2016 Update

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

@@ -0,0 +1,51 @@
+import java.util.ArrayList;
+
+public class AverageLoopLength {
+	private static final int N = 100000;
+	//analytical(n) = sum_(i=1)^n (n!/(n-i)!/n**i)
+	public static float analytical(int n){
+		float[] factorial = new float[n+1];
+		float[] powers = new float[n+1];
+		factorial[0] = powers[0] = 1;
+		for(int i=1;i<=n;i++){
+			factorial[i] = factorial[i-1] * i;
+			powers[i] = powers[i-1] * n;
+		}
+		float sum = 0;
+		//memoized factorial and powers
+		for(int i=1;i<=n;i++){
+			sum += factorial[n]/factorial[n-i]/powers[i];
+		}
+		return sum;
+	}
+	public static float average(int n){
+		float sum = 0;
+		for(int a=0;a<N;a++){
+			int[] random = new int[n];
+			for(int i=0;i<n;i++){
+				random[i] = (int)(Math.random()*n);
+			}
+			ArrayList<Integer> seen = new ArrayList<>(n);
+			int current = 0;
+			int length = 0;
+			while(true){
+				length++;
+				seen.add(current);
+				current = random[current];
+				if(seen.contains(current)){
+					break;
+				}
+			}
+			sum += length;
+		}
+		return sum/N;
+	}
+	public static void main(String args[]){
+		System.out.println(" N    average    analytical    (error)\n===  =========  ============  =========");
+		for(int i=1;i<=20;i++){
+			float avg = average(i);
+			float ana = analytical(i);
+			System.out.println(String.format("%3d  %9.4f  %12.4f  (%6.2f%%)",i,avg,ana,((ana-avg)/ana*100)));;
+		}
+	}
+}