Add Course Schedule in R

[Siddhram]

This PR introduces a clean and well-documented implementation of the Course Schedule problem in R using Kahn’s Algorithm (BFS-based topological sort).

Overview

Courses are modeled as nodes and prerequisites as directed edges (prereq → course). The problem reduces to cycle detection: if the graph is acyclic, all courses can be completed, and a valid topological ordering exists. This implementation provides both a boolean feasibility check and an optional function to return one valid course order.

Features

• BFS-based Kahn’s Algorithm for topological sorting and cycle detection
• Robust input normalization:
  • Accepts prerequisites as a matrix, data.frame, or flat numeric vector
  • Supports both 0-based and 1-based indices (auto-normalized)
• Two public APIs:
  • can_finish(num_courses, prerequisites): returns TRUE/FALSE
  • find_course_order(num_courses, prerequisites): returns a valid order or integer(0) if impossible
• Clear comments and consistent structure with other graph_algorithms scripts
• Embedded examples for quick validation (no external dependencies)

Complexity

• Time Complexity: O(V + E)
• Space Complexity: O(V + E)

Directory

• Updated DIRECTORY.md to include “Course Schedule (Kahn)” under Graph Algorithms

Demonstration

Run the script to execute built-in examples:

From command line / PowerShell:

Rscript "R/graph_algorithms/course_schedule_can_finish.r"