.permuteW(enum).reduce('wrap(sum,perm){
+      sum + (perm.zipWith('==,enum).sum(0) == 0)
+   },0);
+}

Task/Permutations-Derangements/Zkl/permutations-derangements-2.zkl

@@ -0,0 +1,7 @@
+println("Derangements of 0,1,2,3:\n",derangements(4));
+println("\nTable of n vs counted vs calculated derangements:");
+foreach n in (10){
+   println("%2d %-6d %-6d".fmt(n, derangers(n), subFact(n)));
+}
+
+n:=20; println("\n!%d = %d".fmt(n, subFact(n)));

Task/Permutations-Derangements/Zkl/permutations-derangements-3.zkl

@@ -0,0 +1,10 @@
+fcn derangements(n){ //-->Walker
+   enum:=[0..n-1].pump(List);
+   Utils.Helpers.permuteW(enum).tweak('wrap(perm){
+      if(perm.zipWith('==,enum).sum(0)) Void.Skip
+      else perm
+   });
+}
+fcn derangers(n){  // just count # of derangements, w/o saving them
+   derangements(n).reduce('+.fpM("10-",1),0);  // ignore perm --> '+(1,sum)...
+}

Task/Permutations-Derangements/Zkl/permutations-derangements-4.zkl

@@ -0,0 +1,2 @@
+foreach d in (derangements(4)){ println(d) }
+//rest of test code remains the same