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