MCUR98 - Self Numbers

Background

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 ben 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.

Problem

Write a program to output all positive self-numbers less than 1000000 in increasing order, one per line.

Input

There is no input.

Output

All positive self-numbers less than 1000000 in increasing order, one per line.


Added by:abdelkarim
Date:2013-09-15
Time limit:0.400s
Source limit:900B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:Mid-Central USA 1998

hide comments
2015-07-25 21:55:00 :.Mohib.:
Very nice que...!!
2015-01-14 22:21:55 .::Austin::.
Why the size limit???
2015-01-02 13:50:47 Anubhav Balodhi
A classical mathematical question, ac ^_^
2015-01-01 18:32:31 vsri293
cout gives tle..
use printf
2014-12-30 20:56:17 Sayak Haldar
dont use long long, takes additional time to print thus resulting tle
2014-07-17 13:29:41 surayans tiwari(http://bit.ly/1EPzcpv)
cakewalk.. make a seive and its done
2014-01-04 19:57:53 Ankit Kumar
'less' than 1000000 not less than equal to 1000000
Got 1 WA because of it ..
Total 97785 self nos.<1000000 will be there

Last edit: 2013-12-25 06:41:18
2013-12-21 14:58:45 (Tjandra Satria Gunawan)(曾毅昆)
@numerix: awesome speed, all my best I/O in C/C++ can't beat your time record.. congratulations ;-)
2013-12-21 11:50:20 Jumpy
sieves would be better....
or any other algo, suggest me
2013-10-28 16:51:12 Vaibhav Gupta
strange...printf gives tle
and cout accepted !!!
© Spoj.com. All Rights Reserved. Spoj uses Sphere Engine™ © by Sphere Research Labs.