(ZJU-2005复试)-HDOJ-1180-Self Numbers

 

Self Numbers

 

Time Limit: 20000/10000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)

Total Submission(s): 1927    Accepted Submission(s): 828

 

 

Problem 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. 

 

 

Write a program to output all positive self-numbers less than or equal 1000000 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

|

|

|

 

 

#include <iostream>

#include <stdio.h>

using namespace std;

bool s[1000001]={0};

int d(int k)

{

    int n=k;

    while(n)

    {

        k+=n%10;

        n/=10;

    }

    return k;

 

}

int main()

{

    for(int i=1;i<=1000000;++i)

    {

        int j=d(i);

        if(j>1000000)continue;    

        s[j]=1;

    }

    for(int i=1;i<=1000000;++i)

        if(!s[i])cout<<i<<endl;   

    return 0;

}