[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;
}