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[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

 

[LeetCode] Happy Number