Problem:

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

Summary:

若一个整数的各个位数的平方和相加，不断重复这个操作后为1，则这个数为happy number。给出一个数n，判断其是否为happy number。

Analysis:

一个数重复各个位数平方和相加的操作为1时为happy number，那么判断一个数不是happy number的依据，则为各个位数平方和相加无论多少次，依旧不能为1。那么一定是在相加的过程中出现了数的循环，1不含在循环中。

所以只需重复平方和操作，判断每个数的各个位数平方和计算完毕后所得结果有无出现过，若从未出现，则继续计算，否则判断此数不是happy number。

 1 class Solution {
 2 public:
 3     bool isHappy(int n) {
 4         unordered_map<int, int> m;
 5         while (true) {
 6             int sum = 0;
 7             while (n) {
 8                 sum += (n % 10) * (n % 10);
 9                 n /= 10;
10             }
11             
12             n = sum;
13             if (m[sum]++ > 0) {
14                 break;
15             }
16         }
17         
18         return n == 1;
19     }
20 };

LeetCode 202 Happy Number