java 判断一个数是否为“开心数”

题目：

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
1^2 + 9^2 = 82;
8^2 + 2^2 = 68;
6^2 + 8^2 = 100;
1^2 + 0^2 + 0^2 = 1;

解题思路：此题关键是在于如何跳出死循环，用一个Set保存位数平方和，如果出现重复则跳出循环直接返回，算法如下

public class Solution {
    public boolean isHappy(int n) {
        Set set = new HashSet();
        while(mul(n)!=1){
            if(set.contains(mul(n))){
                return false;
            }
            set.add(mul(n));
            mul(n);
            n = mul(n);
        }
        return true;
    }

    public int mul(int n){
        int sum = 0;
        while(n!=0){
            int x = n%10;
            sum = sum + (int)Math.pow(x,2);
            n = n/10;
        }
        return sum;
    }
}