Longest Increasing Subsequence

**Problem Statement:** Given the required input arguments, write an efficient algorithm to solve the **Longest Increasing Subsequence** problem. Implement the required logic as specified by standard definitions for this classic algorithmic challenge. **Hint / Expected Approach:** dp[i] = max(dp[j]+1) j<i OR patience sort O(n log n) **Edge Cases to Consider:** - (1) All same elements - (2) Strictly decreasing - (3) Single element