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Generating a truly random and unbiased maze can be a complex task. Fortunately, there's an algorithm designed specifically for this challenge.

Wilson's algorithm leverages Loop-erased random walks to construct a uniform spanning tree — an unbiased representation of all possible spanning trees. Unlike other common maze generation methods, such as Prim's algorithm, random traversal, or randomized depth-first traversal.

The A* (A-star) algorithm is a popular pathfinding and graph traversal method that efficiently finds the shortest path between two points on a grid, such as from the start to the goal in a maze. It combines the benefits of both Dijkstra's algorithm and greedy best-first search, using a cost function that takes into account both the distance from the starting point and an estimate of the distance to the goal.

This function, known as the f-score, is the sum of two components: the g-score (the cost to reach the current node from the start) and the h-score (the estimated cost from the current node to the goal). A* uses this combined information to prioritize nodes, ensuring that it explores the most promising paths first.

As the algorithm proceeds, it explores neighboring nodes, updating their f-scores and determining the optimal route by considering both the actual distance traveled and the predicted cost to the goal. Nodes are sorted based on their f-scores, with the algorithm always expanding the node with the lowest f-score. This allows A* to efficiently navigate complex mazes, guaranteeing an optimal solution while avoiding unnecessary exploration of less promising paths. The A* algorithm's heuristic approach makes it particularly effective in solving mazes with a balance of accuracy and performance, ensuring that the shortest path is found with minimal computational overhead.