Ugly Number II (K-th Ugly)

**Problem Statement:** Given the required input arguments, write an efficient algorithm to solve the **Ugly Number II (K-th Ugly)** problem. Implement the required logic as specified by standard definitions for this classic algorithmic challenge. **Hint / Expected Approach:** Min-heap or three-pointer DP **Edge Cases to Consider:** - (1) k = 1 (return 1) - (2) Large k - (3) Counting duplicates correctly

Examples

Example 1

Input: 1

Output: 1

Explanation: 1 is ugly

Example 2

Input: 2

Output: 2

Example 3

Input: 3

Output: 3

Constraints

▪Input arguments are within valid ranges
▪Optimize for execution speed
▪Handle null/empty inputs gracefully

Watch Out For Edge Cases

▪k = 1 (return 1)
▪Large k
▪Counting duplicates correctly

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