A*(A星)算法是一种启发式搜索算法,用于找到两点之间最短路径。它是行业标准的原因在于它的效率和准确性。相对于其他寻路算法,它对机器的处理速度和内存的占用比较友好。同时,它能够在寻找路径的同时考虑启发式估价函数(h函数)和实际代价(g函数),可以保证路径的最优性。
以下是A*算法的实现代码,用来求解一个迷宫地图的最短路径。
class AStar:
    def __init__(self, graph):
        self.graph = graph
    
    def heuristic(self, start, end):
        # 使用Manhattan距离作为估价函数
        return abs(start[0] - end[0]) + abs(start[1] - end[1])
    def astar_path(self, start, end):
        frontier = PriorityQueue()
        frontier.put(start, 0)
        
        came_from = {}
        came_from[start] = None
        
        g_score = {node: float("inf") for row in self.graph for node in row}
        g_score[start] = 0
        
        f_score = {node: float("inf") for row in self.graph for node in row}
        f_score[start] = self.heuristic(start, end)
        
        while not frontier.empty():
            current = frontier.get()
            if current == end:
                path = []
                while current in came_from:
                    path.append(current)
                    current = came_from[current]
                return path[::-1] 
            for neighbor in self.get_neighbors(current):
                tentative_g_score = g_score[current] + 1
                if tentative_g_score < g_score[neighbor]:
                    came_from[neighbor] = current
                    g_score[neighbor] = tentative_g_score
                    f_score[neighbor] = tentative_g_score + self.heuristic(neighbor, end)
                    if neighbor not in frontier.queue: