Self Numbers
Time Limit: 20000/10000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 9356 Accepted Submission(s): 4040
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
| | |
Source
就是要输出1000000以内所有不能由其它数字组成的数字。
AC代码如下：
//1128 #include<stdio.h> int f[1000001]; int sum(int a) { int ans=a; while(a) { ans+=a%10; a/=10; } return ans; } int main() { int i; for(i=1;i<1000001;i++) { if(f[i]==0) printf("%d\n",i); f[sum(i)]=1; } return 0; }
