A* Algorithm

The A* (A-Star) algorithm is a valuable algorithm for grid-based path planning. It is widely used in various applications such as robotics, computer vision, and video game AI.

The algorithm combines the advantages of both Dijkstra's algorithm and greedy best-first search. It finds the shortest path between a starting node and a goal node by considering both the cost to reach the current node and the estimated cost to reach the goal node.

Here is an example implementation of the A* algorithm in Python:

1{code}

In this example, we have a graph represented by an adjacency list. The astar_algorithm function takes the graph, starting node, and goal node as inputs and returns the shortest path as a list of nodes. The heuristic function calculates the estimated cost from a node to the goal node, and the reconstruct_path function reconstructs the shortest path based on the came_from dictionary.

The A* algorithm uses a priority queue (implemented as a min-heap) to efficiently explore the nodes. It maintains two sets, open_set and closed_set, to keep track of the nodes that are being considered and the nodes that have been visited.

One important aspect of the A* algorithm is the choice of heuristic function. The heuristic function provides an estimate of the remaining cost from a given node to the goal node. A good heuristic can significantly improve the performance of the algorithm by guiding the search towards the goal. Common heuristics include Euclidean distance, Manhattan distance, and octile distance.

Note: The actual implementation of the graph, adjacency list, and distance calculation may vary depending on the specific application. The example provided here is for illustrative purposes.

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    return None

# A* Algorithm

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def astar_algorithm(graph, start, goal):

    open_set = []

    closed_set = []

    came_from = {}

    g_score = {}

    f_score = {}

​

    # Initialize the starting node

    g_score[start] = 0

    f_score[start] = heuristic(start, goal)

    heapq.heappush(open_set, (f_score[start], start))

​

    while len(open_set) > 0:

        current = heapq.heappop(open_set)[1]

​

        if current == goal:

            return reconstruct_path(came_from, goal)

​

        closed_set.append(current)

​

        for neighbor in graph.adjacent_nodes(current):

            tentative_g_score = g_score[current] + graph.distance(current, neighbor)

​

            if neighbor in closed_set:

                continue

​

            if neighbor not in open_set or tentative_g_score < g_score[neighbor]: