poj1316

Self Numbers

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 20864		Accepted: 11709

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

这题第一眼看上去就觉得应该要用什么特殊方法，要不然会超时，可是最后没想到根本不会超时，我在调试中提交了n次Runtime error，让我几乎快疯了，后来当我把定义的bool数组移到main函数外就ac了，这让我百思不得其解，难道main函数内部定义一个10000长度的bool数组会超过限制吗

 #include <iostream>

 #include <cstdio>

 #include <cstring>

 using namespace std;

 const int MAXn = ;

 int numOf_Digit(int number)

 {

     int sum = number;

     while(number>=)

     {

         sum += number%;

         number /=;

     }

      sum+=number ;

      return sum;

 }

 bool vis[MAXn];

 int main()

 {

     memset(vis,true,sizeof(vis));

     for(int i=;i<;i++)

     {

         int t =numOf_Digit(i);

         vis[t] = false;

     }

     for(int i = ;i<;i++)

         if(vis[i]==true)

             printf("%d\n",i);

     return ;

 }

当然直接把#define 去掉，直接就是vis[10000],并且取消掉那个运算函数，用一句int t = i + i/1000+(i/100)%10+(i/10)%10+i%10; 就可以0MS了，但个人风格，喜欢把功能变成函数

巴特西

poj1316

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