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.
Write a program to output all positive self-numbers less than 10000
in increasing order, one per line.
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
Solution
#include <iostream>
using namespace std;
const long N = 10000; //最大自然数
char Arr[N + 9*4]=
{0}; //是否是被排除的数字？ +9*4是为了要再多放4位数
long DealNum(long n)
{
long sum = n;
while (n != 0)
{
sum += n%10;
n /= 10;
}
return sum;
}
int main()
{
int i;
for(i = 1; i < N; i++)
{
Arr[DealNum(i)] = 1;
}
for(i = 1; i < N; i++)
{
if (!Arr[i])
cout<<i<<endl;
}
return 0;
}