40. leetcode 202. 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

思路：把一个数每一位平方后加和得到一个新的数，然后继续对这个新的数做同样的操作。如果最后能得到一个1，则最原始的数就是一个”Happy Number”。如果在还没达到1的过程中出现循环，则这个数肯定不是。用到C++ 的set。set.count()判断一个数是否在set中，set.insert()，向set 中插入元素。INT_MAX，表示最大整数。

class Solution {
public:
    bool isHappy(int n) {
        if(n==0)
            return false;
        set<long> s;
        while(n<=INT_MAX)
        {
            if(n==1)
                return true;
            if(s.count(n)>0)
                return false;
            s.insert(n);
            n=digitSquare(n);
        }
        return false;
        
    }
    long digitSquare(long num)
    {
        long r=0;
        int t=0;
        while(num)
        {
            t=num%10;
            r+=t*t;
            num/=10;
        }
        return r; 
    }
};