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September 2017 Update

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Ingy döt Net 2017-09-23 10:01:46 +02:00
parent bba7bfd280
commit ba8067c3b7
14570 changed files with 153136 additions and 63871 deletions
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101
Task/Average-loop-length/Java/average-loop-length.java
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@ -1,51 +1,56 @@
import java.util.ArrayList;
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)
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)));;
}
}
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)));
}
}
}