2013
11-11

# Persistent Numbers

The multiplicative persistence of a number is defined by Neil Sloane (Neil J.A. Sloane in The Persistence of a Number published in Journal of Recreational Mathematics 6, 1973, pp. 97-98., 1973) as the number of steps to reach a one-digit number when repeatedly multiplying the digits. Example:

679 -> 378 -> 168 -> 48 -> 32 -> 6.

That is, the persistence of 679 is 6. The persistence of a single digit number is 0. At the time of this writing it is known that there are numbers with the persistence of 11. It is not known whether there are numbers with the persistence of 12 but it is known that if they exists then the smallest of them would have more than 3000 digits.

The problem that you are to solve here is: what is the smallest number such that the first step of computing its persistence results in the given number?

For each test case there is a single line of input containing a decimal number with up to 1000 digits. A line containing -1 follows the last test case.

For each test case you are to output one line containing one integer number satisfying the condition stated above or a statement saying that there is no such number in the format shown below.

0
1
4
7
18
49
51
768
-1


10
11
14
17
29
77
There is no such number.
2688


//* @author
import java.io.*;
import java.util.*;
import java.math.*;
public class Main
{
public static void main(String[] args)
{
BigInteger n,zero,ten;
int count,flag,a[],i,j;
a=new int[2000];
Scanner cin = new Scanner(System.in);
while(cin.hasNext())
{
n = cin.nextBigInteger();
zero=BigInteger.ZERO;
ten=BigInteger.TEN;
if(n.compareTo(BigInteger.valueOf(-1))==0)
break;
if(n.compareTo(ten)< 0)//n< 10
{
System.out.println("1"+n);
continue;
}
flag=0;count=0;
while(true)
{
flag=0;
for(i=9;i>=2;i--)
{
if(n.mod(BigInteger.valueOf(i)).compareTo(zero)==0)
{
flag=1;
a[++count]=i;
n=n.divide(BigInteger.valueOf(i));
break;
}
}
if(n.compareTo(ten)< 0)
{
flag=1;
a[++count]=n.intValue();
break;
}
if(flag==0)//如果存在对于每一个i都不整除的话
break;
}
if(flag==0)
System.out.println("There is no such number.");
else
{
for(i=count;i>=1;i--)
System.out.print(a[i]);
System.out.println();
}
}
}

}

1. 代码是给出了，但是解析的也太不清晰了吧！如 13 abejkcfghid jkebfghicda
第一步拆分为 三部分 (bejk, cfghi, d) * C(13,3)，为什么要这样拆分，原则是什么？

2. bottes vernies blanches

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