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tracks.py
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tracks.py
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from enum import Enum
from time import perf_counter
import turtle
FONT = ("sans-serif", 18, "normal")
DEBUG = False
class Track(Enum):
NE = 1
SE = 2
SW = 3
NW = 4
NS = 5
EW = 6
TEMP = 7
@classmethod
def identify(cls, str):
""" return matching enum from 2 char string, order undefined"""
for tr in cls:
if str[0] in tr.name and str[1] in tr.name:
return tr
class Cell:
def __init__(self, row, col, cell_size):
self.cell_size = cell_size
self.x = col * self.cell_size + self.cell_size / 2
self.y = row * self.cell_size + self.cell_size / 2
self.row = row
self.col = col
self.permanent = False
self.track = None
self.must_connect = ""
self.is_start = False
self.is_end = False
def __str__(self):
return f"R:{self.row} C:{self.col} {self.content} {self.track}"
def is_empty(self):
return self.track is None
def has_dir(self, dir):
if self.track:
return dir in self.track.name
def draw_border(self, t):
t.pensize(1)
t.setpos(self.x, self.y)
t.pendown()
t.color("gray")
if DEBUG:
t.write(f" {self.row},{self.col}", font=FONT)
t.setheading(0)
t.forward(self.cell_size)
t.left(90)
t.forward(self.cell_size)
t.left(90)
t.forward(self.cell_size)
t.left(90)
t.forward(self.cell_size)
t.penup()
def draw_track(self, t, erase=False):
""" Draw the track piece in the cell """
s = self.cell_size
s2 = s / 2
x1 = self.x + s2
x2 = self.x + s
y1 = self.y + s2
y2 = self.y + s
t.pensize(4)
t.penup()
if DEBUG and self.must_connect:
t.goto(x1, y1)
t.write(self.must_connect, font=FONT)
if self.track:
color = "white" if erase else "black"
if self.permanent:
color = "blue"
t.color(color)
if self.track == Track.NS:
t.setheading(90)
t.goto(x1, self.y)
t.pendown()
t.forward(s)
elif self.track == Track.EW:
t.setheading(0)
t.goto(self.x, y1)
t.pendown()
t.forward(s)
elif self.track == Track.NE:
t.goto(x1, y2)
t.pendown()
t.goto(x1, y1)
t.goto(x2, y1)
elif self.track == Track.SE:
t.goto(x1, self.y)
t.pendown()
t.goto(x1, y1)
t.goto(x2, y1)
elif self.track == Track.NW:
t.goto(x1, y2)
t.pendown()
t.goto(x1, y1)
t.goto(self.x, y1)
elif self.track == Track.SW:
t.goto(x1, self.y)
t.pendown()
t.goto(x1, y1)
t.goto(self.x, y1)
t.penup()
turtle.update()
class Layout:
def __init__(self, size=8):
self.size = size
self.scr = turtle.Screen()
self.scr.title("Train tracks")
self.turtle = turtle.Turtle()
turtle.mode("standard")
turtle.screensize(1000, 1000)
self.screen_size = 1000
self.cell_size = self.screen_size / (size + 1)
turtle.setworldcoordinates(0, 0, self.screen_size, self.screen_size)
self.turtle.hideturtle()
self.turtle.speed("fast")
turtle.delay(0)
turtle.tracer(0, 0)
self.turtle.penup()
self.layout = []
for row in range(size):
col_list = []
for col in range(size):
col_list.append(Cell(row, col, self.cell_size))
self.layout.append(col_list)
self.start = 0
self.end = 0
self.move_count = 0
self.move_max = 1000000
self.col_count = []
self.row_count = []
self.col_perm = []
self.row_perm = []
def draw(self, moves=False):
""" Draw the whole layout """
for row in range(self.size):
for col in range(self.size):
cell = self.layout[row][col]
cell.draw_border(self.turtle)
if moves:
s = self.cell_size / 6
self.turtle.goto(cell.x + s, cell.y + s)
self.turtle.write(self.moves(cell))
cell.draw_track(self.turtle)
turtle.update()
row = self.size
self.turtle.color("black")
# Numbers across the top
for col in range(self.size):
x, y = self.coords(row, col)
self.turtle.setpos(x + self.cell_size / 3, y)
self.turtle.write(self.col_constraints[col], font=FONT)
col = self.size
# Numbers down right side
for row in range(self.size - 1, -1, -1):
x, y = self.coords(row, col)
self.turtle.setpos(x + self.cell_size / 6, y + self.cell_size / 3)
self.turtle.write(self.row_constraints[row], font=FONT)
# start and end
x, y = self.coords(self.start, 0)
self.turtle.setpos(x - self.cell_size / 3, y + self.cell_size / 3)
self.turtle.write("A", font=FONT)
x, y = self.coords(0, self.end)
self.turtle.setpos(x + self.cell_size / 3, y - self.cell_size / 2)
self.turtle.write("B", font=FONT)
turtle.update()
def coords(self, row, col):
""" Convert row, column to screen coordinates """
x = col * self.cell_size + self.cell_size / 2
y = row * self.cell_size + self.cell_size / 2
return x, y
def draw_moves(self, cell):
""" debug routine to list all possible moves from a cell """
self.turtle.goto(cell.x, cell.y)
self.turtle.write(self.moves(cell))
def set_constraints(self, values):
""" Takes string of numbers representing top and right side """
v = list(values)
self.col_constraints = [int(i) for i in v[: self.size]]
right = v[self.size :]
right.reverse()
self.row_constraints = [int(i) for i in right]
def add_track(self, track, row, col, start=False, end=False):
"""
Add a permanent piece of track to the layout
Start and end are special cases
"""
cell = self.layout[row][col]
cell.permanent = True
cell.track = Track[track]
if start:
if col != 0:
raise ValueError("Invalid start position")
self.start = row
cell.is_start = True
if end:
if row != 0:
raise ValueError("Invalid end position")
self.end = col
cell.is_end = True
# determine adjacent cells that must connect
if "N" in track:
self.layout[row + 1][col].must_connect += "S"
if "S" in track and row > 0:
self.layout[row - 1][col].must_connect += "N"
if "W" in track and col > 0:
self.layout[row][col - 1].must_connect += "E"
if "E" in track:
self.layout[row][col + 1].must_connect += "W"
def moves(self, cell):
""" return a list of possible moves from a cell """
result = []
r1 = cell.row - 1
r2 = cell.row + 1
c1 = cell.col - 1
c2 = cell.col + 1
if r2 < self.size and (not cell.track or cell.has_dir("N")):
new_cell = self.layout[r2][cell.col]
if not new_cell.track or new_cell.has_dir("S"):
result.append("N")
if r1 >= 0 and (not cell.track or cell.has_dir("S")):
new_cell = self.layout[r1][cell.col]
if not new_cell.track or new_cell.has_dir("N"):
result.append("S")
if c1 >= 0 and (not cell.track or cell.has_dir("W")):
new_cell = self.layout[cell.row][c1]
if not new_cell.track or new_cell.has_dir("E"):
result.append("W")
if c2 < self.size and (not cell.track or cell.has_dir("E")):
new_cell = self.layout[cell.row][c2]
if not new_cell.track or new_cell.has_dir("W"):
result.append("E")
if cell.is_start and "W" in result:
result.remove("W")
if cell.is_end and "S" in result:
result.remove("S")
return result
def check_constraints(self, exact=False):
""" Returns true if all cell counts within limits """
self.row_count = (
[]
) # difference between actual count of occupied cells and expected count
self.row_perm = [] # number of permanent cells in this row
self.col_count = []
self.col_perm = []
for row in range(self.size):
count = 0
perm = 0
for col in range(self.size):
cell = self.layout[row][col]
if cell.track:
count += 1
if cell.permanent:
perm += 1
if exact:
if cell.must_connect and not cell.track:
if DEBUG:
print("Must connect failure")
return False
self.row_count.append(self.row_constraints[row] - count)
self.row_perm.append(perm)
if exact:
if count != self.row_constraints[row]:
if DEBUG:
print(
f"Exact Row {row} failure {count} != {self.row_constraints[row]}"
)
return False
elif count > self.row_constraints[row]:
if DEBUG:
print(f"Row {row} failure {count} > {self.row_constraints[row]}")
return False
for col in range(self.size):
count = 0
perm = 0
for row in range(self.size):
cell = self.layout[row][col]
if cell.track:
count += 1
if cell.permanent:
perm += 1
self.col_count.append(self.col_constraints[col] - count)
self.col_perm.append(perm)
if exact:
if count != self.col_constraints[col]:
if DEBUG:
print(
f"Exact column {col} failure {count} != {self.col_constraints[col]}"
)
return False
elif count > self.col_constraints[col]:
if DEBUG:
print(f"Column {col} failure {count} > {self.col_constraints[col]}")
return False
return True
def not_trapped(self, cell):
""" Return false if trapped one side of a full row or col and need to get to the other side """
for c in range(1, self.size - 1):
if self.col_count[c] == 0:
# ignore cols with a permanent track - if not connected, it may be a path back to other side
if self.col_perm[c] == 0:
if cell.col < c:
for i in range(c + 1, self.size):
if self.col_count[i] > 0:
return False
elif cell.col > c:
for i in range(0, c):
if self.col_count[i] > 0:
return False
for r in range(1, self.size - 1):
if self.row_count[r] == 0:
# ignore rows with a permanent track - if not connected, it may be a path back to other side
if self.row_perm[r] == 0:
if cell.row < r:
for i in range(r + 1, self.size):
if self.row_count[i] > 0:
return False
if cell.row > r:
for i in range(0, 2):
if self.row_count[i] > 0:
return False
return True
def done(self, cell):
if cell.row == 0 and cell.col == self.end:
if self.check_constraints(exact=True):
return True
return False
def move_from(self, cell, dir):
""" move from cell in direction dir """
self.move_count += 1
if self.move_count == self.move_max:
raise ValueError("Max move count reached")
# if self.move_count == 8400:
# self.draw()
# breakpoint()
if DEBUG:
cell.draw_track(self.turtle)
if dir == "N":
from_dir = "S"
new_cell = self.layout[cell.row + 1][cell.col]
elif dir == "S":
from_dir = "N"
new_cell = self.layout[cell.row - 1][cell.col]
elif dir == "E":
from_dir = "W"
new_cell = self.layout[cell.row][cell.col + 1]
elif dir == "W":
from_dir = "E"
new_cell = self.layout[cell.row][cell.col - 1]
undo = False
# temporarily add a track if empty so can calculate constraints
if not new_cell.track:
new_cell.track = Track.TEMP
if self.done(new_cell):
raise ValueError("Solved")
if self.check_constraints():
if self.not_trapped(new_cell):
if new_cell.track == Track.TEMP:
new_cell.track = None
moves = self.moves(new_cell)
if from_dir in moves:
moves.remove(from_dir)
bad_move = False
# must connect cells are special case not handled in move generation
if new_cell.must_connect:
if from_dir in new_cell.must_connect:
to_dir = new_cell.must_connect.replace(from_dir, "")
if to_dir:
moves = to_dir
else:
if len(new_cell.must_connect) == 1:
moves = new_cell.must_connect
else:
# must connect cell is already fully connected
bad_move = True
if not bad_move:
# Recursively explore each possible move, depth first
for to_dir in moves:
if not new_cell.track:
new_cell.track = Track.identify(from_dir + to_dir)
self.move_from(new_cell, to_dir)
else:
if DEBUG:
print("Would be trapped")
# Get here if all moves fail and we need to backtrack
if not new_cell.permanent:
new_cell.track = None
if not cell.permanent:
if DEBUG:
cell.draw_track(self.turtle, erase=True)
cell.track = None
def solve(self):
""" Initiate the recursive solver """
new_cell = self.layout[self.start][0]
moves = self.moves(new_cell)
for to_dir in moves:
self.move_from(new_cell, to_dir)
raise ValueError("Failed to find solution")
def result(self, message, elapsed):
self.draw()
self.turtle.goto(0, 0)
self.turtle.color("black")
self.turtle.write(
f"{message} in {self.move_count} moves. Time:{elapsed:.2f}s", font=FONT
)
self.scr.textinput("Done", "Hit key")
def parse(params):
"""
Structure: Size:Constraints:track-tuple:track-tuple
"""
bits = params.split(":")
size = int(bits[0])
if len(bits[1]) != 2 * size:
raise ValueError("Params wrong - 1")
l = Layout(size)
l.set_constraints(bits[1])
for i in range(2, len(bits)):
c = bits[i]
start = False
end = False
if len(c) == 5:
if c[4] == "s":
start = True
elif c[4] == "e":
end = True
else:
raise ("Params wrong - 2")
l.add_track(c[:2], int(c[2]), int(c[3]), start=start, end=end)
return l
def main():
board = parse("8:2464575286563421:NW60s:SE72:EW24:NS04e") #904
# board = parse("8:3456623347853221:NW30s:SW32:SW62:NS04e") #907
# board = parse("8:8443143523676422:NW00s:NE41:NS45:NS07e") #908
# board = parse("8:1216564534576221:EW40s:NS03e:NS45") #909
# board = parse("8:1225446636611544:EW60s:NS03e:EW75:SE26") #910
# board = parse("8:4533433525853421:SW40s:NE52:NS03e")
board.draw()
try:
start = perf_counter()
board.solve()
except ValueError as e:
end = perf_counter()
elapsed = end - start
board.result(str(e), elapsed)
if __name__ == "__main__":
main()