51 lines
1.3 KiB
C#
51 lines
1.3 KiB
C#
public class AverageLoopLength {
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private static int N = 100000;
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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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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.Next(n);
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}
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var seen = new HashSet<double>(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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Console.WriteLine(" N average analytical (error)");
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Console.WriteLine("=== ========= ============ =========");
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for (int i = 1; i <= 20; i++) {
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var average = AverageLoopLength.average(i);
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var analytical = AverageLoopLength.analytical(i);
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Console.WriteLine("{0,3} {1,10:N4} {2,13:N4} {3,8:N2}%", i, average, analytical, (analytical - average) / analytical * 100);
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}
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}
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}
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