feat: implement Longest Increasing Subsequence algorithm in R

[Sachinn-64]

• Implemented the Longest Increasing Subsequence algorithm in R.
• Finds the length and sequence of the longest strictly increasing subsequence.
• Efficient O(n log n) binary search implementation with O(n²) DP fallback.
• Handles edge cases including empty arrays, duplicates, and single elements.
• Prints DP table, actual LIS sequence, and performance comparisons.
• Time Complexity: O(n log n) optimized, O(n²) basic DP.
• Space Complexity: O(n) for DP array, O(1) for optimized version.

[Copilot]

Pull Request Overview

This PR implements the Longest Increasing Subsequence (LIS) algorithm in R with comprehensive functionality including both basic O(n²) dynamic programming and optimized O(n log n) binary search solutions. The implementation includes edge case handling, performance comparisons, and real-world applications.

• Implements basic DP approach for finding LIS with backtracking to reconstruct the sequence
• Adds optimized binary search solution for improved time complexity
• Provides comprehensive test coverage including edge cases, performance benchmarks, and real-world examples

Reviewed Changes

Copilot reviewed 2 out of 2 changed files in this pull request and generated 3 comments.

File	Description
dynamic_programming/longest_increasing_subsequence.r	Complete LIS algorithm implementation with both basic and optimized approaches, comprehensive testing suite, and documentation
dynamic_programming/0/1_knapsack_problem.r	Separate knapsack problem implementation for comparison/reference

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[Sachinn-64]

@siriak

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[siriak]

Looks good, thanks!