From Wikipedia, the free encyclopedia:

 A happy number is defined by the following process:
 Starting with any positive integer, replace the number by the sum of the squares of its digits, and repeat the process until the number equals   1   (where it will stay),   or it loops endlessly in a cycle which does not include   1.   


 Those numbers for which this process end in   1   are       happy   numbers,   
 while   those numbers   that   do   not   end in   1   are   unhappy   numbers. 


Task

Find and print the first   8   happy numbers.

Display an example of your output here on this page.



See also

   The OEIS entry:   The     happy numbers:   A007770
   The OEIS entry:   The unhappy numbers;   A031177


#include <map>
#include <set>
 
bool happy(int number) {
  static std::map<int, bool> cache;
 
  std::set<int> cycle;
  while (number != 1 && !cycle.count(number)) {
    if (cache.count(number)) {
      number = cache[number] ? 1 : 0;
      break;
    }
    cycle.insert(number);
    int newnumber = 0;
    while (number > 0) {
      int digit = number % 10;
      newnumber += digit * digit;
      number /= 10;
    }
    number = newnumber;
  }
  bool happiness = number == 1;
  for (std::set<int>::const_iterator it = cycle.begin();
       it != cycle.end(); it++)
    cache[*it] = happiness;
  return happiness;
}
 
#include <iostream>
 
int main() {
  for (int i = 1; i < 50; i++)
    if (happy(i))
      std::cout << i << std::endl;
  return 0;
}