A* search: Minimizing the total estimated solution cost

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 A* search is another informed search strategy that combines the advantages of both uniform-cost search and Greedy Best-First Search. It uses a heuristic function to estimate the cost from the current node to the goal node, but also considers the cost of the path to reach the current node.

The A* algorithm works by assigning a cost to each node that is the sum of the cost of the path from the start node to the current node (known as the g-value) and the estimated cost from the current node to the goal node (known as the h-value). The f-value of a node is the sum of the g-value and the h-value.

The A* algorithm then explores the nodes with the lowest f-value first, selecting the node that appears to be the most promising. It continues to explore the nodes until it reaches the goal node or determines that there are no more nodes to explore.

The A* algorithm is guaranteed to find the optimal solution if the heuristic function used is admissible, meaning that it never overestimates the actual cost to reach the goal node. Additionally, if the heuristic function is consistent, meaning that the estimated cost from a node to its successors is always less than or equal to the actual cost, the algorithm is guaranteed to find the optimal solution using the minimum possible amount of memory.

The A* algorithm is commonly used in pathfinding and navigation applications, such as GPS systems and robotics. It is a powerful and efficient algorithm that can find optimal solutions quickly, as long as an admissible and consistent heuristic function is used. However, as with all informed search algorithms, the quality of the heuristic function can greatly impact the algorithm's performance and the quality of the solution it finds.

In summary, the A* algorithm is an informed search strategy that uses both the cost of the path to reach a node and the estimated cost from the current node to the goal node to determine the priority of nodes to explore. It is guaranteed to find the optimal solution if the heuristic function used is admissible and consistent, and it is commonly used in pathfinding and navigation applications.

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