September 2017 Update

Task/Average-loop-length/Zkl/average-loop-length.zkl

@@ -0,0 +1,33 @@
+const N=20;
+
+(" N    average    analytical    (error)").println();
+("===  =========  ============  =========").println();
+foreach n in ([1..N]){
+   a := avg(n);
+   b := ana(n);
+   "%3d  %9.4f  %12.4f  (%6.2f%%)".fmt(
+            n, a, b, ((a-b)/b*100)).println();
+}
+
+fcn f(n){ (0).random(n) }
+
+fcn avg(n){
+   tests := 0d10_000;
+   sum := 0;
+   do(tests){
+      v:=(0).pump(n,List,T(Void,False)).copy();
+      while(1){
+         z := f(n);
+         if(v[z]) break;
+	 v[z] = True;
+	 sum += 1;
+      }
+   }
+   return(sum.toFloat() / tests);
+}
+
+fcn fact(n) { (1).reduce(n,fcn(N,n){N*n},1.0) } //-->Float
+fcn ana(n){
+   n=n.toFloat();
+   (1).reduce(n,'wrap(sum,i){ sum+fact(n)/n.pow(i)/fact(n-i) },0.0);
+}