poj1142 Smith Numbers

Poj1142 Smith Numbers

Smith Numbers
Time Limit: 1000MS Memory Limit: 10000K
Total Submissions: 13854 Accepted: 4716
Description

While skimming his phone directory in 1982, Albert Wilansky, a mathematician of Lehigh University,noticed that the telephone number of his brother-in-law H. Smith had the following peculiar property: The sum of the digits of that number was equal to the sum of the digits of the prime factors of that number. Got it? Smith’s telephone number was 493-7775. This number can be written as the product of its prime factors in the following way:
4937775= 3*5*5*65837

The sum of all digits of the telephone number is 4+9+3+7+7+7+5= 42,and the sum of the digits of its prime factors is equally 3+5+5+6+5+8+3+7=42. Wilansky was so amazed by his discovery that he named this kind of numbers after his brother-in-law: Smith numbers.
As this observation is also true for every prime number, Wilansky decided later that a (simple and unsophisticated) prime number is not worth being a Smith number, so he excluded them from the definition.
Wilansky published an article about Smith numbers in the Two Year College Mathematics Journal and was able to present a whole collection of different Smith numbers: For example, 9985 is a Smith number and so is 6036. However,Wilansky was not able to find a Smith number that was larger than the telephone number of his brother-in-law. It is your task to find Smith numbers that are larger than 4937775!
Input

The input file consists of a sequence of positive integers, one integer per line. Each integer will have at most 8 digits. The input is terminated by a line containing the number 0.
Output

For every number n > 0 in the input, you are to compute the smallest Smith number which is larger than n,and print it on a line by itself. You can assume that such a number exists.
Sample Input

4937774
0
Sample Output

4937775
Source

Mid-Central European Regional Contest 2000

题意 大于n满足你的各个位数之和等于质因子各位数之和。
题解 暴力过。

#include<cstdio>int fun(long long a){    int sum=0;    while(a>0)    {        sum+=a%10;        a/=10;     }     return sum; }bool prime(long long a){    int flag=1;    if (a==1) return false;    if(a==2) return true;    for(int i=2;i*i<a+1;i++)    if(a%i==0)    {        flag=0;        break;    }    if(flag)    return true;    else    return false;}int cnt(long long a){    if(prime(a))    return fun(a);    else    {        for(int i=2;i*i<a+1;i++)        {            if(a%i==0)            return cnt(i)+cnt(a/i);        }    }}int main(){    long long a;    while(scanf("%lld",&a)!=EOF&&a)    {        while(a++)        {            int sum=fun(a);            if(!prime(a)&&fun(a)==cnt(a))            break;        }    printf("%lld\n",a);    }    return 0; } 

这时间倒也不是很多，79ms