Initial data commit

Task/Average-loop-length/Java/average-loop-length.java

@@ -0,0 +1,56 @@
+import java.util.HashSet;
+import java.util.Random;
+import java.util.Set;
+
+public class AverageLoopLength {
+
+    private static final int N = 100000;
+
+    //analytical(n) = sum_(i=1)^n (n!/(n-i)!/n**i)
+    private static double analytical(int n) {
+        double[] factorial = new double[n + 1];
+        double[] powers = new double[n + 1];
+        powers[0] = 1.0;
+        factorial[0] = 1.0;
+        for (int i = 1; i <= n; i++) {
+            factorial[i] = factorial[i - 1] * i;
+            powers[i] = powers[i - 1] * n;
+        }
+        double sum = 0;
+        //memoized factorial and powers
+        for (int i = 1; i <= n; i++) {
+            sum += factorial[n] / factorial[n - i] / powers[i];
+        }
+        return sum;
+    }
+
+    private static double average(int n) {
+        Random rnd = new Random();
+        double sum = 0.0;
+        for (int a = 0; a < N; a++) {
+            int[] random = new int[n];
+            for (int i = 0; i < n; i++) {
+                random[i] = rnd.nextInt(n);
+            }
+            Set<Integer> seen = new HashSet<>(n);
+            int current = 0;
+            int length = 0;
+            while (seen.add(current)) {
+                length++;
+                current = random[current];
+            }
+            sum += length;
+        }
+        return sum / N;
+    }
+
+    public static void main(String[] args) {
+        System.out.println(" N    average    analytical    (error)");
+        System.out.println("===  =========  ============  =========");
+        for (int i = 1; i <= 20; i++) {
+            double avg = average(i);
+            double ana = analytical(i);
+            System.out.println(String.format("%3d  %9.4f  %12.4f  (%6.2f%%)", i, avg, ana, ((ana - avg) / ana * 100)));
+        }
+    }
+}