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.

Example 1:

Input: n = 19
Output: true
Explanation:
1^2 + 9^2 = 82
8^2 + 2^2 = 68
6^2 + 8^2 = 100
1^2 + 0^2 + 0^2 = 1

Example 2:

Input: n = 2
Output: false

Constraints:

1 <= n <= 2^31 - 1

Approach 1: Floyd's Tortoise and Hare

As stated clearly in the problem, loops endlessly in a cycle, So we can solve this by using Floyd's Tortoise and Hare algorithm.

It's a simple cycle detection algorithm, where one pointer traverses twice as fast as another, once two pointers meet, we can trace back to where the cycle begins.

Time Complexity: $O(m)$ , where $m$ - # of cycles

Space complexity: $O(1)$

class Solution {
    public boolean isHappy(int n) {
        int slow = n, fast = n;
        do {
            slow = digitSquareSum(slow);
            fast = digitSquareSum(digitSquareSum(fast));
        } while (slow != fast);
        return slow == 1 ? true : false;
    }

    public int digitSquareSum(int num) {
        int ans = 0;
        while (num > 0) {
            int digit = num % 10;
            ans += digit * digit;
            num /= 10;
        }
        return ans;
    }
}

impl Solution {
    fn nxt(mut n: i32) -> i32 {
        let mut res = 0;
        while n > 0 {
            let d = n % 10;
            res += d * d;
            n /= 10;
        }
        res
    }

    pub fn is_happy(n: i32) -> bool {
        let mut slow = n;
        let mut fast = Solution::nxt(n);
        while fast != 1 && slow != fast {
            slow = Solution::nxt(slow);
            fast = Solution::nxt(Solution::nxt(fast));
        }
        return fast == 1;
    }
}

class Solution:
    def next_num(self, n: int) -> int:
        # initialize num as 0
        num = 0
        # while our number exists: loop
        while n:
            # add ones digit squared to num
            num += (n % 10) ** 2
            # integer division to remove ones digit.
            n = n // 10
        return num

    def isHappy(self, n: int) -> bool:
        ## Cycle Detection - initialize slow/fast pointers
        slow, fast = n, self.next_num(n)
        ## Since we will always reach a cycle at some point
        ## loop until fast reaches slow
        while slow != fast:
            # move fast pointer 2 numbers, slow 1.
            fast = self.next_num(self.next_num(fast))
            slow = self.next_num(slow)
        # If the cycle location ends on 1, we are happy, else False.
        return fast == 1

0202 - Happy Number (Easy)

Problem Link

Problem Statement

Approach 1: Floyd's Tortoise and Hare

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