**一. 题目描述** 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 1^2 + 9^2 = 82 （各个位的平方和）  8^2 + 2^2 = 68  6^2 + 8^2 = 100  1^2 + 0^2 + 0^2 = 1 **二. 题目分析** 题目要求对任意一个正整数，不断各个数位上数字的平方和，若经过若干次运算后结果收敛到1，则该数字为Happy Number，**不是Happy Number的数在经过多次运算后会从某个数开始陷入循环**。这道题目我们只用根据规则进行计算，并使用一个map存储已经出现过的数字，这样每轮计算完成后查找map，若发现值已存在，证明已陷入循环，可跳出循环并判定该整数不是Happy Number。 更多关于Happy Number的知识可参考：[http://baike.baidu.com/link?url=slZGeshN-Igmd4geJ7PZ9hPwk_PZGZK6QttvzH5TpUiQIPy8qZAmG6o9-5-x-Eu2WGoQuhnASB7alb2ecEatpVj0C9-3DaQPjy0Cpvmvp7AB3IiKy6vu1Qb8FhCbj_Eg1Nt4ba9FDzZT1BzbQcsL5a](http://baike.baidu.com/link?url=slZGeshN-Igmd4geJ7PZ9hPwk_PZGZK6QttvzH5TpUiQIPy8qZAmG6o9-5-x-Eu2WGoQuhnASB7alb2ecEatpVj0C9-3DaQPjy0Cpvmvp7AB3IiKy6vu1Qb8FhCbj_Eg1Nt4ba9FDzZT1BzbQcsL5a) **三. 示例代码** ~~~ #include <iostream> #include <map> using namespace std; class Solution { public: bool isHappy(int n) { if (n < 0) return false; if (n == 1) return true; map<int, bool> showNum; while (true) { int temp = 0; while (n) { temp += (n % 10) * (n % 10); n /= 10; } if (temp == 1) return true; else if (showNum[temp] == true) // 陷入循环，判为非快乐数 return false; else { showNum[temp] = true; n = temp; } } } }; ~~~ 一些测试结果：  **四. 小结** 无