202. Happy Number

📝 Problem Details

• Title: 200. Happy Number
• Link: https://leetcode.com/problems/happy-number/
• Difficulty: Easy
• Tags/Categories: Math Hashmap

Happy Number: 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 if the number does not result in 1, it will loop endlessly (a cycle) numbers for which this process ends in 1 are happy return true if n is a happy number, and false if not

💡 Explanation of Solution

1. use a hashset to track all previously seen numbers
2. repeatedly compute the sum of the squares of the digits of the current number
	- convert n to a string
	- iterate through each character in the string 
	- convert char to integer
	- sum the squares of the digits
3. if we encounter 1, return true (its a happy number)
4. if we encounter a number already in the set, return false (cycle detected)

⌛ Complexity Analysis

Time Complexity: O(log n)
Space Complexity: O(log n)

💻 Implementation of Solution

class Solution {
public:
    bool isHappy(int n) {
        unordered_set<int> seen;
        
        while (n != 1) {
            if (seen.count(n)) return false;  // Cycle detected
            seen.insert(n);
 
            int newNum = 0;
            string numStr = to_string(n);  // Convert to string
            for (char c : numStr) {
                int digit = c - '0';  // Convert character to integer
                newNum += digit * digit;
            }
            
            n = newNum;
        }
        
        return true;  // If we reach 1, it's a happy number
    }
};