The A* algorithm is a widely used pathfinding algorithm in computer science and artificial intelligence. It is an informed search algorithm that efficiently finds the shortest path between two points on a graph or grid. A* combines the advantages of Dijkstra's algorithm (guaranteed shortest path) and greedy best-first search (efficiency) by using a heuristic to guide its search.

1. Class Definitions:

• Cell: Represents a single cell in the grid. Each cell has attributes for its coordinates (x, y) and whether it is traversable.
• Grid: Initializes a grid of cells with a specified width and height. It also includes functions to manipulate individual cells, such as setting them as obstacles or checking their traversability status.

2. Distance Calculation:

• euclidean_distance: Computes the Euclidean distance between two points in a twodimensional space. It utilizes the Pythagorean theorem to calculate the distance between pairs of coordinates.

3. A* Search Algorithm:

• a_star: Performs the A* search algorithm to find the optimal path from a starting cell to a goal cell on the grid. It manages an open set as a priority queue to evaluate nodes based on their estimated total cost (f_score). The algorithm iterates through neighboring cells, updates the path if a better route is found, and adds unvisited neighbors to the open set until the goal cell is discovered.

4. Neighborhood Generation:

• get_neighbors: Generates neighboring cells that are traversable and within the grid boundaries. It searches for cells in the cardinal directions (left, right, top, bottom) relative to the given cell.

5. Path Reconstruction:

• reconstruct_path: Reconstructs the optimal path from the came_from dictionary generated during A* search. It traces the parent cells backward from the goal cell to the starting cell.

6. Graphical User Interface (GUI):

• main: Creates an interactive GUI using IPywidgets for users to input grid dimensions, add obstacles, set start and goal positions, and visualize the pathfinding process. When the visualize button is clicked, the grid, obstacles, start, goal, and optimal path are displayed using Matplotlib.