September Morn Update

Task/Average-loop-length/00META.yaml

@@ -0,0 +1 @@
+--- {}

Task/Average-loop-length/Perl/average-loop-length.pl

@@ -0,0 +1,21 @@
+use List::Util qw(sum reduce);
+
+sub find_loop {
+    my($n) = @_;
+    my($r,@seen);
+    while () { $seen[$r] = $seen[($r = int(1+rand $n))] ? return sum @seen : 1 }
+}
+
+print " N    empiric      theoric      (error)\n";
+print "===  =========  ============  =========\n";
+
+my $MAX    = 20;
+my $TRIALS = 1000;
+
+for my $n (1 .. $MAX) {
+    my $empiric = ( sum map { find_loop($n) } 1..$TRIALS ) / $TRIALS;
+    my $theoric = sum map { (reduce { $a*$b } $_**2, ($n-$_+1)..$n ) / $n ** ($_+1) } 1..$n;
+
+    printf "%3d  %9.4f  %12.4f   (%5.2f%%)\n",
+            $n,  $empiric, $theoric, 100 * ($empiric - $theoric) / $theoric;
+}

Task/Average-loop-length/R/average-loop-length.r

@@ -0,0 +1,34 @@
+expected <- function(size) {
+  result <- 0
+  for (i in 1:size) {
+    result <- result + factorial(size) / size^i / factorial(size -i)
+  }
+  result
+}
+
+knuth <- function(size) {
+  v <- sample(1:size, size, replace = TRUE)
+
+  visit <- vector('logical',size)
+  place <- 1
+  visit[[1]] <- TRUE
+  steps <- 0
+
+  repeat {
+    place <- v[[place]]
+    steps <- steps + 1
+    if (visit[[place]]) break
+    visit[[place]] <- TRUE
+  }
+  steps
+}
+
+cat(" N    average    analytical     (error)\n")
+cat("===  =========  ============  ==========\n")
+for (num in 1:20) {
+  average <- mean(replicate(1e6, knuth(num)))
+  analytical <- expected(num)
+  error <- abs(average/analytical-1)*100
+
+  cat(sprintf("%3d%11.4f%14.4f  ( %4.4f%%)\n", num, round(average,4), round(analytical,4), round(error,2)))
+}

Task/Average-loop-length/Simula/average-loop-length.simula

@@ -0,0 +1,65 @@
+BEGIN
+
+   REAL PROCEDURE FACTORIAL(N); INTEGER N;
+   BEGIN
+      REAL RESULT;
+      INTEGER I;
+      RESULT := 1.0;
+      FOR I := 2 STEP 1 UNTIL N DO
+         RESULT := RESULT * I;
+      FACTORIAL := RESULT;
+   END FACTORIAL;
+
+   REAL PROCEDURE ANALYTICAL (N); INTEGER N;
+   BEGIN
+      REAL SUM, RN;
+      INTEGER I;
+      RN := N;
+      FOR I := 1 STEP 1 UNTIL N DO
+      BEGIN
+         SUM := SUM + FACTORIAL(N) / FACTORIAL(N - I) / RN ** I;
+      END;
+      ANALYTICAL := SUM;
+   END ANALYTICAL;
+
+   REAL PROCEDURE EXPERIMENTAL(N); INTEGER N;
+   BEGIN
+      INTEGER NUM;
+      INTEGER COUNT;
+      INTEGER RUN;
+      FOR RUN := 1 STEP 1 UNTIL TESTS DO
+      BEGIN
+         BOOLEAN ARRAY BITS(1:N);
+         INTEGER I;
+         FOR I := 1 STEP 1 UNTIL N DO
+         BEGIN
+            NUM := RANDINT(1,N,SEED);
+            IF BITS(NUM) THEN GOTO L;
+            BITS(NUM) := TRUE;
+            COUNT := COUNT + 1;
+         END FOR I;
+      L:
+      END FOR RUN;
+      EXPERIMENTAL := COUNT / TESTS;
+   END EXPERIMENTAL;
+
+   INTEGER SEED, TESTS;
+   SEED := ININT;
+   TESTS := 1000000;
+   BEGIN
+      REAL A, E, ERR;
+      INTEGER I;
+      OUTTEXT(" N  AVG    CALC   %DIFF"); OUTIMAGE;
+      FOR I := 1 STEP 1 UNTIL 20 DO
+      BEGIN
+         A := ANALYTICAL(I);
+         E := EXPERIMENTAL(I);
+         ERR := (ABS(E-A)/A)*100.0;
+         OUTINT(I, 2);
+         OUTFIX(E, 4, 7);
+         OUTFIX(A, 4, 10);
+         OUTFIX(ERR, 4, 10);
+         OUTIMAGE;
+      END FOR I;
+   END;
+END

Task/Average-loop-length/VBA/average-loop-length.vba

@@ -0,0 +1,37 @@
+Const MAX = 20
+Const ITER = 1000000
+
+Function expected(n As Long) As Double
+    Dim sum As Double
+    For i = 1 To n
+        sum = sum + WorksheetFunction.Fact(n) / n ^ i / WorksheetFunction.Fact(n - i)
+    Next i
+    expected = sum
+End Function
+
+Function test(n As Long) As Double
+    Dim count As Long
+    Dim x As Long, bits As Long
+    For i = 1 To ITER
+        x = 1
+        bits = 0
+        Do While Not bits And x
+            count = count + 1
+            bits = bits Or x
+            x = 2 ^ (Int(n * Rnd()))
+        Loop
+    Next i
+    test = count / ITER
+End Function
+
+Public Sub main()
+    Dim n As Long
+    Debug.Print " n     avg.     exp.  (error%)"
+    Debug.Print "==   ======   ======  ========"
+    For n = 1 To MAX
+        av = test(n)
+        ex = expected(n)
+        Debug.Print Format(n, "@@"); "  "; Format(av, "0.0000"); "   ";
+        Debug.Print Format(ex, "0.0000"); "  ("; Format(Abs(1 - av / ex), "0.000%"); ")"
+    Next n
+End Sub