148 lines
5.0 KiB
Python
148 lines
5.0 KiB
Python
"""
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Dijkstra算法实现
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Dijkstra算法是一种用于计算单源最短路径的经典算法
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"""
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import heapq
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from typing import List, Tuple, Optional, Dict, Set
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class Dijkstra:
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"""
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Dijkstra算法实现
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Dijkstra算法是一种用于计算单源最短路径的经典算法
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"""
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def __init__(self):
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"""初始化Dijkstra算法"""
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self.stats = {
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'nodes_visited': 0,
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'max_queue_size': 0
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}
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def find_path(self, grid: List[List[int]], start: Tuple[int, int], goal: Tuple[int, int]) -> Optional[List[Tuple[int, int]]]:
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"""
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使用Dijkstra算法查找路径
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Args:
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grid: 网格地图，0表示可通行，1表示障碍物
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start: 起点坐标 (row, col)
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goal: 终点坐标 (row, col)
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Returns:
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路径坐标列表，如果找不到路径则返回None
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"""
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# 重置统计信息
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self.stats = {
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'nodes_visited': 0,
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'max_queue_size': 0
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}
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# 获取网格尺寸
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rows = len(grid)
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cols = len(grid[0]) if rows > 0 else 0
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# 检查起点和终点是否有效
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if not (0 <= start[0] < rows and 0 <= start[1] < cols):
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return None
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if not (0 <= goal[0] < rows and 0 <= goal[1] < cols):
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return None
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if grid[start[0]][start[1]] == 1 or grid[goal[0]][goal[1]] == 1:
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return None
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# 初始化优先队列
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priority_queue = []
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heapq.heappush(priority_queue, (0, start))
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# 初始化距离和父节点字典
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distances: Dict[Tuple[int, int], float] = {start: 0}
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parent: Dict[Tuple[int, int], Tuple[int, int]] = {}
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visited: Set[Tuple[int, int]] = set()
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# 8方向移动（包括对角线）
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directions = [
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(-1, 0), (1, 0), (0, -1), (0, 1), # 上下左右
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(-1, -1), (-1, 1), (1, -1), (1, 1) # 对角线
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]
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while priority_queue:
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# 更新统计信息
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self.stats['nodes_visited'] += 1
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self.stats['max_queue_size'] = max(self.stats['max_queue_size'], len(priority_queue))
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# 取出距离最小的节点
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current_distance, current = heapq.heappop(priority_queue)
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# 如果已经访问过，跳过
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if current in visited:
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continue
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# 标记为已访问
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visited.add(current)
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# 如果到达目标节点
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if current == goal:
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# 重构路径
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path = self._reconstruct_path(parent, current)
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return path
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# 检查所有邻居节点
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for dr, dc in directions:
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neighbor = (current[0] + dr, current[1] + dc)
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# 检查邻居节点是否在网格范围内
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if not (0 <= neighbor[0] < rows and 0 <= neighbor[1] < cols):
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continue
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# 检查邻居节点是否为障碍物
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if grid[neighbor[0]][neighbor[1]] == 1:
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continue
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# 检查邻居节点是否已访问
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if neighbor in visited:
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continue
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# 计算移动代价
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if abs(dr) + abs(dc) == 2: # 对角线移动
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move_cost = 1.414 # √2
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else: # 直线移动
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move_cost = 1.0
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# 计算到邻居节点的距离
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distance = current_distance + move_cost
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# 如果找到更短路径
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if neighbor not in distances or distance < distances[neighbor]:
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# 更新距离和父节点
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distances[neighbor] = distance
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parent[neighbor] = current
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heapq.heappush(priority_queue, (distance, neighbor))
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# 未找到路径
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return None
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def _reconstruct_path(self, parent: Dict[Tuple[int, int], Tuple[int, int]], current: Tuple[int, int]) -> List[Tuple[int, int]]:
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"""
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重构路径
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Args:
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parent: 父节点字典
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current: 当前节点
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Returns:
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路径坐标列表
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"""
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path = [current]
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while current in parent:
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current = parent[current]
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path.append(current)
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path.reverse()
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return path
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def get_stats(self) -> Dict[str, int]:
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"""
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获取算法统计信息
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Returns:
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统计信息字典
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"""
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return self.stats.copy() |