G - Self Numbers(2.2.1)

Submit Status

Description

In 1949 the Indian mathematician D.R. Kaprekar discovered a class of numbers called self-numbers. For any positive integer n, define d(n) to be n plus the sum of the digits of n. (The d stands for digitadition, a term coined by Kaprekar.) For example, d(75) = 75 + 7 + 5 = 87. Given any positive integer n as a starting point, you can construct the infinite increasing sequence of integers n, d(n), d(d(n)), d(d(d(n))), .... For example, if you start with 33, the next number is 33 + 3 + 3 = 39, the next is 39 + 3 + 9 = 51, the next is 51 + 5 + 1 = 57, and so you generate the sequence

33, 39, 51, 57, 69, 84, 96, 111, 114, 120, 123, 129, 141, ...
The number n is called a generator of d(n). In the sequence above, 33 is a generator of 39, 39 is a generator of 51, 51 is a generator of 57, and so on. Some numbers have more than one generator: for example, 101 has two generators, 91 and 100. A number with no generators is a self-number. There are thirteen self-numbers less than 100: 1, 3, 5, 7, 9, 20, 31, 42, 53, 64, 75, 86, and 97.

Input

No input for this problem.

Output

Write a program to output all positive self-numbers less than 10000 in increasing order, one per line.

Sample Output

1
3
5
7
9
20
31
42
53
64
 |
 |       <-- a lot more numbers
 |
9903
9914
9925
9927
9938
9949
9960
9971
9982
9993
代码：
#include <iostream>
using namespace std;
#define N 10000
unsigned g[N];
unsigned sum(unsigned n)//计算各位的数字之和
{
    if(n<10)
        return n;
    else
        return ((n%10)+sum(n/10));
}
void in_sequence(unsigned n)
{
    while(n<N)
    {
        unsigned next=n+sum(n);//计算他的下一个满足题意的数
        if(next>=N||g[next]!=next)//如果达到上限或者为非字数则返回空
            return ;
        g[next]=n;
        n=next;
    }
}
int main()
{
    unsigned n;
     for(n=1;n<N;n++)
         g[n]=n;
    for(n=1;n<N;n++)
        in_sequence(n);
    for(n=1;n<N;n++)
    {
        if(g[n]==n)
        cout<<n<<endl;
    }

    return 0;
}