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

思路分析：这题比较简单，就是不断的做各个位置数字的平方加和操作，看是否会产生1。但是有一个地方要注意，就是怎么判断出现了循环，这里定义了一个Set，保存所有出现过的数字，对于计算得到的新的和，如果没有在Set中出现，就添加到Set中继续进行平方求和；否则，就是遇到了已经出现的数字，出现了循环，可以直接结束循环，返回false。

AC Code

public class Solution {

public boolean isHappy(int n) {
    HashSet appearedNums = new HashSet();
    while(!appearedNums.contains(n)){
        appearedNums.add(n);
        int sum = 0;
        while(n != 0){
            int digit = n % 10;
            n /= 10;
            sum += Math.pow(digit,2);
        }
        n = sum;
        if(sum == 1) return true;
    }
    return false;
    }
}