A* Pathfinding Visualization

Legend

How It Works

The A* Pathfinding algorithm is a widely-used method for finding the shortest path between two points. It visualizes the search process by progressively expanding a search space (blue cells) and ultimately marking the shortest path (yellow cells).

Heuristic and Search Details

A* uses a heuristic to guide its search. This heuristic is calculated as the sum of three parameters:

• g(n): The exact cost of the path from the start node to the current node.
• h(n): The estimated cost from the current node to the goal node, often based on Manhattan Distance in grid-based environments.
• f(n): The total estimated cost of the path through the current node: f(n) = g(n) + h(n).

At each step, the algorithm selects the node with the lowest f(n) from the open set (unvisited neighbors). This balance of exact and estimated costs allows A* to prioritize efficient paths while avoiding unnecessary exploration.

Unweighted vs Weighted Grids

For simplicity, this grid is unweighted, meaning that all edges have the same cost, and the search space is uniform. As a result, Dijkstra and BFS would form a concentric ring pattern expanding outwards from the source node, exploring all neighbors level by level.

If the grid were weighted, the cost of traveling between cells would vary depending on the weight assigned to each cell, affecting the pathfinding process. In this scenario:

• A* would still prioritize the path with the lowest f(n), but the g(n) value would change to reflect the different weights, impacting the overall search and the path chosen.
• Dijkstra’s algorithm would also be affected, as the varying weights would influence the shortest path calculation, potentially resulting in a different path than when the grid is unweighted.
• BFS cannot be effectively used on a weighted grid, as it assumes all steps have the same cost and cannot account for varying edge costs.

Visualization Details

• Blue cells represent nodes visited during the search, indicating the algorithm’s exploration of possible paths.
• Yellow cells highlight the shortest path from the start (green) to the destination (red).
• Black cells are obstacles that the algorithm avoids, dynamically shaping the search space.