202. Happy Number

Write an algorithm to determine if a number n 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.
• 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.

Return true if n is a happy number, and false if not.

• Time : O(n) n is cycle of formula
• Space : O(1)

class Solution {
public:
    bool isHappy(int n) {
        int slow = n, fast = n;
        do {
            slow = convert(slow);
            fast = convert(convert(fast));
        }while(slow != fast);
        return slow == 1;
    }
    int convert(int n) {
        int res = 0, tmp;
        while(n) {
            tmp = n % 10;
            res += tmp * tmp;
            n /= 10;
        }
        return res;
    }
};

• Time : O(n) n is cycle of formula
• Space : O(n)

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