poj_1316_Self_Numbers.cpp

Problem Links:

poj1316,

Problem:

Self Numbers

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 14666		Accepted: 8252

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 Input

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

Source

Mid-Central USA 1998

Solution:

Basically, it’s the most straight forward simulation problem. Just set all the non-self numbers as true, and then display the false ones.

Source Code:

//Tue Apr 13 15:17:05 CDT 2010
#include <vector>
#include <list>
#include <map>
#include <set>
#include <deque>
#include <queue>
#include <stack>
#include <bitset>
#include <algorithm>
#include <functional>
#include <numeric>
#include <utility>
#include <sstream>
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <cctype>
#include <string>
#include <cstring>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <ctime>

using namespace std;
map<int, bool> mp;
int main(int argc, const char* argv[])
{
    freopen("input.in", "r", stdin);
    freopen("output.out", "w", stdout);
    for (int i = 1; i <= 10000; i++)
    {
        stringstream s;
        string str;
        s << i;
        str = s.str();
        int sum = i;
        for (int j = 0; j < (int) str.size(); j++)
        {
            sum += str[j] - '0';
        }
        mp[sum] = true;
        if (mp[i] == false)
            cout << i << endl;
    }
    fclose(stdin);
    fclose(stdout);
    return 0;
}