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 both O(n²) dynamic programming and O(n log n) optimized binary search approaches. The implementation includes comprehensive testing and real-world examples.

• Adds complete LIS algorithm with both basic DP and optimized binary search implementations
• Includes comprehensive test cases covering edge cases, performance comparisons, and real-world stock price analysis
• Provides helper functions for visualization and analysis of the DP table and results

Reviewed Changes

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

File	Description
dynamic_programming/lonest_increasing_subsequence.r	Complete implementation of LIS algorithm with both O(n²) and O(n log n) solutions, comprehensive testing suite, and real-world examples
dynamic_programming/1_knapsack_problem.r	Implementation of 0/1 Knapsack problem for comparison and context within the dynamic programming collection

Comments suppressed due to low confidence (1)

dynamic_programming/lonest_increasing_subsequence.r:1

• Corrected spelling of 'lonest' to 'longest' in filename.

# Longest Increasing Subsequence (Dynamic Programming)

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[Copilot]

The dp_table field is redundant as it duplicates the dp_array field with identical content. Consider removing this duplication to simplify the return structure.

[Copilot]

Pull Request Overview

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

---

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[Copilot]

The filename contains a typo: 'lonest' should be 'longest'.

[Copilot]

The function recalculates the entire DP solution unnecessarily. Since the DP array was already computed on lines 145-152, the LIS sequence should be extracted from that existing computation instead of calling the main function again.

Suggested change

	# For simplicity, return just one LIS (same as the main function)
	# Finding all possible LIS is complex and not essential for the algorithm demonstration
	result <- longest_increasing_subsequence(nums)
	return(list(result$lis_sequence))
	# For simplicity, extract just one LIS using the computed DP array
	# Finding all possible LIS is complex and not essential for the algorithm demonstration
	# Backtrack to find one LIS sequence
	lis_sequence <- c()
	current_length <- max_length
	for (i in seq(n, 1)) {
	if (dp[i] == current_length) {
	lis_sequence <- c(nums[i], lis_sequence)
	current_length <- current_length - 1
	}
	if (current_length == 0) break
	}
	return(list(lis_sequence))

[Sachinn-64]

@si