Add House Robber dynamic programming algorithm in R

[Siddhram]

This PR introduces a complete and well-documented implementation of the House Robber problem in R.

Overview

The implementation provides solutions for maximizing the amount of money that can be robbed from a row of houses without alerting the police. It includes a space-optimized O(1) DP approach that tracks only two rolling states and an optional tabulation variant for clarity, along with embedded examples.

Features

• Space-optimized O(1) DP:
  For each house i:
  • take = nums[i] + prev2 (rob current, skip previous)
  • notTake = prev1 (skip current)
  • curr = max(take, notTake)
  • Update prev2 = prev1; prev1 = curr
• Tabulation DP (O(n)) for pedagogical completeness
• Handles empty and single-element arrays
• Consistent comments and structure with other dynamic_programming scripts

Complexity

• Time Complexity: O(n)
• Space Complexity:
  • O(1) for the rolling DP solution
  • O(n) for tabulation

Directory

• Updated DIRECTORY.md to include “House Robber” under Dynamic Programming

Demonstration

Run the script to execute built-in examples:

From Windows command line:

Rscript "R/dynamic_programming/house_robber.r"