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Smith Numbers
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:
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 |
AC代码:
1 #include<iostream> 2 3 using namespace std; 4 5 int CalDigitsSum(int num) 6 { 7 int sum = 0; 8 while(num) 9 { 10 sum += num % 10; 11 num /= 10; 12 } 13 return sum; 14 } 15 16 int PrimaryCal(int num) 17 { 18 int total = 0; 19 int tempNum = num; 20 for(int i = 2; i * i <= num; i++) 21 { 22 int temp; 23 if(num % i == 0) 24 temp = CalDigitsSum(i); 25 while(num % i == 0) 26 { 27 total += temp; 28 num /= i; 29 } 30 } 31 if(tempNum == num) 32 return -1; 33 if(num != 1) 34 total += CalDigitsSum(num); 35 return total; 36 } 37 38 int main() 39 { 40 int n; 41 while(1) 42 { 43 cin >> n; 44 if(n == 0) 45 break; 46 for(int i = n + 1; ; i++) 47 { 48 if(CalDigitsSum(i) == PrimaryCal(i)) 49 { 50 cout << i << endl; 51 break; 52 } 53 } 54 } 55 return 0; 56 }
