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
8^2 + 2^2 = 68
6^2 + 8^2 = 100
1^2 + 0^2 + 0^2= 1

朴素的解法。用快慢指针来标记环路。

#include <iostream>
#include <vector>
using namespace std;

class Solution {
public:
    bool isHappy(int n) {
        int slow = solve_num(n);
        int fast = solve_num(slow);
        if (slow == 1)
            return true;
        while (slow != fast) {
            slow = solve_num(slow);
            if (slow == 1)
                return true;
            fast = solve_num(fast);
            fast = solve_num(fast);
        }
        return false;
    }

    int solve_num(int n) {
        int bw = 0;
        int sum = 0;
        while (n != 0) {
            bw = n % 10;
            sum += bw * bw;
            n /= 10;
        }
        return sum;
    }

};