Add A* (A-star) Search Algorithm in R

[Siddhram]

This PR introduces a fully documented implementation of the A* (A-star) search algorithm in R, designed to find the least-cost path from a start node to a goal node in a weighted graph.

Overview

The a_star_search function combines the path cost from the start (g-score) with a heuristic estimate (h-score) to the goal, computing f = g + h. With an admissible and consistent heuristic, A* guarantees optimal shortest paths. By default, with a zero heuristic, A* reduces to Dijkstra’s algorithm.

Features

• Finds shortest paths from a start to a goal node
• Supports custom heuristics for informed search
• Can operate on generic adjacency-list graphs or grid-based graphs
• Handles weighted graphs with positive weights
• Returns:
  • g_scores (distance from start)
  • f_scores (g + h)
  • predecessor array for path reconstruction
  • found flag indicating success
  • path from start to goal if reachable
• Includes helper functions for grid-to-graph conversion and Manhattan heuristic
• Provides demonstration examples:
  • Grid-based pathfinding example (with Manhattan heuristic)
  • Generic adjacency-list example (A* behaves as Dijkstra with zero heuristic)

Complexity

• Time Complexity: O((V + E) log V) with a binary heap priority queue
• Space Complexity: O(V)

Demonstration

Run the included examples to see A* in action on both grid-based and generic adjacency-list graphs. The results include the shortest path and distance from the start node to the goal node.

[Copilot]

Pull Request Overview

Adds an A* (A-star) search algorithm implementation in R, including grid helpers and demonstration examples.

• Implements a_star_search for adjacency-list graphs with heuristic support.
• Adds grid_to_graph and a Manhattan heuristic factory for grid-based pathfinding.
• Includes runnable examples demonstrating grid and generic graph usage.

[siriak]

Looks good, thanks!