[LeetCode202]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
Credits:
Special thanks to @mithmatt and @ts for adding this problem and creating all test cases.

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这道题虽然是easy但是第二遍看过来居然一下子想不到什么时候loop应该停止。其实试一下就知道了：如果不是happy number 算着算着就会回到某个数字。比如2，算着算着就回到了4。

知道这个，就可以用一个hashtable记录产生的结果。

有两种方法，第一种就是用hashtable，比较直观：

class Solution {
public:
    bool isHappy(int n) {
        int res = 0;
        while(n){
            res += (n%10) * (n%10);
            n /= 10;
        }
        if(table.count(res)) return false;
        else table.insert(res);
        return (res == 1) ? true : isHappy(res);
    }
private: unordered_set<int> table;
};

另一种利用linked list 找cycle也很厉害。。

    int next(int n){
        int res = 0;
        while (n) {
            res +=(n%10) * (n%10);
            n /=10;
        }
        return res;
    }

    bool isHappy(int n) {
        int slow = n;
        int fast = next(n);
        while (slow != fast) {
            slow = next(slow);
            fast = next(next(fast));
        }
        return slow ==1;
    }