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.

 

 

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

 

 

根据快乐数的计算方法，我们很难在有限步骤内确定一个数是否是快乐数，但使用排除法的话，我们可以尝试确定一个数不是快乐数。根据题意，当计算出现无限循环的时候就不是快乐数。出现无限循环的说明产生了相同的结果，而判断相同结果只要用Set就行了。