Leetcode 202: Happy Number

https://leetcode.com/problems/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

Code

class Solution(object):
    def isHappy(self, n):
        """
        :type n: int
        :rtype: bool
        """
        if n <= 0:
            return False
        
        nums = set()
        
        while True:
            n = sum([int(d)**2 for d in str(n)])
            if n == 1:
                return True
            if n in nums:
                return False
            nums.add(n)
            

 

Idea

A number if happy if it has 1 in its happy loop. If a number is unhappy, it will endless loop, meaning at some point the square sum of digits will have repeated values. In my code, I am using a set to record the square sum in the loop. Whenever we see repeated square sum, we return unhappy. Of course, this method requires O(N) space, where N is the size of digits of the given number.

Another method is to use the idea of Floyd Cycle Detection algorithm: create a fast and a slow pointer. If fast pointer has the same value as the slow pointer, there must be a cycle. If the point they meet has the value, the number is happy.

int digitSquareSum(int n) {
    int sum = 0, tmp;
    while (n) {
        tmp = n % 10;
        sum += tmp * tmp;
        n /= 10;
    }
    return sum;
}

bool isHappy(int n) {
    int slow, fast;
    slow = fast = n;
    do {
        slow = digitSquareSum(slow);
        fast = digitSquareSum(fast);
        fast = digitSquareSum(fast);
    } while(slow != fast);
    if (slow == 1) return 1;
    else return 0;
}

Refs: https://leetcode.com/discuss/33055/my-solution-in-c-o-1-space-and-no-magic-math-property-involved