[UVA] 640 - Self Numbers
Self Numbers
| Self Numbers |
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<stdio.h>
#include<stdlib.h>
#include<string.h>
char x[1000001];
int main() {
memset(x, 0, sizeof(x));
int i, j, tmp;
for(i = 1; i <= 999999; i++) {
j = i, tmp = 0;
while(j) {
tmp += j%10;
j /= 10;
}
if(tmp+i <= 1000000)
x[tmp+i] = 1;
}
for(i = 1; i <= 1000000; i++)
if(!x[i])
printf("%d\n", i);
return 0;
}
以下作法會更快
#include<stdio.h>
#include<string.h>
char x[1000001], y[1000001];
int main() {
memset(x, 0, sizeof(x));
memset(y, 0, sizeof(y));
int i, j, ti;
for(i = 0; i <= 999999; i++) {
if(i < 100000) {
for(j = 0, ti = 10*i; j < 10; j++)
y[ti+j] = y[i]+j;
}
if(i+y[i] <= 1000000)
x[i+y[i]] = 1;
}
for(i = 1; i <= 1000000; i++)
if(!x[i])
printf("%d\n", i);
return 0;
}