AI Tile Puzzle Solver
An AI that takes an unsolved tile puzzle and optimally solves the puzzle
Introduction
This was another project for my Artificial Intelligence class, where I was tasked with using my understanding of different search strategies and the ramificatinos of using different heurisitcs to solve a modified version of the classic 8 tile puzzle. The puzzle exists on a 3x3 grid with one open āblankā space. The goal state is where the open tile is on the top left, followed by all the tiles in numerical order.
The program takes randomly generated puzzles and uses search strategies to optimally solve it.
Search Strategies
I implemented Uniform-Cost, Greedy best-first and A* search to find the shortest path to the goal.
The searches are implemented following the heurisitcs, ānumber of misplced tilesā, āManhattan Distanceā and a modified Manhattan distance that takes into account the different transition costs. Each strategy is then compared to how the basic Breadth First Search would solve the puzzle.
Code
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from queue import PriorityQueue
import sys
import puzz
import pdqpq
GOAL_STATE = puzz.EightPuzzleBoard("012345678")
def solve_puzzle(start_state, flavor):
"""Perform a search to find a solution to a puzzle.
Args:
start_state (EightPuzzleBoard): the start state for the search
flavor (str): tag that indicate which type of search to run. Can be one of the following:
'bfs' - breadth-first search
'ucost' - uniform-cost search
'greedy-h1' - Greedy best-first search using a misplaced tile count heuristic
'greedy-h2' - Greedy best-first search using a Manhattan distance heuristic
'greedy-h3' - Greedy best-first search using a weighted Manhattan distance heuristic
'astar-h1' - A* search using a misplaced tile count heuristic
'astar-h2' - A* search using a Manhattan distance heuristic
'astar-h3' - A* search using a weighted Manhattan distance heuristic
Returns:
A dictionary containing describing the search performed, containing the following entries:
'path' - list of 2-tuples representing the path from the start to the goal state (both
included). Each entry is a (str, EightPuzzleBoard) pair indicating the move and
resulting successor state for each action. Omitted if the search fails.
'path_cost' - the total cost of the path, taking into account the costs associated with
each state transition. Omitted if the search fails.
'frontier_count' - the number of unique states added to the search frontier at any point
during the search.
'expanded_count' - the number of unique states removed from the frontier and expanded
(successors generated)
"""
if flavor.find('-') > -1:
strat, heur = flavor.split('-')
else:
strat, heur = flavor, None
if strat == 'bfs':
return BreadthFirstSolver(GOAL_STATE).solve(start_state)
elif strat == 'ucost':
return UniformCostSolver(GOAL_STATE).solve(start_state)
elif strat == 'greedy':
return GreedySolver(GOAL_STATE).solve(start_state)
elif strat == 'astar':
return AStarSolver(GOAL_STATE, heur).solve(start_state)
# elif strat == 'astar-h1':
# return AStarSolver(GOAL_STATE).solve(start_state,'h1')
#
# elif strat == 'astar-h2':
# return AStarSolver(GOAL_STATE).solve(start_state,'h2')
#
# elif strat == 'astar-h3':
# return AStarSolver(GOAL_STATE).solve(start_state,'h3')
else:
raise ValueError("Unknown search flavor '{}'".format(flavor))
def get_test_puzzles():
"""Return sample start states for testing the search strategies.
Returns:
A tuple containing three EightPuzzleBoard objects representing start states that have an
optimal solution path length of 3-5, 10-15, and >=25 respectively.
"""
#
# fill in function body here
#
move_in_three = puzz.EightPuzzleBoard("312459678")
move_in_ten = puzz.EightPuzzleBoard("320518467")
move_in_twenty_five = puzz.EightPuzzleBoard("876021534")
return move_in_three, move_in_ten, move_in_twenty_five # fix this line!
def print_table(flav__results, include_path=False):
"""Print out a comparison of search strategy results.
Args:
flav__results (dictionary): a dictionary mapping search flavor tags result statistics. See
solve_puzzle() for detail.
include_path (bool): indicates whether to include the actual solution paths in the table
"""
result_tups = sorted(flav__results.items())
c = len(result_tups)
na = "{:>12}".format("n/a")
rows = [ # abandon all hope ye who try to modify the table formatting code...
"flavor " + "".join(["{:>12}".format(tag) for tag, _ in result_tups]),
"--------" + (" " + "-" * 10) * c,
"length " + "".join(["{:>12}".format(len(res['path'])) if 'path' in res else na
for _, res in result_tups]),
"cost " + "".join(["{:>12,}".format(res['path_cost']) if 'path_cost' in res else na
for _, res in result_tups]),
"frontier" + ("{:>12,}" * c).format(*[res['frontier_count'] for _, res in result_tups]),
"expanded" + ("{:>12,}" * c).format(*[res['expanded_count'] for _, res in result_tups])
]
if include_path:
rows.append("path")
longest_path = max([len(res['path']) for _, res in result_tups if 'path' in res])
print("longest", longest_path)
for i in range(longest_path):
row = " "
for _, res in result_tups:
if len(res.get('path', [])) > i:
move, state = res['path'][i]
row += " " + move[0] + " " + str(state)
else:
row += " " * 12
rows.append(row)
print("\n" + "\n".join(rows), "\n")
class PuzzleSolver:
"""Base class for 8-puzzle solver."""
def __init__(self, goal_state):
self.parents = {} # state -> parent_state
self.expanded_count = 0
self.frontier_count = 0
self.goal = goal_state
def get_path(self, state):
"""Return the solution path from the start state of the search to a target.
Results are obtained by retracing the path backwards through the parent tree to the start
state for the search at the root.
Args:
state (EightPuzzleBoard): target state in the search tree
Returns:
A list of EightPuzzleBoard objects representing the path from the start state to the
target state
"""
path = []
while state is not None:
path.append(state)
state = self.parents[state]
path.reverse()
return path
def get_cost(self, state):
"""Calculate the path cost from start state to a target state.
Transition costs between states are equal to the square of the number on the tile that
was moved.
Args:
state (EightPuzzleBoard): target state in the search tree
Returns:
Integer indicating the cost of the solution path
"""
cost = 0
path = self.get_path(state)
for i in range(1, len(path)):
x, y = path[i - 1].find(None) # the most recently moved tile leaves the blank behind
tile = path[i].get_tile(x, y)
cost += int(tile) ** 2
return cost
def get_results_dict(self, state):
"""Construct the output dictionary for solve_puzzle()
Args:
state (EightPuzzleBoard): final state in the search tree
Returns:
A dictionary describing the search performed (see solve_puzzle())
"""
results = {}
results['frontier_count'] = self.frontier_count
results['expanded_count'] = self.expanded_count
if state:
results['path_cost'] = self.get_cost(state)
path = self.get_path(state)
moves = ['start'] + [path[i - 1].get_move(path[i]) for i in range(1, len(path))]
results['path'] = list(zip(moves, path))
return results
def solve(self, start_state):
# TODO: May need to put stuff in here
"""Carry out the search for a solution path to the goal state.
Args:
start_state (EightPuzzleBoard): start state for the search
Returns:
A dictionary describing the search from the start state to the goal state.
"""
raise NotImplementedError('Classed inheriting from PuzzleSolver must implement solve()')
class BreadthFirstSolver(PuzzleSolver):
"""Implementation of Breadth-First Search based on PuzzleSolver"""
def __init__(self, goal_state):
self.frontier = pdqpq.FifoQueue()
self.explored = set()
super().__init__(goal_state)
def add_to_frontier(self, node):
"""Add state to frontier and increase the frontier count."""
self.frontier.add(node)
self.frontier_count += 1
def expand_node(self, node):
"""Get the next state from the frontier and increase the expanded count."""
self.explored.add(node)
self.expanded_count += 1
return node.successors()
def solve(self, start_state):
self.parents[start_state] = None
self.add_to_frontier(start_state)
if start_state == self.goal: # edge case
return self.get_results_dict(start_state)
while not self.frontier.is_empty():
node = self.frontier.pop() # get the next node in the frontier queue
succs = self.expand_node(node)
for move, succ in succs.items():
if (succ not in self.frontier) and (succ not in self.explored):
self.parents[succ] = node
# BFS checks for goal state _before_ adding to frontier
if succ == self.goal:
return self.get_results_dict(succ)
else:
self.add_to_frontier(succ)
# if we get here, the search failed
return self.get_results_dict(None)
class UniformCostSolver(PuzzleSolver):
"""Implementation of Uniform-Cost Search based on PuzzleSolver"""
def __init__(self, goal_state):
self.frontier = pdqpq.PriorityQueue()
self.explored = set() # set function creates a set object and are in random order
# key: child, value: (parent, direction of move, cost up to child)
# self.tracker = {start_state: (None,"start", 0)}
super().__init__(goal_state)
##TODO/ MAJOR WE NEED TO MODIFY EXPAND NODE SO THAT IT ORDERS THEM BY LOWEST COST
def add_to_frontier(self, node, cost):
"""Add state to frontier and increase the frontier count."""
# Frontier is an instance of Priority Queue
self.frontier.add(node, priority = cost)
self.frontier_count += 1
def expand_node(self, node):
"""Get the next state from the frontier and increase the expanded count."""
self.explored.add(node)
self.expanded_count += 1
return node.successors()
# Need to account for the weights and cost in UCS
def solve(self, start_state):
self.parents[start_state] = None
self.add_to_frontier(start_state, 0)
if start_state == self.goal: # edge case
return self.get_results_dict(start_state)
while not self.frontier.is_empty():
node = self.frontier.pop() # get the next node in the frontier queue
if node == self.goal:
return self.get_results_dict(node)
succs = self.expand_node(node)
for move, succ in succs.items():
if (succ not in self.frontier) and (succ not in self.explored):
self.parents[succ] = node
# UCS checks for goal state _before_ adding to frontier
if succ == self.goal:
return self.get_results_dict(succ)
else:
self.add_to_frontier(succ, self.get_cost(succ))
elif succ in self.frontier:
prev_node = self.parents[succ]
prev_cost = self.get_cost(prev_node)
new_cost = prev_cost + self.get_cost(succ)
self.parents[succ] = succ
if self.frontier.get(succ) > new_cost:
#need to update, possibly may need to remove then add???
self.add_to_frontier(succ, self.get_cost(succ))
else:
self.parents[succ] = prev_node
# if we get here, the search failed
return self.get_results_dict(None)
class GreedySolver(PuzzleSolver):
"""Implementation of Greedy-First Search based on PuzzleSolver"""
def __init__(self, goal_state):
self.frontier = pdqpq.FifoQueue()
self.explored = set()
super().__init__(goal_state)
def add_to_frontier(self, node):
"""Add state to frontier and increase the frontier count."""
self.frontier.add(node)
self.frontier_count += 1
def expand_node(self, node):
"""Get the next state from the frontier and increase the expanded count."""
self.explored.add(node)
self.expanded_count += 1
return node.successors()
def solve(self, start_state):
self.parents[start_state] = None
self.add_to_frontier(start_state)
if start_state == self.goal: # edge case
return self.get_results_dict(start_state)
while not self.frontier.is_empty():
node = self.frontier.pop() # get the next node in the frontier queue
succs = self.expand_node(node)
for move, succ in succs.items():
if (succ not in self.frontier) and (succ not in self.explored):
self.parents[succ] = node
# BFS checks for goal state _before_ adding to frontier
if succ == self.goal:
return self.get_results_dict(succ)
else:
self.add_to_frontier(succ)
# if we get here, the search failed
return self.get_results_dict(None)
class AStarSolver(PuzzleSolver):
"""Implementation of A* Search based on PuzzleSolver"""
# AStar will be exactly like UCost, but the cost will also account for the heuristic for the priority queue.
# The heuristic will depend on what the algorithm passes through
def __init__(self, goal_state, heur):
self.frontier = pdqpq.PriorityQueue()
self.explored = set() # set function creates a set object and are in random order
self.heur = heur
super().__init__(goal_state)
def add_to_frontier(self, node, cost):
"""Add state to frontier and increase the frontier count."""
# Frontier is an instance of Priority Queue
self.frontier.add(node, priority = cost)
self.frontier_count += 1
def expand_node(self, node):
"""Get the next state from the frontier and increase the expanded count."""
self.explored.add(node)
self.expanded_count += 1
return node.successors()
def get_h_cost(self, state):
if self.heur == 'h1':
cost = 0
str_puzz = str(state)
for i in range(1, 9):
if i != int(str_puzz[i]):
cost += 1
return cost
elif self.heur == 'h2':
cost = 0
for i in range(1, 9):
x, y = state.find(str(i))
x0, y0 = GOAL_STATE.find(str(i))
cost += abs(x - x0) + abs(y - y0)
return cost
elif self.heur == 'h3':
cost = 0
for i in range(0, 9):
x, y = state.find(str(i))
x0, y0 = GOAL_STATE.find(str(i))
score = abs(x - x0) + abs(y - y0)
cost += score * i ** 2
return cost
# Need to account for the weights and cost in UCS
def solve(self, start_state):
self.parents[start_state] = None
self.add_to_frontier(start_state, 0)
if start_state == self.goal: # edge case
return self.get_results_dict(start_state)
while not self.frontier.is_empty():
node = self.frontier.pop() # get the next node in the frontier queue
if node == self.goal:
return self.get_results_dict(node)
succs = self.expand_node(node)
for move, succ in succs.items():
if (succ not in self.frontier) and (succ not in self.explored):
self.parents[succ] = node
# UCS checks for goal state _before_ adding to frontier
if succ == self.goal:
return self.get_results_dict(succ)
else:
self.add_to_frontier(succ, self.get_cost(succ))
elif succ in self.frontier:
prev_node = self.parents[succ]
prev_cost = self.get_cost(prev_node)
# Get the h_cost
h_cost = self.get_h_cost(succ)
new_cost = prev_cost + self.get_cost(succ) + h_cost
self.parents[succ] = succ
if self.frontier.get(succ) > new_cost:
#need to update, possibly may need to remove then add???
self.add_to_frontier(succ, self.get_cost(succ))
else:
self.parents[succ] = prev_node
# if we get here, the search failed
return self.get_results_dict(None)
############################################
if __name__ == '__main__':
# parse the command line args
start = puzz.EightPuzzleBoard(sys.argv[1])
if sys.argv[2] == 'all':
flavors = ['bfs', 'ucost', 'greedy-h1', 'greedy-h2',
'greedy-h3', 'astar-h1', 'astar-h2', 'astar-h3']
else:
flavors = sys.argv[2:]
# run the search(es)
results = {}
for flav in flavors:
print("solving puzzle {} with {}".format(start, flav))
results[flav] = solve_puzzle(start, flav)
print_table(results, include_path=False) # change to True to see the paths!