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;
}
