[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 = 1Credits:Special thanks to @mithmatt and @ts for adding this problem and creating all test cases.    Hide Company Tags UberHide Tags Hash Table MathHide Similar Problems (E) Add Digits (E) Ugly Number

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;    }