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tobias
2024-12-20 08:30:31 +01:00
parent 733be845de
commit 8e422c38c6
3 changed files with 1105 additions and 0 deletions
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949
16/16.ipynb Normal file
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@@ -0,0 +1,949 @@
{
"cells": [
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
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]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Rechecking the imports and retrying the execution\n",
"\n",
"# Importing NetworkX again to ensure proper initialization\n",
"import networkx as nx\n",
"\n",
"# Retry defining and executing the code\n",
"with open('testinput','r') as infile:\n",
" ascii_map = infile.read()\n",
"\n",
"def parse_ascii_map(ascii_map):\n",
" graph = nx.DiGraph() # Directed graph for flexibility with edge weights\n",
" rows = ascii_map.strip().split(\"\\n\")\n",
" height, width = len(rows), len(rows[0])\n",
" directions = [(-1, 0), (1, 0), (0, -1), (0, 1)] # Up, Down, Left, Right\n",
"\n",
" start, end = None, None\n",
" for y, row in enumerate(rows):\n",
" for x, char in enumerate(row):\n",
" if char != '#': # Not a wall\n",
" graph.add_node((x, y))\n",
" if char == 'S':\n",
" start = (x, y)\n",
" elif char == 'E':\n",
" end = (x, y)\n",
"\n",
" # Add edges for neighbors\n",
" for dx, dy in directions:\n",
" nx_new, ny_new = x + dx, y + dy\n",
" if 0 <= nx_new < width and 0 <= ny_new < height and rows[ny_new][nx_new] != '#':\n",
" graph.add_edge((x, y), (nx_new, ny_new), weight=1)\n",
" return graph, start, end\n",
"\n",
"def find_shortest_path(graph, start, end):\n",
" try:\n",
" path = nx.shortest_path(graph, source=start, target=end, weight='weight')\n",
" cost = nx.shortest_path_length(graph, source=start, target=end, weight='weight')\n",
" return path, cost\n",
" except nx.NetworkXNoPath:\n",
" return None, float('inf')\n",
"\n",
"# Parse and solve\n",
"graph, start, end = parse_ascii_map(ascii_map)\n",
"path, cost = find_shortest_path(graph, start, end)\n",
"\n",
"path, cost\n"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
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" 135512)"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import networkx as nx\n",
"\n",
"# Define directions and corresponding movements\n",
"DIRECTIONS = ['N', 'E', 'S', 'W']\n",
"MOVEMENTS = {\n",
" 'N': (0, -1), # Move up\n",
" 'E': (1, 0), # Move right\n",
" 'S': (0, 1), # Move down\n",
" 'W': (-1, 0) # Move left\n",
"}\n",
"\n",
"# Parse the ASCII map into a graph with movement and turning costs\n",
"def parse_ascii_map_with_costs(ascii_map):\n",
" graph = nx.DiGraph() # Directed graph for handling edge weights\n",
" rows = ascii_map.strip().split(\"\\n\")\n",
" height, width = len(rows), len(rows[0])\n",
"\n",
" start, end = None, None\n",
" for y, row in enumerate(rows):\n",
" for x, char in enumerate(row):\n",
" if char != '#': # Walkable space\n",
" for direction in DIRECTIONS: # Add a node for each direction\n",
" graph.add_node((x, y, direction))\n",
" if char == 'S': # Starting point\n",
" start = (x, y, 'E') # Assume starting direction is North\n",
" elif char == 'E': # Ending point\n",
" end = (x, y)\n",
"\n",
" # Add edges for moving forward\n",
" for direction in DIRECTIONS:\n",
" dx, dy = MOVEMENTS[direction]\n",
" nx_new, ny_new = x + dx, y + dy\n",
" if 0 <= nx_new < width and 0 <= ny_new < height and rows[ny_new][nx_new] != '#':\n",
" graph.add_edge((x, y, direction), (nx_new, ny_new, direction), weight=1)\n",
"\n",
" # Add edges for turning (clockwise and counterclockwise)\n",
" for i, direction in enumerate(DIRECTIONS):\n",
" next_dir = DIRECTIONS[(i + 1) % 4] # Clockwise\n",
" prev_dir = DIRECTIONS[(i - 1) % 4] # Counterclockwise\n",
" graph.add_edge((x, y, direction), (x, y, next_dir), weight=1000)\n",
" graph.add_edge((x, y, direction), (x, y, prev_dir), weight=1000)\n",
" return graph, start, end\n",
"\n",
"# Find the shortest path with the new graph\n",
"def find_shortest_path_with_costs(graph, start, end):\n",
" try:\n",
" # Extract all possible end states (any direction at the endpoint)\n",
" end_nodes = [(end[0], end[1], d) for d in DIRECTIONS]\n",
" shortest_cost = float('inf')\n",
" best_path = None\n",
"\n",
" # Evaluate paths to all possible orientations at the endpoint\n",
" for end_node in end_nodes:\n",
" try:\n",
" path = nx.shortest_path(graph, source=start, target=end_node, weight='weight')\n",
" cost = nx.shortest_path_length(graph, source=start, target=end_node, weight='weight')\n",
" if cost < shortest_cost:\n",
" shortest_cost = cost\n",
" best_path = path\n",
" except nx.NetworkXNoPath:\n",
" continue\n",
" return best_path, shortest_cost\n",
" except nx.NetworkXNoPath:\n",
" return None, float('inf')\n",
"\n",
"# Example ASCII map\n",
"with open('input','r') as infile:\n",
" ascii_map = infile.read()\n",
"\n",
"# Parse the map and solve\n",
"graph, start, end = parse_ascii_map_with_costs(ascii_map)\n",
"path, cost = find_shortest_path_with_costs(graph, start, end)\n",
"\n",
"# Output the results\n",
"path, cost\n"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Minimum Cost to Reach the End: 135512\n"
]
}
],
"source": [
"import heapq\n",
"\n",
"# Define directions and corresponding movements\n",
"DIRECTIONS = ['N', 'E', 'S', 'W']\n",
"MOVEMENTS = {\n",
" 'N': (0, -1), # Move up\n",
" 'E': (1, 0), # Move right\n",
" 'S': (0, 1), # Move down\n",
" 'W': (-1, 0) # Move left\n",
"}\n",
"\n",
"def solve_maze_with_costs(ascii_map):\n",
" rows = ascii_map.strip().split(\"\\n\")\n",
" height, width = len(rows), len(rows[0])\n",
"\n",
" # Find start and end positions\n",
" start, end = None, None\n",
" for y, row in enumerate(rows):\n",
" for x, char in enumerate(row):\n",
" if char == 'S':\n",
" start = (x, y, 'E') # Start facing North\n",
" elif char == 'E':\n",
" end = (x, y)\n",
" \n",
" # Priority queue for Dijkstra's algorithm\n",
" pq = []\n",
" heapq.heappush(pq, (0, start)) # (cost, (x, y, direction))\n",
"\n",
" # Visited states: {(x, y, direction): cost}\n",
" visited = {}\n",
"\n",
" while pq:\n",
" cost, (x, y, direction) = heapq.heappop(pq)\n",
"\n",
" # Goal check: If we reach the endpoint\n",
" if (x, y) == end:\n",
" return cost\n",
"\n",
" # Avoid revisiting with higher cost\n",
" if (x, y, direction) in visited and visited[(x, y, direction)] <= cost:\n",
" continue\n",
" visited[(x, y, direction)] = cost\n",
"\n",
" # 1. Move forward\n",
" dx, dy = MOVEMENTS[direction]\n",
" nx, ny = x + dx, y + dy\n",
" if 0 <= nx < width and 0 <= ny < height and rows[ny][nx] != '#':\n",
" heapq.heappush(pq, (cost + 1, (nx, ny, direction)))\n",
"\n",
" # 2. Rotate clockwise\n",
" next_direction = DIRECTIONS[(DIRECTIONS.index(direction) + 1) % 4]\n",
" heapq.heappush(pq, (cost + 1000, (x, y, next_direction)))\n",
"\n",
" # 3. Rotate counterclockwise\n",
" prev_direction = DIRECTIONS[(DIRECTIONS.index(direction) - 1) % 4]\n",
" heapq.heappush(pq, (cost + 1000, (x, y, prev_direction)))\n",
" \n",
" return float('inf') # No path found\n",
"\n",
"# Example ASCII map\n",
"with open('input','r') as infile:\n",
" ascii_map = infile.read()\n",
"\n",
"# Solve the maze\n",
"cost = solve_maze_with_costs(ascii_map)\n",
"print(\"Minimum Cost to Reach the End:\", cost)\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
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