How does the A* algorithm determine the best path?

The A* algorithm determines the best path by summing the cost to reach the current node and an estimate of the cost to reach the goal from that node, known as the heuristic. This method allows A* to evaluate nodes in a way that balances both the actual cost incurred to reach the node so far and the estimated cost to complete the journey to the goal. By combining these two factors, the algorithm effectively prioritizes which node to explore next based on both what has already been achieved and what still needs to be done, thus guiding it towards the most promising paths.

Using this approach not only enables A* to find the shortest path efficiently, but it also ensures that the search is directed towards areas of the search space that are likely to yield the optimal solution, rather than exploring randomly or exhaustively visiting every node.