Add Maximal Square dynamic programming algorithm in R

[Siddhram]

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

Overview

The implementation provides solutions to find the area of the largest square containing only 1s in a binary matrix. It includes both a 2D DP approach with padding and a 1D space-optimized variant, along with embedded examples and explanatory comments.

Features

• 2D DP with padding:
  • dp[r+1][c+1] = 1 + min(dp[r][c+1], dp[r+1][c], dp[r][c]) when matrix[r][c] == 1
  • Tracks the maximum side length; returns area = max_side^2
• Space-optimized 1D DP:
  • Reduces memory to O(n) using a rolling array and prev-diagonal carry
  • Supports both character ('0'/'1') and numeric (0/1) matrices
• Includes embedded examples and outputs
• Consistent comments and structure with other DP files

Complexity

• Time Complexity: O(m·n)
• Space Complexity:
  • 2D DP: O(m·n)
  • 1D optimized: O(n)

Directory

• Updated DIRECTORY.md to include “Maximal Square” under Dynamic Programming

Demonstration

Run the script to execute built-in examples:

From Windows command line:

Rscript "R/dynamic_programming/maximal_square.r"