/*
|\ _,,,---,,_
/,`.-'`' -. ;-;;,_
|,4- ) )-,_..;\ ( `'-'
'---''(_/--' `-'\_)
Meow do you do γ½(β´∀`β)οΎ
*/
import java.math.BigDecimal;
import java.math.BigInteger;
import java.util.Scanner;
public class Main {
static BigDecimal take(int n, int r) {
BigInteger a = BigInteger.ONE;
for (int i = 0; i < r; i++) {
a = a.multiply(BigInteger.valueOf(n - i));
a = a.divide(BigInteger.valueOf(1+i));
}
BigDecimal b = new BigDecimal(a);
b = b.divide(BigDecimal.valueOf(Math.pow(3, n-1)), 50, BigDecimal.ROUND_HALF_DOWN);
return b;
}
public static void main(String[] args) {
Scanner scanner = new Scanner(System.in);
int n = scanner.nextInt();
BigDecimal[] f = new BigDecimal[101];
f[1] = BigDecimal.ZERO;
for (int i = 2; i <= n; i++) {
BigDecimal p = BigDecimal.ZERO;
BigDecimal s = BigDecimal.ZERO;
for (int j = 1; j < i; j++) {
BigDecimal t = take(i, j);
p = p.add(t);
s = s.add(t.multiply(f[j].add(BigDecimal.ONE)));
}
s = s.subtract(p.subtract(BigDecimal.ONE));
f[i] = s.divide(p, 10, BigDecimal.ROUND_HALF_DOWN);
}
System.out.println(f[n].toString());
}
}
Solution for NTU 2015.3.14
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