**一. 題目描述** 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 （各個位的平方和）? 8^2 + 2^2 = 68? 6^2 + 8^2 = 100? 1^2 + 0^2 + 0^2 = 1 **二. 題目分析** 題目要求對任意一個正整數，不斷各個數位上數字的平方和，若經過若干次運算后結果收斂到1，則該數字為Happy Number，**不是Happy Number的數在經過多次運算后會從某個數開始陷入循環**。這道題目我們只用根據規則進行計算，并使用一個map存儲已經出現過的數字，這樣每輪計算完成后查找map，若發現值已存在，證明已陷入循環，可跳出循環并判定該整數不是Happy Number。 更多關于Happy Number的知識可參考：[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. 示例代碼** ~~~ #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) // 陷入循環，判為非快樂數 return false; else { showNum[temp] = true; n = temp; } } } }; ~~~ 一些測試結果：  **四. 小結** 無