202. Happy Number

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

• 12 + 92 = 82
• 82 + 22 = 68
• 62 + 82 = 100
• 12 + 02 + 02 = 1

Solution:

Use a Hashset to track all the numbers that has been checked. If the number is appeared again, which means the process loops in a cycle, so the number is not happy. If the number ends at 1 which means the number is happy.

 public boolean isHappy(int n) {  
     Set<Integer> set=new HashSet<Integer>();  
     while(n!=1){  
       set.add(n);  
       n=calculateSum(n);  
       if(set.contains(n)) return false;  
     }  
     return true;  
   }  
   public int calculateSum(int n){  
     int sum=0;  
     while(n>0){  
       int dig=n%10;  
       sum+=dig*dig;  
       n=n/10;  
     }  
     return sum;  
   }  

Another classic way to detect cycle is use walker and runner like we did in detecting cycle for linked list.

 public boolean isHappy(int n) {  
     int walker=n;  
     int runner=calculateSum(n);  
     while(walker!=runner){  
       walker=calculateSum(walker);  
       runner=calculateSum(calculateSum(runner));  
     }  
     return walker==1;  
   }  
   public int calculateSum(int n){  
     int sum=0;  
     while(n>0){  
       int dig=n%10;  
       sum+=dig*dig;  
       n=n/10;  
     }  
     return sum;  
   }