[leetcode] 202. Happy Number

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本文介绍了一种简单有效的算法来判断一个数字是否为快乐数。快乐数是指通过将该数替换为其各位数字平方之和并重复此过程，最终能得到1的正整数。文章详细解释了如何利用哈希表避免无限循环，并提供了清晰的C++代码实现。

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

这道题是确定一个数字是否是happy number，题目难度为easy。

按照题目规则，很自然会使用Hash Table，将每次计算的结果存入Hash Table，直到结果是1表明数字是happy number，在这之前如果遇到相同的结果则不是happy number。具体代码：

class Solution {
public:
    bool isHappy(int n) {
        unordered_set<int> num;
        while(true) {
            int sum = 0;
            while(n) {
                sum += (n%10)*(n%10);
                n /= 10;
            }
            n = sum;
            if(sum == 1) return true;
            if(num.find(sum) != num.end()) return false;
            else num.insert(sum);
        }
    }
};

另外还有数学的方法，感兴趣的同学可以自己证明。