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MCS 275 Spring 2023 Homework 6 (method 2)
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def depth_first_
maze_solution
(M,path=None,verbose=False):
def depth_first_
all_
maze_solution
s
(M,path=None,verbose=False):
"""
"""
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Find
solution
to Maze `M` that begin
s
with `path` (if given),
Find
all
solution
s
to Maze `M` that begin
with `path` (if given),
returning
either that solution as
a
list
of Point2 objects or
returning
a list where every entry is itself
a
sub
list
representing a
None if no such
solution
exists
.
single
solution
to the maze
.
"""
"""
if path == None:
if path == None:
# no path was specified, initialize it with [M.start]
# no path was specified, initialize it with [M.start]
path = [ M.start ]
path = [ M.start ]
if verbose:
if verbose:
print("Considering:",path)
print("Considering:",path)
if path[-1] == M.goal:
if path[-1] == M.goal:
# path ends with goal, meaning it's a solution
# path ends with goal, meaning it's a solution
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return
path
return
[path] # Put the
path
into a list
possible_next_locations = M.free_neighbors(path[-1])
possible_next_locations = M.free_neighbors(path[-1])
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solutions = []
for x in possible_next_locations:
for x in possible_next_locations:
if x in path:
if x in path:
# skip x
# skip x
continue # do not execute the rest of the loop body
continue # do not execute the rest of the loop body
# immediately begin the next iteration.
# immediately begin the next iteration.
# x should be considered
# x should be considered
new_path = path + [x]
new_path = path + [x]
# Ask for a solution that continues from new_path
# Ask for a solution that continues from new_path
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solution = depth_first_
maze_solution
(M,new_path,verbose)
solution = depth_first_
all_
maze_solution
s
(M,new_path,verbose)
if
solution
: # None is falsy, while a nonempty list is truthy
if
len(
solution
) > 0:
return
solution
solutions.extend(solution) # Keep all
solution
s found from recursive call
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# What now? If we end up here, it means no next step leads to a solution
# Always return our list of solutions (which may be empty)
# Hence `path` leads to only dead ends
return
solutions
# We therefore BACKTRACK
if verbose:
print("GIVING UP ON:",path)
return
None
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def depth_first_maze_solution(M,path=None,verbose=False): """ Find solution to Maze `M` that begins with `path` (if given), returning either that solution as a list of Point2 objects or None if no such solution exists. """ if path == None: # no path was specified, initialize it with [M.start] path = [ M.start ] if verbose: print("Considering:",path) if path[-1] == M.goal: # path ends with goal, meaning it's a solution return path possible_next_locations = M.free_neighbors(path[-1]) for x in possible_next_locations: if x in path: # skip x continue # do not execute the rest of the loop body # immediately begin the next iteration. # x should be considered new_path = path + [x] # Ask for a solution that continues from new_path solution = depth_first_maze_solution(M,new_path,verbose) if solution: # None is falsy, while a nonempty list is truthy return solution # What now? If we end up here, it means no next step leads to a solution # Hence `path` leads to only dead ends # We therefore BACKTRACK if verbose: print("GIVING UP ON:",path) return None
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def depth_first_all_maze_solutions(M,path=None,verbose=False): """ Find all solutions to Maze `M` that begin with `path` (if given), returning a list where every entry is itself a sublist representing a single solution to the maze. """ if path == None: # no path was specified, initialize it with [M.start] path = [ M.start ] if verbose: print("Considering:",path) if path[-1] == M.goal: # path ends with goal, meaning it's a solution return [path] # Put the path into a list possible_next_locations = M.free_neighbors(path[-1]) solutions = [] for x in possible_next_locations: if x in path: # skip x continue # do not execute the rest of the loop body # immediately begin the next iteration. # x should be considered new_path = path + [x] # Ask for a solution that continues from new_path solution = depth_first_all_maze_solutions(M,new_path,verbose) if len(solution) > 0: solutions.extend(solution) # Keep all solutions found from recursive call # Always return our list of solutions (which may be empty) return solutions
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