UVa 1583 Digit Generator(数学)

题意 假设a加上a全部数位上的数等于b时 a称为b的 generator  求给定数的最小 generator 

给的数n是小于100,000的  考虑到全部数位和最大的数99,999的数位和也才45  因此我们仅仅须要从n-45到n枚举即可了

      #include<cstdio>  
#include<cstring>  
using namespace std;  
int t, n, a, b, ans, l;  
int main()  
{  
    scanf ("%d", &t);  
    while (t--)  
    {  
        scanf ("%d", &n);  
        ans = 0;  
        for (int i = n-50; i < n; ++i)  
        {  
            a = b = i;  
            while (b)  
            {  
                a += b % 10;  
                b /= 10;  
            }  
            if (a + b == n)  
            {  
                ans = i;  
                break;  
            }  
        }  
        printf ("%d\n", ans);  
    }  
    return 0;  
} 
    

For a positive integer  N  , the digit-sum of  N  is defined as the sum of  N  itself and its digits. When  M  is the digitsum of  N  , we call  N  a  generator  of  M  .

For example, the digit-sum of  245  is  256 (= 245 + 2 + 4 + 5) . Therefore,  245  is a generator of  256 .

Not surprisingly, some numbers do not have any generators and some numbers have more than one generator. For example, the generators of  216  are  198  and  207 .

You are to write a program to find the smallest generator of the given integer.

Input  

Your program is to read from standard input. The input consists of  T  test cases. The number of test cases  T  is given in the first line of the input. Each test case takes one line containing an integer  N  ,  1 N 100, 000  .

Output  

Your program is to write to standard output. Print exactly one line for each test case. The line is to contain a generator of  N  for each test case. If  N  has multiple generators, print the smallest. If  N  does not have any generators, print  0 .

The following shows sample input and output for three test cases.

Sample Input  

      3 
216 
121 
2005

    

Sample Output  

      198 
0 
1979