[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

快乐数有以下的特性：在给定的进位制下，该数字所有数位(digits)的平方和，得到的新数再次求所有数位的平方和，如此重复进行，最终结果必为1。

非快乐数有以下的特性：所有不快乐数的数位平方和计算，最後都会进入 4 → 16 → 37 → 58 → 89 → 145 → 42 → 20 → 4 的循环中。

所以外层循环：判断是否为快乐数和非快乐数。内层循环对n进行快乐数分解计算。

class Solution {
public:
    bool isHappy(int n) {
        while (n != 1 && n != 4) {
            int sum = 0, tmp = 0;
            while (n != 0) {
                tmp = n % 10;
                sum += tmp * tmp;
                n /= 10;
            }
            n = sum;
        }
        return n == 1;
    }
};
// 3 ms