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cube_solver.py
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cube_solver.py
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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Wed Apr 7 15:05:06 2021
@author: syxtreme
"""
import pandas as pd
import numpy as np
import argparse
from warnings import warn
from python_tsp.exact import solve_tsp_dynamic_programming
from matplotlib import pyplot as plt
from uuid import uuid4
class Direction():
"""Class to store and manipulate directions.
"""
STAY = "stay"
UP = "up"
DOWN = "down"
LEFT = "left"
RIGHT = "right"
FORWARDS = "forwards"
BACKWARDS = "backwards"
""" O U
O O F R
O O L B
O D
"""
LIST = [ # list ordered according to portals
"forwards", "up", "right",
"left", "down", "backwards"
]
@classmethod
def invert(cls, direction): # returns the inverse of a direction
if direction == cls.STAY:
return cls.STAY
if direction == cls.UP:
return cls.DOWN
if direction == cls.DOWN:
return cls.UP
if direction == cls.LEFT:
return cls.RIGHT
if direction == cls.RIGHT:
return cls.LEFT
if direction == cls.FORWARDS:
return cls.BACKWARDS
if direction == cls.BACKWARDS:
return cls.FORWARDS
class Cell():
"""Class to store information about the individual cells
"""
M_MANHATAN = 1
M_EUCLID = 2
M_EUCLID_SQ = 3
useMetric = M_EUCLID # metric for the heuristic function
def __init__(self, number, cube):
"""Initialize a cell
Parameters
----------
number : int
The cell number.
cube : Cube
The parent cube object.
"""
self._number = number
self._cube = cube
self._neighbors = {key: None for key in Direction.LIST} # create an empty neighbor list
self._pos = None # 3D position is unknown, should be assigned later using "set_pos"
def set_pos(self, x, y, z):
""" Set position in the cube, in 3D coordinate system.
X-axis corresponds to LEFT-RIGHT (right is positive)
Y-axis corresponds to DOWN-UP (down is positive)
Z-axis corresponds to FORWARDS-BACKWARDS (forward is positive)
Parameters
----------
x : int
y : int
z : int
"""
self._cube.grid[x, y, z] = self
self._pos = np.r_[x, y, z]
def set_goal(self, goal):
"""Set goal and initialize for path search.
Parameters
----------
goal : Cell
A goal for the path search.
"""
if type(goal) is not Cell:
goal = self._cube[goal]
self._goal = goal
self.route = 0
self.parent = None
self._heuristic = self.__heuristicFunction()
def _add_neighbor(self, number, direction):
"""Adds a neighbor for the cell.
Parameters
----------
number : int
The number of the neighboring cell.
direction : str (Direction)
The direction of the neighbor from this cell.
"""
if number not in self._cube:
self._cube.create_cell(number)
self._neighbors[direction] = self._cube[number]
def __getitem__(self, direction):
return self._neighbors[direction]
def __setitem__(self, direction, number):
self._add_neighbor(number, direction)
@property
def number(self):
return self._number
@property
def pos(self):
return self._pos
@property
def neighbors(self):
return self._neighbors
@property
def heuristic(self):
return self._heuristic
@property
def value(self):
return self.route + self.heuristic
def __heuristicFunction(self):
# A function to compute distance estimate to the goal
d = self.pos - self._goal.pos
if self.useMetric == self.M_MANHATAN:
return np.sum(d)
elif self.useMetric == self.M_EUCLID:
return np.linalg.norm(d)
class Cube():
"""A class that holds the information about the cube.
"""
SIDE = 6 # number of cells per side
MAX_DIST = 12 # fixed max distance search parameter
USE_FIXED_MAX_DIST = False # True if MAX_DIST should be used instead of the maxDist from data
def __init__(self):
self.cells = np.empty((self.SIDE**3, ), dtype=np.object) # create a linear list of cells
self.grid = np.empty((self.SIDE, self.SIDE, self.SIDE), dtype=np.object) # create 3D grid of cells
def add_cell(self, cell):
"""Adds an existing cell to the cube.
Parameters
----------
cell : Cell
A cell.
"""
self.cells[cell.number - 1] = cell
def create_cell(self, cell_number):
"""Creates and adds a new cell to the cube.
Parameters
----------
cell_number : int
The number of the cell.
"""
self.add_cell(Cell(cell_number, self))
def __getitem__(self, key):
# Convenience function to get a cell by its number
if type(key) is int:
return self.cells[key - 1]
# return next((c for c in self.cells if c is not None and c.number == key))
elif type(key) is tuple:
return self.grid[key]
def __contains__(self, obj):
if type(obj) is Cell:
return obj in self.cells
if type(obj) is int:
return self[obj] is not None
# def __setitem__(self, key, val):
# if type(key) is int:
# cell = next((c in self.cells if c.number == key))
# cell
# elif type(key) is tuple:
# return self.grid[key]
def _gridify(self, cell, x, y, z):
# A recursive function that organizes all known cells to a 3D grid.
# Probably...
setattr(cell, "visited", True) # this is to know that a cell was already processed
# Next, some conditions to wrap around the cube.
if x < 0:
x = self.SIDE - 1
if y < 0:
y = self.SIDE - 1
if z < 0:
z = self.SIDE - 1
if x >= self.SIDE:
x = 0
if y >= self.SIDE:
y = 0
if z >= self.SIDE:
z = 0
cell.set_pos(x, y, z) # set cell 3D position and add it to the grid
for d, n in cell.neighbors.items(): # for all neighbors
if n is None or hasattr(n, "visited"): # if not processed before
continue
# got to the neighbor, change grid pos and process it
if d == Direction.UP:
self._gridify(n, x, y - 1, z)
if d == Direction.DOWN:
self._gridify(n, x, y + 1, z)
if d == Direction.LEFT:
self._gridify(n, x - 1, y, z)
if d == Direction.RIGHT:
self._gridify(n, x + 1, y, z)
if d == Direction.FORWARDS:
self._gridify(n, x, y, z + 1)
if d == Direction.BACKWARDS:
self._gridify(n, x, y, z - 1)
def construct_grid(self):
"""Assigns all known cells to their positions in 3D grid
"""
startn = self[1]
self._gridify(startn, 0, 0, 0)
for c in self.cells: # cleanup
if c is not None:
delattr(c, "visited")
def search(self, start_number, goal_number, silent=True):
"""Searches for a shortest path from the start to the goal.
Parameters
----------
start : int
Starting cell number
goal_number : int
Goal cell number
silent : bool, optional
Returns
-------
tuple(list, list)
path = list of cells to go through (including the start and the goal cells).
directions = list of directions to take to go from the start to the goal.
"""
if start_number not in self: # if start_number is not yet in the cube
warn("The starting cell is not yet known!")
return
if goal_number not in self:
warn("The goal cell is not yet known!")
return
# some preparations
maxDist = 0
goal = self[goal_number]
for c in self.cells:
if c is not None:
c.set_goal(goal)
maxDist += 1
# this function does the actual search
# The node is the last cell in search, so should be the goal cell.
node = self.__searchPath(start_number, maxDist)
# if the search yielded no result or the result is not the goal.
if node is None or node.number != goal_number:
warn("Search did not find any path!")
return
path = []
directions = []
while node.parent: # trace backwards from the goal to the start
path.append(node)
node = node.parent
path.append(self[start_number]) # add the starting cell
path.reverse() # invert so that the path is from start to goal
n = len(path)
for i, node in enumerate(path): # generate directions
if i < n - 1:
next_num = path[i + 1].number
else:
break
directions.append(next((k for k, v in node.neighbors.items() if v.number == next_num)))
if not silent:
print("Found path\nPath length = {}\nUsed metric: {}.".format(len(path), Cell.useMetric))
return path, directions
def __searchPath(self, start, maxDist):
# This is an implementation of an A* algorithm.
ol = list() # open list
cl = list() # closed list
ol.append(self[start])
if self.USE_FIXED_MAX_DIST:
maxDist = self.MAX_DIST
limit = 0
while True:
best = self.__findClosest(ol, maxDist)
if best is None:
warn("Open list is empty, could not find path!")
return
if best.heuristic == 0:
break
ol.remove(best)
cl.append(best)
for n in best.neighbors.values():
if not self.__inlist(n, cl) and not self.__inlist(n, ol):
n.route = best.route + 1
n.parent = best
ol.append(n)
limit += 1
if limit > maxDist:
warn(f"Distance limit of {maxDist} reached, could not find path!")
return
return best
def __findClosest(self, li, maxDist):
# Helper function for the search
val = maxDist
best = None
for n in li:
if n.value < val:
val = n.value
best = n
return best
def __inlist(self, node, li):
# Helper function for the search
for n in li:
if np.all(n.pos == node.pos):
return True
return False
def getPath(self, points):
"""Function to find path that goes through all requested points/cells.
When only two numbers are provided (go from X to Y), a simple A* is used.
When more numbers are provided, all-vs-all distances are computed and
a TSP (traveling salesman problem) optimization is done to find the shortest
route through all nodes.
Parameters
----------
points : list of ints
List of cell numbers to go through.
Returns
-------
tuple(list, list)
A tuple of two lists. The first lists contains all the cell numbers on the path.
The second list contains directions to take to go through all the cells.
"""
n_points = len(points)
if n_points == 0:
warn(f"No point provided, nothing to do!")
else:
for p in points: # check if all the points are known
if p not in self:
warn(f"The cell number {p} is not yet known!")
return
if n_points == 1:
warn(f"Only one point provided! To go from cell {points[0]} to {points[0]}, simply do nothing!")
return [self[points[0]], self[points[0]]], [Direction.STAY]
elif n_points == 2:
try:
path, directions = self.search(points[0], points[1])
except Exception as e:
warn(f"I can't find a path from {points[0]} to {points[1]}!")
return
else:
print(f"To go from {points[0]} to {points[1]}, use these directions:\n\t{directions}\n\tPath = {[c.number for c in path]}")
return path, directions
elif n_points > 2:
paths = {} # helper vars to keep the partial results
dirs = {}
dmat = np.zeros((n_points, n_points)) # compute a pair-wise distance matrix
for i in range(n_points):
for j in range(i + 1, n_points):
try:
path, directions = self.search(points[i], points[j])
except Exception as e:
continue
paths[(i, j)] = path
paths[(j, i)] = list(reversed(path)) # inverse is the same but inverted
dirs[(i, j)] = directions
dirs[(j, i)] = [Direction.invert(d) for d in reversed(directions)]
dmat[i, j] = len(directions)
dmat[j, i] = len(directions)
dmat[:, 0] = 0 # needed to solve open TSP
# print(dmat)
nodes, distance = solve_tsp_dynamic_programming(dmat) # magic
t_directions = []
t_path = []
# generate path and directions from the TSP result
for i, (a, b) in enumerate(zip(nodes[:-1], nodes[1:])):
t_directions += dirs[a, b]
if i == 0:
t_path += paths[a, b]
else:
t_path += paths[a, b][1:]
t_path_numbers = [c.number for c in t_path]
all_in = True
for p in points: # check if the path really contains all the points
if p not in t_path_numbers:
all_in = False
break
if not all_in:
warn(f"Could not find a path connecting al the points!")
return
print(f"To go through {points}, use these directions:\n\t{t_directions}\n\tPath = {t_path_numbers}")
return t_path, t_directions
@property
def all_known(self): # Returns True if all cells are known
return not np.any([c is None for c in self.cells])
@property
def is_complete(self): # Returns True if all cells are known and all their neighbors are known
return not np.any([c is None or np.any([n is None for n in c.neighbors.values()]) for c in self.cells])
# %%
parser = argparse.ArgumentParser()
parser.add_argument("input_table", help="CSV file to be processed.")
parser.add_argument("--points", "-p", help="Point of the path", type=int, nargs="+")
parser.add_argument("--draw", "-d", help="Draws the slices of the cube.", action="store_true")
parser.add_argument("--draw-gates", "-g", help="Draws the slices of the cube with gates", action="store_true")
# args = parser.parse_args(["Mapa CUBE - Hárok1.csv"] + "-p 15 63".split())
# args = parser.parse_args(["Mapa CUBE - Hárok1.csv"] + "-p 15 63 86".split())
# args = parser.parse_args(["Mapa CUBE - Hárok1.csv"] + "-p 15 63 86 104 178".split())
# args = parser.parse_args(["Mapa CUBE - Hárok1.csv", "-g"])
# args = parser.parse_args()
table = pd.read_csv(args.input_table, header=None)
columns, rows = np.ogrid[0:len(table.columns):3, 0:table.index.stop:3]
cube = Cube()
for r in rows.ravel():
for c in columns.ravel():
if cube.is_complete:
break
data = table.iloc[r:r+3, c:c+3]
if not data.shape == (3, 3):
continue
cell_num = data.iloc[1, 1]
if np.isnan(cell_num): # invalid cell
continue
cell_num = int(cell_num)
neighbors = pd.concat((data.iloc[0, 0:3], data.iloc[2, 0:3])).to_numpy()
if np.any(np.isnan(neighbors)): # also invalid
continue
neighbors = neighbors.astype(np.int).tolist()
if cell_num not in cube:
cube.create_cell(cell_num)
cell = cube[cell_num]
for n, d in zip(neighbors, Direction.LIST):
cell[d] = n
cube.construct_grid()
#%%
# path, directions = cube.search(1, 216)
# print(directions)
# print([c.number for c in path])
if args.draw:
fig, axs = plt.subplots(2, 3)
i = 0
for rax in axs:
for ax in rax:
ax.axis('tight')
ax.axis('off')
plane = []
for row in cube.grid[:, :, i]:
plane.append([c.number for c in row])
ax.table(plane,loc='center')
i += 1
plt.savefig(f"{uuid4()}.png")
if args.draw_gates:
for i in range(cube.SIDE):
fig, ax = plt.subplots()
ax.axis('tight')
ax.axis('off')
plane = []
for row in cube.grid[:, :, i]:
line = []
for c in row:
nn = np.asanyarray([c[d].number
for d in Direction.LIST]).reshape(2, 3)
elem = np.vstack([nn[0], [0, c.number, 0], nn[1]])
line.append(elem)
plane.append(np.hstack(line))
plane = np.vstack(plane)
ax.table(plane.tolist(), loc='center')
plt.savefig(f"{uuid4()}_{i}.png")
if args.points is not None:
points = np.asarray(args.points).ravel().tolist()
print(f"Path points: {points}")
cube.getPath(points)