202. Happy Number

Problem

Difficulty: Easy
Tags: Hash Table, Math, Two Pointers

Intuition

I thought it could be hard problem. to prove some number is un-happy, I have to show that there is an loop in the happy-cycle. which means I have to store all the numbers of the happy cycle. but it is wrong to expect every n will have short happy-cycle.

Approach

according to the wikipedia, only one and seven are happy number. And I don’t know how but, every cycle will contain at least one single digit number. so I looped the function until n is less than 10, and return true only if n is 1 or 7.

Solution

bool isHappy(int n) {
    if(n<10){
        if (n == 1 || n == 7){
            return true;
        }
        else{
            return false;
        }
    }
    else{
        int foo = n;
        int tmp = 0;
        while (foo > 0){
            tmp += (foo % 10) * (foo % 10);
            foo /= 10;
        }
        return isHappy(tmp);
    }
}

Complexity

Time: The AI says the time complexity is $O(\log n)$ but I don’t know how to prove.
Space: $O(\log n)$ same with above.

Thoughts

I don’t know anything about this. I might need more algebra lectures to understand this thingy.