284 lines
8.5 KiB
Python
284 lines
8.5 KiB
Python
#!/usr/bin/env python
|
|
# coding: utf-8
|
|
|
|
#
|
|
# Imports
|
|
#
|
|
|
|
import matplotlib.pyplot as plt
|
|
import numpy as np
|
|
import time
|
|
from typing import Optional, NewType
|
|
from abc import ABC, abstractmethod
|
|
from queue import Queue
|
|
|
|
#
|
|
# Type and interfaces definition
|
|
#
|
|
|
|
Point2D = NewType("Point2D", tuple[int, int])
|
|
# type Point2D = tuple[int, int] # tuple(x, y)
|
|
type Path = list[Point2D]
|
|
|
|
class Map:
|
|
"""
|
|
2D map consisting of cells with given cost
|
|
"""
|
|
# array not defined as private, as plotting utilities work with it directly
|
|
array: np.ndarray
|
|
_visited_nodes: int
|
|
|
|
def __init__(self, width: int, height: int) -> None:
|
|
assert width > 0
|
|
assert height > 0
|
|
rows = height
|
|
cols = width
|
|
self.array = np.zeros((rows, cols), dtype=np.float64)
|
|
self._visited_nodes = 0
|
|
|
|
def Randomize(self, low: float = 0.0, high: float = 1.0) -> None:
|
|
self.array = np.random.uniform(low, high, self.array.shape)
|
|
|
|
def IsPointValid(self, point: Point2D) -> bool:
|
|
x, y = point
|
|
y_max, x_max = self.array.shape
|
|
x_in_bounds = (0 <= x < x_max)
|
|
y_in_bounds = (0 <= y < y_max)
|
|
return x_in_bounds and y_in_bounds
|
|
|
|
def GetNeighbours(self, center_point: Point2D) -> list[Point2D]:
|
|
"""
|
|
Get list of neighboring points (without actually visiting them)
|
|
"""
|
|
points: list[Point2D] = []
|
|
x_center, y_center = center_point
|
|
for x in range(-1,2):
|
|
for y in range(-1,2):
|
|
if x == 0 and y == 0:
|
|
continue
|
|
p = Point2D((x + x_center, y + y_center))
|
|
if self.IsPointValid(p):
|
|
points.append(p)
|
|
return points
|
|
|
|
def GetPointCost(self, point: Point2D) -> float:
|
|
x, y = point
|
|
row, col = y, x
|
|
return self.array[(row, col)]
|
|
|
|
def GetPathCost(self, path: Path) -> float:
|
|
return sum([self.GetPointCost(p) for p in path])
|
|
|
|
def ResetVisitedCount(self) -> None:
|
|
self._visited_nodes = 0
|
|
|
|
def GetVisitedCount(self) -> int:
|
|
return self._visited_nodes
|
|
|
|
def Visit(self, point: Point2D) -> float:
|
|
"""
|
|
Visit the node and return its cost
|
|
"""
|
|
if not self.IsPointValid(point):
|
|
raise ValueError("Point out of bounds")
|
|
self._visited_nodes += 1
|
|
return self.GetPointCost(point)
|
|
|
|
#
|
|
# Drawing utilities
|
|
#
|
|
|
|
class Visualizer:
|
|
_axes: Optional[plt.Axes]
|
|
_cmap: plt.Colormap
|
|
_cmap_counter: int
|
|
|
|
def __init__(self):
|
|
self._axes = None
|
|
self._cmap = plt.get_cmap('tab10')
|
|
self._cmap_counter = 0
|
|
|
|
def DrawMap(self, m: Map):
|
|
M, N = m.array.shape
|
|
_, ax = plt.subplots()
|
|
ax.imshow(m.array, cmap='gist_earth', origin='lower', interpolation='none')
|
|
self._axes = ax
|
|
|
|
def DrawPath(self, path: Path, label: str = "Path"):
|
|
|
|
"""
|
|
Draw path on a map. Note that DrawMap has to be called first
|
|
"""
|
|
assert self._axes is not None, "DrawMap must be called first"
|
|
xs, ys = zip(*path)
|
|
color = self._cmap(self._cmap_counter)
|
|
self._cmap_counter += 1
|
|
self._axes.plot(xs, ys, 'o-', color=color, label=label)
|
|
self._axes.plot(xs[0], ys[0], 'o', color='lime', markersize=8) # starting point
|
|
self._axes.plot(xs[-1], ys[-1], 'o', color='magenta', markersize=8) # end point
|
|
|
|
#
|
|
# Pathfinding implementations
|
|
#
|
|
|
|
class PathFinderBase(ABC):
|
|
name: str
|
|
_map: Optional[Map]
|
|
_elapsed_time_ns: int
|
|
_visited_node_count: int
|
|
|
|
def __init__(self) -> None:
|
|
self._map = None
|
|
self._elapsed_time_ns = 0
|
|
self._visited_node_count = 0
|
|
|
|
|
|
def SetMap(self, m: Map) -> None:
|
|
self._map = m
|
|
|
|
def CalculatePath(self, start: Point2D, end: Point2D) -> Optional[Path]:
|
|
"""
|
|
Calculate path on a given map.
|
|
Note: map must be set first using SetMap
|
|
"""
|
|
assert self._map is not None, "SetMap must be called first"
|
|
self._map.ResetVisitedCount()
|
|
start_time = time.perf_counter_ns()
|
|
res = self._CalculatePath(start, end)
|
|
stop_time = time.perf_counter_ns()
|
|
self._elapsed_time_ns = stop_time - start_time
|
|
self._visited_node_count = self._map.GetVisitedCount()
|
|
return res
|
|
|
|
@abstractmethod
|
|
def _CalculatePath(self, start: Point2D, end: Point2D) -> Optional[Path]:
|
|
"""
|
|
This method must be implemented by the derived classes
|
|
"""
|
|
|
|
def GetStats(self) -> tuple[int, int]:
|
|
"""
|
|
Return performance stats for the last calculation:
|
|
- elapsed time in nanoseconds,
|
|
- number of visited nodes during search
|
|
"""
|
|
return self._elapsed_time_ns, self._visited_node_count
|
|
|
|
|
|
class DFS(PathFinderBase):
|
|
"""
|
|
Recursive depth-first search; returns first path it finds
|
|
Not very efficient performance and memory-wise,
|
|
also returns very sub-optimal paths
|
|
"""
|
|
|
|
name = "Depth First Search"
|
|
|
|
def _CalculatePath(self,
|
|
point: Point2D,
|
|
end_point: Point2D,
|
|
path: Optional[list[Point2D]] = None,
|
|
visited: Optional[set[Point2D]] = None) -> Optional[Path]:
|
|
if visited is None:
|
|
visited = set()
|
|
if path is None:
|
|
path = list()
|
|
if self._map is None:
|
|
return None # to make mypy happy
|
|
# We don't need to know cost in this case, but we still want to track
|
|
# how many nodes we've visited
|
|
_ = self._map.Visit(point)
|
|
# we keep visited nodes in separate list and set,
|
|
# as membership check is faster for set than for list,
|
|
# but set is not ordered
|
|
visited.add(point)
|
|
path.append(point)
|
|
if point == end_point:
|
|
return path
|
|
for neighbor in self._map.GetNeighbours(point):
|
|
if neighbor not in visited:
|
|
res = self._CalculatePath(neighbor, end_point, path, visited)
|
|
if res:
|
|
return res
|
|
return None
|
|
|
|
|
|
class BFS(PathFinderBase):
|
|
"""
|
|
Iterative breadh-first search. Finds optimal path and creates flow-field,
|
|
so it would be good match for static maps with lots of agents with one
|
|
destination.
|
|
Compared to A*, this is more computationally expensive if we only want
|
|
to find path for one agent.
|
|
"""
|
|
|
|
name = "Breadth First Search"
|
|
# flow field and distance map
|
|
_came_from: dict[Point2D, Point2D]
|
|
_distance: dict[Point2D, float]
|
|
|
|
def _CalculatePath(self, start_point: Point2D, end_point: Point2D) -> Optional[Path]:
|
|
frontier: Queue[Point2D] = Queue()
|
|
frontier.put(end_point) # we start the computation from the end point
|
|
self._came_from: dict[Point2D, Optional[Point2D]] = { end_point: None }
|
|
self._distance: dict[Point2D, float] = { end_point: 0.0 }
|
|
|
|
# build "flow map"
|
|
while not frontier.empty():
|
|
current = frontier.get()
|
|
for next_point in self._map.GetNeighbours(current):
|
|
if next_point not in self._came_from:
|
|
frontier.put(next_point)
|
|
#self._distance[next_point] = self._distance[current] + 1.0
|
|
self._distance[next_point] = self._distance[current] + self._map.Visit(next_point)
|
|
self._came_from[next_point] = current
|
|
# find actual path
|
|
path: Path = []
|
|
current = start_point
|
|
path.append(current)
|
|
while self._came_from[current] is not None:
|
|
current = self._came_from[current]
|
|
path.append(current)
|
|
return path
|
|
|
|
|
|
class A_star(PathFinderBase):
|
|
|
|
name = "A*"
|
|
|
|
#
|
|
# Calculate paths using various methods and visualize them
|
|
#
|
|
|
|
def main():
|
|
# Define the map and start/stop points
|
|
m = Map(15,10)
|
|
m.Randomize()
|
|
starting_point: Point2D = Point2D((14,8))
|
|
end_point: Point2D = Point2D((1,1))
|
|
|
|
path_finder_classes: list[type[PathFinderBase]] = [
|
|
DFS,
|
|
BFS,
|
|
]
|
|
|
|
v = Visualizer()
|
|
v.DrawMap(m)
|
|
|
|
for pfc in path_finder_classes:
|
|
path_finder = pfc()
|
|
path_finder.SetMap(m)
|
|
path = path_finder.CalculatePath(starting_point, end_point)
|
|
elapsed_time, visited_nodes = path_finder.GetStats()
|
|
if path is not None:
|
|
cost = m.GetPathCost(path)
|
|
print(f"{path_finder.name:22}: took {elapsed_time/1e6:.3f} ms, visited {visited_nodes} nodes, cost {cost:.2f}")
|
|
v.DrawPath(path)
|
|
else:
|
|
print(f"{path_finder.name}: No path found")
|
|
|
|
plt.show()
|
|
|
|
if __name__ == "__main__":
|
|
main()
|