Smith Numbers
| Time Limit: 1000MS | Memory Limit: 10000K | |
| Total Submissions: 8209 | Accepted: 2867 |
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!
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
先开始一直在想算法，不过后来看了帖子才知道暴力也可以，而且还很快。。（擦，什么鸟数据。。）
Source Code
| Problem: 1142 | User: bingshen | |
| Memory: 204K | Time: 32MS | |
| Language: C++ | Result: Accepted |
- Source Code
#include<stdio.h> #include<algorithm> using namespace std; bool prime(int n) { int i; for(i=2;i*i<=n;i++) if(n%i==0) return false; return true; } int getsum(int x) { int sum=0; while(x) { sum=sum+x%10; x=x/10; } return sum; } bool judge(int x) { int sum1,sum2=0,i,num=0; int p[10000]; sum1=getsum(x); for(i=2;i*i<=x;i++) { if(x%i==0) { p[num++]=i; // printf("%d/n",i); x=x/i; while(x%i==0) { // printf("%d/n",i); p[num++]=i; x=x/i; } } if(x==1) break; } if(x>1) { p[num++]=x; // printf("%d/n",x); } for(i=0;i<num;i++) { sum2=sum2+getsum(p[i]); // printf("%d ",p[i]); } // printf("/n"); if(sum1==sum2) return true; else return false; } int main() { int n,i; while(scanf("%d",&n)!=EOF) { if(n==0) break; for(i=n+1;;i++) { if(prime(i)) continue; if(judge(i)) { printf("%d/n",i); break; } } } return 0; }