[LeetCode] 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

思路：采用set保存之前碰到过的数，借此判断是否出现循环

复杂度：

代码：

public class Solution {
    public boolean isHappy(int n) {
        Set<Integer> set=new HashSet<Integer>();
        return cycle(n, set);
    }
    public boolean cycle(int k,Set<Integer> set)
    {
        String sk=Integer.toString(k);
        int sum=0;
        for(int i=0;i<sk.length();i++)
        {
            sum+=(sk.charAt(i)-'0')*(sk.charAt(i)-'0');
        }
        if(sum==1) return true;
        if(set.contains(sum)) return false;
        set.add(sum);
        return cycle(sum, set);
    }
}

优化：

扩展：