Write an algorithm to determine if a number is "happy".
A happy number is a number 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 ends in 1 are happy numbers.
**Example: **19 is a happy number

First Thought

This solution is in low efficiency. For every integer which is not a happy number, we will need to go through a complete cycle of its looping.

bool isHappy(int n){
  unordered_set<int> hash;
  while(hash.insert(n)){
    int indice = n%10, temp = 0;
    while(n > 0){
      temp += indice*indice;
      n = n/10;
      indice = n%10;
    }
    if(temp == 1) return true;
    else n = temp;
  }
  return false;
}

Improved version

This one is much better. Firstly, it used a math fact that each integer not a happy number, in its cycle, there will always be a 4.
Reason can be found : http://en.wikipedia.org/wiki/Happy_number#Sequence_behavior

bool isHappy(int n){
  int magic = 4;
  while(1){
    if(n == 1) return true;
    if(n == 4) return false;
    int indice = n%10, temp = 0;
    while(n > 0){
      temp += indice*indice;
      n = n/10;
      indice = n%10;
    }
    n = temp;
  }
  return false;
}