[PKU] P1316: Self Numbers
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
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 Input
Sample Output
|
1 |
1<br>3<br>5<br>7<br>9<br>20<br>31<br>42<br>53<br>64<br> |<br> | <-- a lot more numbers<br> |<br>9903<br>9914<br>9925<br>9927<br>9938<br>9949<br>9960<br>9971<br>9982<br>9993 |
Source
Solution:
[#M_ more.. | less.. ||
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import java.util.Arrays; public class P1316 { /** * @param args */ public static void main(String[] args) { // TODO Auto-generated method stub int[] array = new int[10100]; Arrays.fill(array, 0); for(int i=0; i<=9; i++){ for(int j=0; j<=9; j++){ for(int k=0; k<=9; k++){ for(int l=0; l<=9; l++){ array[i*1001+j*101+k*11+l*2]=1; } } } } for(int i=1; i<=10000; i++){ if(array[i]==0){ System.out.println(i); } } } } |
