Smith Numbers(分解质因数)
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:
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 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 }
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