Issue Proposal: House Robber (LeetCode Problem 198)

Description I would like to contribute an optimized and efficient C++ solution for the problem House Robber (LeetCode Problem 198).

Plan of Contribution • Implement all three approaches in a structured and well-commented manner. • Add test cases for validation. • Ensure readability and clarity in code.

Approaches & Complexity Analysis 1. Recursion + Memoization • Time Complexity: O(n) • Space Complexity: O(n) (DP array + recursion stack) 2. Tabulation (Bottom-Up DP) • Time Complexity: O(n) • Space Complexity: O(n) (DP array) 3. Space Optimized DP (Final Solution) • Time Complexity: O(n) • Space Complexity: O(1) (only two variables used)

Example Output For input: [2,7,9,3,1] The output will be: 12

Do let me know if this contribution works for the repository, and if there are any formatting or placement rules I should follow. Looking forward for your response

Thanks, Sayan (Github: @singhsayan)