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Safak
2025-05-12 12:59:24 +02:00
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{
"cells": [
{
"cell_type": "markdown",
"id": "e063ba00",
"metadata": {},
"source": [
"# A* Algorithm"
]
},
{
"cell_type": "markdown",
"id": "868592a7",
"metadata": {},
"source": [
"## Install Requirements"
]
},
{
"cell_type": "markdown",
"id": "26dff129",
"metadata": {},
"source": [
"create a virtual environment in current directory by \n",
"\n",
"```\n",
"python3 -m venv .env # macos\n",
"python -m venv .env # linux\n",
"```"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "55fa613b",
"metadata": {
"ExecuteTime": {
"end_time": "2025-05-07T21:40:23.660320Z",
"start_time": "2025-05-07T21:40:22.973705Z"
}
},
"outputs": [],
"source": [
"%pip install pygame"
]
},
{
"cell_type": "markdown",
"id": "db35c098",
"metadata": {},
"source": [
"## Imports"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "e7034eee",
"metadata": {
"ExecuteTime": {
"end_time": "2025-05-07T21:40:23.825797Z",
"start_time": "2025-05-07T21:40:23.718944Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"pygame 2.6.1 (SDL 2.28.4, Python 3.13.3)\n",
"Hello from the pygame community. https://www.pygame.org/contribute.html\n"
]
}
],
"source": [
"import pygame\n",
"import math"
]
},
{
"cell_type": "markdown",
"id": "77d18f1b",
"metadata": {},
"source": [
"## Global Variables"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "60b63344",
"metadata": {
"ExecuteTime": {
"end_time": "2025-05-07T21:40:23.877569Z",
"start_time": "2025-05-07T21:40:23.873797Z"
}
},
"outputs": [],
"source": [
"BLACK = (0, 0, 0)\n",
"WHITE = (255, 255, 255)\n",
"BLUE = (0, 0, 255)\n",
"GREEN = (0, 255, 0)\n",
"RED = (255, 0, 0)\n",
"ORANGE = (255, 165, 0)\n",
"GREY = (128, 128, 128)\n",
"\n",
"WIDTH = 25\n",
"HEIGHT = 25\n",
"MARGIN = 3\n"
]
},
{
"cell_type": "markdown",
"id": "87a05a3b",
"metadata": {},
"source": [
"## Classes "
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "84ad596c",
"metadata": {
"ExecuteTime": {
"end_time": "2025-05-07T21:40:24.013443Z",
"start_time": "2025-05-07T21:40:24.010202Z"
}
},
"outputs": [],
"source": [
"class Queue:\n",
" def __init__(self, type, sort_by = ''):\n",
" self.type = type\n",
" self.items = []\n",
" self.sort_by = sort_by\n",
"\n",
" def clear(self):\n",
" self.items.clear()\n",
" \n",
" def is_empty(self):\n",
" if len(self.items) > 0:\n",
" return False\n",
" else:\n",
" return True\n",
"\n",
" def push(self, element):\n",
" self.items.append(element)\n",
" '''\n",
" queue = [element_0, element_1, ... , element_n] <- element_n+1\n",
" '''\n",
" if self.type == 'PRIO':\n",
" '''\n",
" Sorting so lowest cost/ value is at [0]\n",
" queue = [element_0 < element_1 < ... < element_n < element_n+1]\n",
" '''\n",
" if self.sort_by == '':\n",
" self.items.sort(key=lambda item: item.value)\n",
" elif self.sort_by == 'f':\n",
" self.items.sort(key=lambda item: item.f)\n",
"\n",
" def pop(self):\n",
" if not self.is_empty():\n",
" if self.type == 'LIFO':\n",
" ''' LIFO\n",
" queue = [element_0, elemente_1, ... , element_n]\n",
" -> pop element_n\n",
" '''\n",
" return self.items.pop()\n",
" else:\n",
" ''' FIFO & PRIO\n",
" queue = [element_0, element_1, ... , element_n]\n",
" -> pop element_0\n",
" '''\n",
" return self.items.pop(0)\n",
" return None"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "d3b77c0a",
"metadata": {
"ExecuteTime": {
"end_time": "2025-05-07T21:40:24.044268Z",
"start_time": "2025-05-07T21:40:24.041113Z"
}
},
"outputs": [],
"source": [
"class Field:\n",
" def __init__(self, x, y):\n",
" self.x = x\n",
" self.y = y\n",
" self.state = \"free\" # states: free, obstacale, start, target\n",
"\n",
" self.g = float('inf')\n",
" self.h = 0\n",
" self.f = float('inf')\n",
" self.parent = None\n",
"\n",
" def draw(self, screen):\n",
" # state based coloring\n",
" color = WHITE\n",
" if self.state == \"obstacale\":\n",
" color = BLACK\n",
" elif self.state == \"start\":\n",
" color = BLUE\n",
" elif self.state == \"target\":\n",
" color = GREEN\n",
" elif self.state == \"path\":\n",
" color = ORANGE\n",
" elif self.state == \"current\":\n",
" color = RED\n",
" elif self.state == \"visited\":\n",
" color = GREY\n",
"\n",
" x_calc = (MARGIN + WIDTH) * self.x + MARGIN\n",
" y_calc = (MARGIN + HEIGHT) * (grid_size - 1 - self.y) + MARGIN # flipping\n",
"\n",
" pygame.draw.rect(\n",
" screen,\n",
" color,\n",
" [x_calc, y_calc, WIDTH, HEIGHT]\n",
" )"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "b3d9f04f",
"metadata": {
"ExecuteTime": {
"end_time": "2025-05-07T21:40:24.125218Z",
"start_time": "2025-05-07T21:40:24.120389Z"
}
},
"outputs": [],
"source": [
"class Grid:\n",
" def __init__(self, cols, rows):\n",
" self.cols = cols # x\n",
" self.rows = rows # y\n",
" self.grid = []\n",
"\n",
" i = 0\n",
" while i < cols: # col = x\n",
" col = []\n",
" j = 0\n",
" while j < rows: # row = y\n",
" col.append(Field(i, j)) # (x,y)\n",
" j += 1\n",
" self.grid.append(col)\n",
" i += 1\n",
"\n",
" self.start = None\n",
" self.target = None\n",
"\n",
" def draw(self, screen):\n",
" for col in self.grid:\n",
" for field in col:\n",
" field.draw(screen)\n",
"\n",
" def heuristic(self, field):\n",
" return math.sqrt((field.x - self.target[0]) ** 2 + (field.y - self.target[1]) ** 2)\n",
"\n",
" def get_state(self, x, y):\n",
" return self.grid[x][y].state\n",
"\n",
" def set_state(self, state, x, y):\n",
" if state == \"free\" or state == \"obstacale\" or state == \"start\" or state == \"target\" or state == \"path\" or state == \"current\" or state == \"visited\":\n",
" self.grid[x][y].state = state\n",
"\n",
" def set_free(self, x, y):\n",
" self.set_state(\"free\", x, y)\n",
"\n",
" def set_obstacle(self, x, y):\n",
" self.set_state(\"obstacale\", x, y)\n",
" \n",
" def set_current(self, x, y):\n",
" self.set_state(\"current\", x, y)\n",
" \n",
" def set_visited(self, x,y):\n",
" self.set_state(\"visited\", x, y)\n",
"\n",
" def set_path(self, x, y):\n",
" if not (x == self.start[0] and y == self.start[1]) and not (x == self.target[0] and y == self.target[1]):\n",
" self.set_state(\"path\", x, y)\n",
"\n",
" def set_start(self, x, y):\n",
" # reset old start if it exits\n",
" if self.start:\n",
" self.set_free(self.start[0], self.start[1])\n",
"\n",
" self.set_state(\"start\", x, y)\n",
" self.grid[x][y].parent = self.grid[x][y]\n",
" self.grid[x][y].g = 0\n",
" self.grid[x][y].h = self.heuristic(self.grid[x][y])\n",
" self.grid[x][y].f = self.grid[x][y].h + self.grid[x][y].g\n",
" self.start = (x, y)\n",
"\n",
" def set_target(self, x, y):\n",
" # reset old target if it exits\n",
" if self.target:\n",
" self.set_free(self.target[0], self.target[1])\n",
"\n",
" self.set_state(\"target\", x, y)\n",
"\n",
" self.target = (x, y)"
]
},
{
"cell_type": "markdown",
"id": "a01bed4a",
"metadata": {},
"source": [
"## Defining Grid Parameters"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "53c20ed6",
"metadata": {
"ExecuteTime": {
"end_time": "2025-05-07T21:40:24.289574Z",
"start_time": "2025-05-07T21:40:24.250017Z"
}
},
"outputs": [],
"source": [
"grid_size = 20\n",
"window_width = grid_size * (WIDTH + MARGIN) + MARGIN\n",
"window_height = grid_size * (HEIGHT + MARGIN) + MARGIN\n",
"size = (window_width, window_height) # made size variable\n",
"\n",
"start = (0, 0)\n",
"target = (19, 19)\n",
"grid = Grid(grid_size, grid_size)\n",
"\n",
"# check if start an target are valid\n",
"if 0 <= start[0] < grid.cols and 0 <= target[0] < grid.cols and 0 <= start[1] < grid.cols and 0 <= target[\n",
" 1] < grid.cols:\n",
" grid.set_target(target[0], target[1])\n",
" grid.set_start(start[0], start[1])\n"
]
},
{
"cell_type": "markdown",
"id": "e67b33e5",
"metadata": {},
"source": [
"### Creating Obsticales"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "d01d53b0",
"metadata": {
"ExecuteTime": {
"end_time": "2025-05-07T21:40:24.329858Z",
"start_time": "2025-05-07T21:40:24.327366Z"
}
},
"outputs": [],
"source": [
"for i in range(0, 10):\n",
" grid.set_obstacle(9, i)\n",
"\n",
"for j in range(4, 10):\n",
" grid.set_obstacle(j, 9)\n",
"\n",
"for i in range(9, 20):\n",
" grid.set_obstacle(16, i)"
]
},
{
"cell_type": "markdown",
"id": "334e0e61",
"metadata": {},
"source": [
"## Initialize A* Parameters"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "d480bcf1",
"metadata": {
"ExecuteTime": {
"end_time": "2025-05-07T21:40:24.378185Z",
"start_time": "2025-05-07T21:40:24.374640Z"
}
},
"outputs": [],
"source": [
"open = Queue('PRIO', 'f')\n",
"open.push(grid.grid[0][0])\n",
"closed = Queue('PRIO', 'f')\n",
"neighbors = []\n",
"path = []\n",
"done = False"
]
},
{
"cell_type": "markdown",
"id": "6898177d",
"metadata": {},
"source": [
"## Initialize PyGame Window"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "a8c78a46",
"metadata": {
"ExecuteTime": {
"end_time": "2025-05-07T21:40:25.086317Z",
"start_time": "2025-05-07T21:40:24.429636Z"
}
},
"outputs": [],
"source": [
"pygame.init()\n",
"screen = pygame.display.set_mode(size)\n",
"pygame.display.set_caption(\"A* Algorithm\")\n",
"clock = pygame.time.Clock()\n",
"\n",
"def update_screen():\n",
" screen.fill(BLACK)\n",
" grid.draw(screen)\n",
" pygame.display.flip()\n",
" clock.tick(30)"
]
},
{
"cell_type": "markdown",
"id": "3939b45f",
"metadata": {},
"source": [
"## A*-Algorithm"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "4c138642",
"metadata": {
"ExecuteTime": {
"end_time": "2025-05-07T21:40:49.022562Z",
"start_time": "2025-05-07T21:40:25.146989Z"
}
},
"outputs": [],
"source": [
"while not done:\n",
" for event in pygame.event.get():\n",
" if event.type == pygame.QUIT:\n",
" done = True\n",
"\n",
" while not open.is_empty():\n",
" current_field = open.pop()\n",
" grid.set_current(current_field.x, current_field.y)\n",
" \n",
" update_screen()\n",
"\n",
" if current_field.x == grid.target[0] and current_field.y == grid.target[1]: \n",
" path.append(current_field)\n",
" grid.set_path(current_field.x, current_field.y)\n",
" \n",
" while not (current_field.x == grid.start[0] and current_field.y == grid.start[1]):\n",
" current_field = current_field.parent\n",
" path.insert(0, current_field)\n",
" grid.set_path(current_field.x, current_field.y)\n",
"\n",
" update_screen()\n",
"\n",
" open.clear()\n",
" done = True\n",
"\n",
"\n",
" closed.push(current_field)\n",
" grid.set_visited(current_field.x, current_field.y)\n",
"\n",
"\n",
" for dx, dy in [(0, -1), (-1, 0), (0, 1), (1, 0)]:\n",
" nx = current_field.x + dx\n",
" ny = current_field.y + dy\n",
"\n",
" if 0 <= nx < grid.cols and 0 <= ny < grid.rows:\n",
" neighbor = grid.grid[nx][ny]\n",
"\n",
" if neighbor.state == \"obstacale\" or closed.items.__contains__(neighbor):\n",
" continue\n",
"\n",
" tentative_g = current_field.g + 1\n",
"\n",
" if tentative_g < neighbor.g:\n",
" neighbor.parent = current_field\n",
" neighbor.g = tentative_g\n",
" neighbor.h = grid.heuristic(neighbor)\n",
" neighbor.f = neighbor.g + neighbor.h\n",
"\n",
" if open.items.__contains__(neighbor):\n",
" open.items.sort(key=lambda item: item.f)\n",
" else:\n",
" open.push(neighbor)\n",
"\n",
" update_screen()\n",
" \n",
"if len(path) == 0:\n",
" print(\"No path between\")\n",
"else:\n",
" path.print()\n",
"\n",
"pygame.quit()"
]
}
],
"metadata": {
"kernelspec": {
"display_name": ".env",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.13.3"
}
},
"nbformat": 4,
"nbformat_minor": 5
}

51
P1/graph.py
View File

@@ -1,12 +1,11 @@
from prettytable import PrettyTable
from pygame.event import set_keyboard_grab
from utils import *
class Node:
def __init__(self, name, x=None, y=None, state="free"):
def __init__(self, name, x=None, y=None):
self.parent = None
self.name = name
self.edges = []
@@ -42,7 +41,7 @@ class Graph:
for node in node_list:
edge_values = ['X'] * len(node_list)
for edge in node.edges:
edge_values[next((i for i, e in enumerate(node_list) if e.name == edge.end.name), -1)] = edge.g
edge_values[next((i for i, e in enumerate(node_list) if e.name == edge.end.name), -1)] = edge.value
t.add_row([node.name] + edge_values)
print(t)
@@ -53,36 +52,42 @@ class Queue:
self.items = []
self.sort_by = sort_by
def empty(self):
return len(self.items) == 0
def clear(self):
self.items.clear()
def pop(self):
if not self.empty():
if self.type == 'LIFO':
''' LIFO
queue = [node_0, node_1, ... , node_n]
-> pop node_n
'''
return self.items.pop()
def is_empty(self):
if len(self.items) > 0:
return False
else:
''' FIFO & PRIO
queue = [node_0, node_1, ... , node_n]
-> pop node_0
'''
return self.items.pop(0)
return None
return True
def push(self, node):
self.items.append(node)
def push(self, element):
self.items.append(element)
'''
queue = [node_0, node_1, ... , node_n] <- node_n+1
queue = [element_0, element_1, ... , element_n] <- element_n+1
'''
if self.type == 'PRIO':
'''
Sorting so lowest cost/ value is at [0]
queue = [node_0 < node_1 < ... < node_n < node_n+1]
queue = [element_0 < element_1 < ... < element_n < element_n+1]
'''
if self.sort_by == '':
self.items.sort(key=lambda item: item.value)
elif self.sort_by == 'f':
self.items.sort(key=lambda item: item.f)
def pop(self):
if not self.is_empty():
if self.type == 'LIFO':
''' LIFO
queue = [element_0, elemente_1, ... , element_n]
-> pop element_n
'''
return self.items.pop()
else:
''' FIFO & PRIO
queue = [element_0, element_1, ... , element_n]
-> pop element_0
'''
return self.items.pop(0)
return None

88
P1/grid.py
View File

@@ -40,8 +40,10 @@ class Field:
color = GREEN
elif self.state == "path":
color = ORANGE
elif self.state == "current":
color = RED
elif self.state == "visited":
color = WHITE
color = GREY
x_calc = (MARGIN + WIDTH) * self.x + MARGIN
y_calc = (MARGIN + HEIGHT) * (grid_size - 1 - self.y) + MARGIN # flipping
@@ -52,13 +54,15 @@ class Field:
[x_calc, y_calc, WIDTH, HEIGHT]
)
'''
# Render the heuristic value as text
if self.state != "obstacale": # Don't display on obstacles
# Create a font object
font = pygame.font.Font(None, 16) # None means default font, 14 is the size
# Round the heuristic value to 1 decimal place for better display
f_text = f"{self.f:.1f}"
f_text = f"{self.g:.1f}"
# Render the text
text = font.render(f_text, True, BLACK) # True for anti-aliasing, BLACK for text color
@@ -68,6 +72,7 @@ class Field:
# Draw the text on the screen
screen.blit(text, text_rect)
'''
class Grid:
@@ -101,7 +106,7 @@ class Grid:
return self.grid[x][y].state
def set_state(self, state, x, y):
if state == "free" or state == "obstacale" or state == "start" or state == "target" or state == "path" or state == "visited":
if state == "free" or state == "obstacale" or state == "start" or state == "target" or state == "path" or state == "current" or state == "visited":
self.grid[x][y].state = state
def set_free(self, x, y):
@@ -110,14 +115,16 @@ class Grid:
def set_obstacle(self, x, y):
self.set_state("obstacale", x, y)
def set_current(self, x, y):
self.set_state("current", x, y)
def set_visited(self, x,y):
self.set_state("visited", x, y)
def set_path(self, x, y):
if not (x == self.start[0] and y == self.start[1]) and not (x == self.target[0] and y == self.target[1]):
self.set_state("path", x, y)
def set_visited(self, x, y):
if not (x == self.start[0] and y == self.start[1]) and not (x == self.target[0] and y == self.target[1]):
self.set_state("visited", x, y)
def set_start(self, x, y):
# reset old start if it exits
if self.start:
@@ -127,7 +134,7 @@ class Grid:
self.grid[x][y].parent = self.grid[x][y]
self.grid[x][y].g = 0
self.grid[x][y].h = self.heuristic(self.grid[x][y])
self.grid[x][y].f = self.grid[x][y].h + self.grid[x][y].g
self.start = (x, y)
def set_target(self, x, y):
@@ -144,7 +151,7 @@ class Grid:
Initializing the Grid
'''
start = (0, 0)
target = (19, 19)
target = (19, 0)
grid = Grid(grid_size, grid_size)
# check if start an target are valid
@@ -163,7 +170,7 @@ for i in range(9, 20):
grid.set_obstacle(16, i)
'''
Initializing A* Comps
Initializing A* Components
'''
open = Queue('PRIO', 'f')
@@ -172,9 +179,11 @@ closed = Queue('PRIO', 'f')
neighbors = []
path = []
pygame.init()
'''
Initializing Visuals
'''
# window
pygame.init()
window_width = grid_size * (WIDTH + MARGIN) + MARGIN
window_height = grid_size * (HEIGHT + MARGIN) + MARGIN
size = (window_width, window_height) # made size variable
@@ -185,11 +194,19 @@ pygame.display.set_caption("A* Algorithm")
done = False
clock = pygame.time.Clock()
while not done:
for event in pygame.event.get():
if event.type == pygame.QUIT:
done = True
def a_star():
neighbor = None
while not open.empty():
while not open.is_empty():
current_field = open.pop()
grid.set_current(current_field.x, current_field.y)
screen.fill(BLACK)
grid.draw(screen)
pygame.display.flip()
clock.tick(15)
if current_field.x == grid.target[0] and current_field.y == grid.target[1]:
path.append(current_field)
@@ -198,61 +215,44 @@ def a_star():
current_field = current_field.parent
path.insert(0, current_field)
grid.set_path(current_field.x, current_field.y)
grid.draw(screen)
pygame.display.flip()
clock.tick(15)
open.clear()
break
closed.push(current_field)
grid.set_visited(current_field.x, current_field.y)
# Nachbarn finden
for dx, dy in [(0, -1), (-1, 0), (0, 1), (1, 0)]:
nx = current_field.x + dx
ny = current_field.y + dy
# Prüfen, ob der Nachbar gültig ist
if 0 <= nx < grid.cols and 0 <= ny < grid.rows:
neighbor = grid.grid[nx][ny]
# Hindernis oder bereits in geschlossener Liste -> überspringen
if neighbor.state == "obstacale" or neighbor in [item for item in closed.items]:
if neighbor.state == "obstacale" or closed.items.__contains__(neighbor):
continue
# Neuen g-Wert berechnen
tentative_g = current_field.g + 1 # Kosten für einen Schritt = 1
tentative_g = current_field.g + 1
# Wenn Nachbar nicht in offener Liste oder neuer Pfad besser
if neighbor not in [item for item in open.items] or tentative_g < neighbor.g:
if tentative_g < neighbor.g:
neighbor.parent = current_field
neighbor.g = tentative_g
neighbor.h = grid.heuristic(neighbor)
neighbor.f = neighbor.g + neighbor.h
# Knoten zur offenen Liste hinzufügen oder aktualisieren
if neighbor not in [item for item in open.items]:
open.push(neighbor)
else:
# Queue aktualisieren
if open.items.__contains__(neighbor):
open.items.sort(key=lambda item: item.f)
else:
open.push(neighbor)
def a_star_main():
global done
while not done:
for event in pygame.event.get():
if event.type == pygame.QUIT:
done = True
a_star()
screen.fill(BLACK)
grid.draw(screen)
# refresh display
pygame.display.flip()
# refreshrate
clock.tick(120)
a_star_main()
clock.tick(30)
pygame.quit()

8
P1/main.py
View File

@@ -25,17 +25,15 @@ romania = Graph(['Or', 'Ne', 'Ze', 'Ia', 'Ar', 'Si', 'Fa',
def main():
# Task 1
graph = romania
ucs(graph, 'Si', 'Bu')
ucs(graph, 'Ti', 'Bu')
graph = romania
bfs(graph, 'Si', 'Bu')
bfs(graph, 'Ti', 'Bu')
graph = romania
dfs(graph, 'Si', 'Bu')
dfs(graph, 'Ti', 'Bu')
# Task 3 A*
a_star_main()
if __name__ == "__main__":
main()

2
P1/search.py
View File

@@ -63,5 +63,3 @@ def dfs(graph, start_node_name, target_node_name):
def ucs(graph, start_node_name, target_node_name):
traverse(graph, Queue('PRIO'), start_node_name, target_node_name)

45
P1/utils.py
View File

@@ -1,47 +1,2 @@
def getNode(name, l):
return next((i for i in l if i.name == name), -1)
def print_grid_direct(self, path=None):
"""
Gibt das Grid in der Konsole aus, direkt wie es im Array gespeichert ist.
Die y-Achse nimmt nach unten zu (0 ist oben), entsprechend der Array-Struktur.
Optionaler Parameter 'path' ist eine Liste von (x,y)-Koordinaten, die den Pfad darstellen.
"""
# Symbole für verschiedene Zustände
symbols = {
"free": ".",
"obstacale": "#", # Tippfehler aus Original-Code beibehalten
"start": "S",
"target": "G",
"path": "o"
}
# Ausgabe des Grids mit Koordinatenachsen
print("\n ", end="")
# Obere x-Achsen-Beschriftung
for x in range(self.cols):
print(f"{x:2d}", end=" ")
print("\n " + "-" * (self.cols * 3))
# Grid mit y-Achsen-Beschriftung
for y in range(self.rows):
print(f"{y:2d} |", end=" ")
for x in range(self.cols):
field = self.grid[x][y]
if path and (x, y) in path and field.state != "start" and field.state != "target":
print(f"{symbols['path']:2s}", end=" ")
else:
print(f"{symbols[field.state]:2s}", end=" ")
print() # Zeilenumbruch
print("\nLegende:")
print(" . = frei")
print(" # = Hindernis")
print(" S = Start")
print(" G = Ziel")
print(" o = Pfad")
# Zusätzliche Statistiken, falls ein Pfad vorhanden ist
if path:
print(f"Pfadlänge: {len(path)} Felder")