Happy Number

Problem:

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

Solution:

class Solution {
public:
    // Since, we don't care about sorted order of keys, we should use unordered data structure instead of ordered(std::map or std::set -> store keys in       // sorted order in binary search tree format: log n insertion, lookup time)
    // And among unordered_map and unordered_set, we'll use unordered_set since we don't need values related to keys in this problem.
    // unordered (set or map) use hashtables internally (not trees), so lookup/insertion time is constant. Drawback is: keys are not sorted as in BST.
    
    bool check_num(int a, unordered_set<int> &set) {
        if (set.find(a) != set.end())
            return true;
        set.insert(a);
        return false;
    }
    bool isHappy(int n) {
        int num = n;
        int new_num =  0;
        unordered_set<int> set;
        while (1) {
            while (n != 0) {
                new_num += pow(n % 10, 2);
                n /= 10;
            }
            if (new_num == 1)
                return true;
            else if (check_num(new_num, set))
                return false;
            n = new_num;
            new_num = 0;
        }
    }
};