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search.py
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# search.py
# ---------
# Licensing Information:
# Please DO NOT DISTRIBUTE OR PUBLISH solutions to this project.
# You are free to use and extend these projects for EDUCATIONAL PURPOSES ONLY.
# The Hunt The Wumpus AI project was developed at University of Arizona
# by Clay Morrison ([email protected]), spring 2013.
# This project extends the python code provided by Peter Norvig as part of
# the Artificial Intelligence: A Modern Approach (AIMA) book example code;
# see http://aima.cs.berkeley.edu/code.html
# In particular, the following files come directly from the AIMA python
# code: ['agents.py', 'logic.py', 'search.py', 'utils.py']
# ('logic.py' has been modified by Clay Morrison in locations with the
# comment 'CTM')
# The file ['minisat.py'] implements a slim system call wrapper to the minisat
# (see http://minisat.se) SAT solver, and is directly based on the satispy
# python project, see https://github.com/netom/satispy .
"""Search (Chapters 3-4)
The way to use this code is to subclass Problem to create a class of problems,
then create problem instances and solve them with calls to the various search
functions."""
from utils import *
import math, random, sys, time, bisect, string
#______________________________________________________________________________
class Problem(object):
"""The abstract class for a formal problem. You should subclass
this and implement the methods actions and result, and possibly
__init__, goal_test, and path_cost. Then you will create instances
of your subclass and solve them with the various search functions."""
def __init__(self, initial, goal=None):
"""The constructor specifies the initial state, and possibly a goal
state, if there is a unique goal. Your subclass's constructor can add
other arguments."""
self.initial = initial; self.goal = goal
def actions(self, state):
"""Return the actions that can be executed in the given
state. The result would typically be a list, but if there are
many actions, consider yielding them one at a time in an
iterator, rather than building them all at once."""
abstract
def result(self, state, action):
"""Return the state that results from executing the given
action in the given state. The action must be one of
self.actions(state)."""
abstract
def goal_test(self, state):
"""Return True if the state is a goal. The default method compares the
state to self.goal, as specified in the constructor. Override this
method if checking against a single self.goal is not enough."""
return state == self.goal
def path_cost(self, c, state1, action, state2):
"""Return the cost of a solution path that arrives at state2 from
state1 via action, assuming cost c to get up to state1. If the problem
is such that the path doesn't matter, this function will only look at
state2. If the path does matter, it will consider c and maybe state1
and action. The default method costs 1 for every step in the path."""
return c + 1
def value(self, state):
"""For optimization problems, each state has a value. Hill-climbing
and related algorithms try to maximize this value."""
abstract
#______________________________________________________________________________
class Node:
"""A node in a search tree. Contains a pointer to the parent (the node
that this is a successor of) and to the actual state for this node. Note
that if a state is arrived at by two paths, then there are two nodes with
the same state. Also includes the action that got us to this state, and
the total path_cost (also known as g) to reach the node. Other functions
may add an f and h value; see best_first_graph_search and astar_search for
an explanation of how the f and h values are handled. You will not need to
subclass this class."""
def __init__(self, state, parent=None, action=None, path_cost=0):
"Create a search tree Node, derived from a parent by an action."
update(self, state=state, parent=parent, action=action,
path_cost=path_cost, depth=0)
if parent:
self.depth = parent.depth + 1
def __repr__(self):
return "<Node %s>" % (self.state,)
def expand(self, problem):
"List the nodes reachable in one step from this node."
return [self.child_node(problem, action)
for action in problem.actions(self.state)]
def child_node(self, problem, action):
"Fig. 3.10"
next = problem.result(self.state, action)
return Node(next, self, action,
problem.path_cost(self.path_cost, self.state, action, next))
def solution(self):
"Return the sequence of actions to go from the root to this node."
return [node.action for node in self.path()[1:]]
def path(self):
"Return a list of nodes forming the path from the root to this node."
node, path_back = self, []
while node:
path_back.append(node)
node = node.parent
return list(reversed(path_back))
# We want for a queue of nodes in breadth_first_search or
# astar_search to have no duplicated states, so we treat nodes
# with the same state as equal. [Problem: this may not be what you
# want in other contexts.]
def __eq__(self, other):
return isinstance(other, Node) and self.state == other.state
def __hash__(self):
return hash(self.state)
#______________________________________________________________________________
class SimpleProblemSolvingAgentProgram:
"""Abstract framework for a problem-solving agent. [Fig. 3.1]"""
def __init__(self, initial_state=None):
update(self, state=initial_state, seq=[])
def __call__(self, percept):
self.state = self.update_state(self.state, percept)
if not self.seq:
goal = self.formulate_goal(self.state)
problem = self.formulate_problem(self.state, goal)
self.seq = self.search(problem)
if not self.seq: return None
return self.seq.pop(0)
def update_state(self, percept):
abstract
def formulate_goal(self, state):
abstract
def formulate_problem(self, state, goal):
abstract
def search(self, problem):
abstract
#______________________________________________________________________________
# Uninformed Search algorithms
def tree_search(problem, frontier):
"""Search through the successors of a problem to find a goal.
The argument frontier should be an empty queue.
Don't worry about repeated paths to a state. [Fig. 3.7]"""
frontier.append(Node(problem.initial))
while frontier:
node = frontier.pop()
if problem.goal_test(node.state):
return node
frontier.extend(node.expand(problem))
return None
def graph_search(problem, frontier):
"""Search through the successors of a problem to find a goal.
The argument frontier should be an empty queue.
If two paths reach a state, only use the first one. [Fig. 3.7]"""
frontier.append(Node(problem.initial))
explored = set()
while frontier:
node = frontier.pop()
if problem.goal_test(node.state):
return node
explored.add(node.state)
frontier.extend(child for child in node.expand(problem)
if child.state not in explored
and child not in frontier)
return None
def breadth_first_tree_search(problem):
"Search the shallowest nodes in the search tree first."
return tree_search(problem, FIFOQueue())
def depth_first_tree_search(problem):
"Search the deepest nodes in the search tree first."
return tree_search(problem, Stack())
def depth_first_graph_search(problem):
"Search the deepest nodes in the search tree first."
return graph_search(problem, Stack())
def breadth_first_search(problem):
"[Fig. 3.11]"
node = Node(problem.initial)
if problem.goal_test(node.state):
return node
frontier = FIFOQueue()
frontier.append(node)
explored = set()
while frontier:
node = frontier.pop()
explored.add(node.state)
for child in node.expand(problem):
if child.state not in explored and child not in frontier:
if problem.goal_test(child.state):
return child
frontier.append(child)
return None
def best_first_graph_search(problem, f):
"""Search the nodes with the lowest f scores first.
You specify the function f(node) that you want to minimize; for example,
if f is a heuristic estimate to the goal, then we have greedy best
first search; if f is node.depth then we have breadth-first search.
There is a subtlety: the line "f = memoize(f, 'f')" means that the f
values will be cached on the nodes as they are computed. So after doing
a best first search you can examine the f values of the path returned."""
f = memoize(f, 'f')
node = Node(problem.initial)
if problem.goal_test(node.state):
return node
frontier = PriorityQueue(min, f)
frontier.append(node)
explored = set()
while frontier:
node = frontier.pop()
if problem.goal_test(node.state):
return node
explored.add(node.state)
for child in node.expand(problem):
if child.state not in explored and child not in frontier:
frontier.append(child)
elif child in frontier:
incumbent = frontier[child]
if f(child) < f(incumbent):
del frontier[incumbent]
frontier.append(child)
return None
def uniform_cost_search(problem):
"[Fig. 3.14]"
return best_first_graph_search(problem, lambda node: node.path_cost)
def depth_limited_search(problem, limit=50):
"[Fig. 3.17]"
def recursive_dls(node, problem, limit):
if problem.goal_test(node.state):
return node
elif node.depth == limit:
return 'cutoff'
else:
cutoff_occurred = False
for child in node.expand(problem):
result = recursive_dls(child, problem, limit)
if result == 'cutoff':
cutoff_occurred = True
elif result is not None:
return result
return if_(cutoff_occurred, 'cutoff', None)
# Body of depth_limited_search:
return recursive_dls(Node(problem.initial), problem, limit)
def iterative_deepening_search(problem):
"[Fig. 3.18]"
for depth in xrange(sys.maxint):
result = depth_limited_search(problem, depth)
if result != 'cutoff':
return result
#______________________________________________________________________________
# Informed (Heuristic) Search
greedy_best_first_graph_search = best_first_graph_search
# Greedy best-first search is accomplished by specifying f(n) = h(n).
def astar_search(problem, h=None):
"""A* search is best-first graph search with f(n) = g(n)+h(n).
You need to specify the h function when you call astar_search, or
else in your Problem subclass."""
h = memoize(h or problem.h, 'h')
return best_first_graph_search(problem, lambda n: n.path_cost + h(n))
#______________________________________________________________________________
# Other search algorithms
def recursive_best_first_search(problem, h=None):
"[Fig. 3.26]"
h = memoize(h or problem.h, 'h')
def RBFS(problem, node, flimit):
if problem.goal_test(node.state):
return node, 0 # (The second value is immaterial)
successors = node.expand(problem)
if len(successors) == 0:
return None, infinity
for s in successors:
s.f = max(s.path_cost + h(s), node.f)
while True:
successors.sort(lambda x,y: cmp(x.f, y.f)) # Order by lowest f value
best = successors[0]
if best.f > flimit:
return None, best.f
if len(successors) > 1:
alternative = successors[1].f
else:
alternative = infinity
result, best.f = RBFS(problem, best, min(flimit, alternative))
if result is not None:
return result, best.f
node = Node(problem.initial)
node.f = h(node)
result, bestf = RBFS(problem, node, infinity)
return result
def hill_climbing(problem):
"""From the initial node, keep choosing the neighbor with highest value,
stopping when no neighbor is better. [Fig. 4.2]"""
current = Node(problem.initial)
while True:
neighbors = current.expand(problem)
if not neighbors:
break
neighbor = argmax_random_tie(neighbors,
lambda node: problem.value(node.state))
if problem.value(neighbor.state) <= problem.value(current.state):
break
current = neighbor
return current.state
def exp_schedule(k=20, lam=0.005, limit=100):
"One possible schedule function for simulated annealing"
return lambda t: if_(t < limit, k * math.exp(-lam * t), 0)
def simulated_annealing(problem, schedule=exp_schedule()):
"[Fig. 4.5]"
current = Node(problem.initial)
for t in xrange(sys.maxint):
T = schedule(t)
if T == 0:
return current
neighbors = current.expand(problem)
if not neighbors:
return current
next = random.choice(neighbors)
delta_e = problem.value(next.state) - problem.value(current.state)
if delta_e > 0 or probability(math.exp(delta_e/T)):
current = next
def and_or_graph_search(problem):
"[Fig. 4.11]"
unimplemented()
def online_dfs_agent(s1):
"[Fig. 4.21]"
unimplemented()
def lrta_star_agent(s1):
"[Fig. 4.24]"
unimplemented()
#______________________________________________________________________________
# Genetic Algorithm
def genetic_search(problem, fitness_fn, ngen=1000, pmut=0.1, n=20):
"""Call genetic_algorithm on the appropriate parts of a problem.
This requires the problem to have states that can mate and mutate,
plus a value method that scores states."""
s = problem.initial_state
states = [problem.result(s, a) for a in problem.actions(s)]
random.shuffle(states)
return genetic_algorithm(states[:n], problem.value, ngen, pmut)
def genetic_algorithm(population, fitness_fn, ngen=1000, pmut=0.1):
"[Fig. 4.8]"
for i in range(ngen):
new_population = []
for i in len(population):
fitnesses = map(fitness_fn, population)
p1, p2 = weighted_sample_with_replacement(population, fitnesses, 2)
child = p1.mate(p2)
if random.uniform(0, 1) < pmut:
child.mutate()
new_population.append(child)
population = new_population
return argmax(population, fitness_fn)
class GAState:
"Abstract class for individuals in a genetic search."
def __init__(self, genes):
self.genes = genes
def mate(self, other):
"Return a new individual crossing self and other."
c = random.randrange(len(self.genes))
return self.__class__(self.genes[:c] + other.genes[c:])
def mutate(self):
"Change a few of my genes."
abstract
#_____________________________________________________________________________
# The remainder of this file implements examples for the search algorithms.
#______________________________________________________________________________
# Graphs and Graph Problems
class Graph:
"""A graph connects nodes (verticies) by edges (links). Each edge can also
have a length associated with it. The constructor call is something like:
g = Graph({'A': {'B': 1, 'C': 2})
this makes a graph with 3 nodes, A, B, and C, with an edge of length 1 from
A to B, and an edge of length 2 from A to C. You can also do:
g = Graph({'A': {'B': 1, 'C': 2}, directed=False)
This makes an undirected graph, so inverse links are also added. The graph
stays undirected; if you add more links with g.connect('B', 'C', 3), then
inverse link is also added. You can use g.nodes() to get a list of nodes,
g.get('A') to get a dict of links out of A, and g.get('A', 'B') to get the
length of the link from A to B. 'Lengths' can actually be any object at
all, and nodes can be any hashable object."""
def __init__(self, dict=None, directed=True):
self.dict = dict or {}
self.directed = directed
if not directed: self.make_undirected()
def make_undirected(self):
"Make a digraph into an undirected graph by adding symmetric edges."
for a in self.dict.keys():
for (b, distance) in self.dict[a].items():
self.connect1(b, a, distance)
def connect(self, A, B, distance=1):
"""Add a link from A and B of given distance, and also add the inverse
link if the graph is undirected."""
self.connect1(A, B, distance)
if not self.directed: self.connect1(B, A, distance)
def connect1(self, A, B, distance):
"Add a link from A to B of given distance, in one direction only."
self.dict.setdefault(A,{})[B] = distance
def get(self, a, b=None):
"""Return a link distance or a dict of {node: distance} entries.
.get(a,b) returns the distance or None;
.get(a) returns a dict of {node: distance} entries, possibly {}."""
links = self.dict.setdefault(a, {})
if b is None: return links
else: return links.get(b)
def nodes(self):
"Return a list of nodes in the graph."
return self.dict.keys()
def UndirectedGraph(dict=None):
"Build a Graph where every edge (including future ones) goes both ways."
return Graph(dict=dict, directed=False)
def RandomGraph(nodes=range(10), min_links=2, width=400, height=300,
curvature=lambda: random.uniform(1.1, 1.5)):
"""Construct a random graph, with the specified nodes, and random links.
The nodes are laid out randomly on a (width x height) rectangle.
Then each node is connected to the min_links nearest neighbors.
Because inverse links are added, some nodes will have more connections.
The distance between nodes is the hypotenuse times curvature(),
where curvature() defaults to a random number between 1.1 and 1.5."""
g = UndirectedGraph()
g.locations = {}
## Build the cities
for node in nodes:
g.locations[node] = (random.randrange(width), random.randrange(height))
## Build roads from each city to at least min_links nearest neighbors.
for i in range(min_links):
for node in nodes:
if len(g.get(node)) < min_links:
here = g.locations[node]
def distance_to_node(n):
if n is node or g.get(node,n): return infinity
return distance(g.locations[n], here)
neighbor = argmin(nodes, distance_to_node)
d = distance(g.locations[neighbor], here) * curvature()
g.connect(node, neighbor, int(d))
return g
romania = UndirectedGraph(Dict(
A=Dict(Z=75, S=140, T=118),
B=Dict(U=85, P=101, G=90, F=211),
C=Dict(D=120, R=146, P=138),
D=Dict(M=75),
E=Dict(H=86),
F=Dict(S=99),
H=Dict(U=98),
I=Dict(V=92, N=87),
L=Dict(T=111, M=70),
O=Dict(Z=71, S=151),
P=Dict(R=97),
R=Dict(S=80),
U=Dict(V=142)))
romania.locations = Dict(
A=( 91, 492), B=(400, 327), C=(253, 288), D=(165, 299),
E=(562, 293), F=(305, 449), G=(375, 270), H=(534, 350),
I=(473, 506), L=(165, 379), M=(168, 339), N=(406, 537),
O=(131, 571), P=(320, 368), R=(233, 410), S=(207, 457),
T=( 94, 410), U=(456, 350), V=(509, 444), Z=(108, 531))
australia = UndirectedGraph(Dict(
T=Dict(),
SA=Dict(WA=1, NT=1, Q=1, NSW=1, V=1),
NT=Dict(WA=1, Q=1),
NSW=Dict(Q=1, V=1)))
australia.locations = Dict(WA=(120, 24), NT=(135, 20), SA=(135, 30),
Q=(145, 20), NSW=(145, 32), T=(145, 42), V=(145, 37))
class GraphProblem(Problem):
"The problem of searching a graph from one node to another."
def __init__(self, initial, goal, graph):
Problem.__init__(self, initial, goal)
self.graph = graph
def actions(self, A):
"The actions at a graph node are just its neighbors."
return self.graph.get(A).keys()
def result(self, state, action):
"The result of going to a neighbor is just that neighbor."
return action
def path_cost(self, cost_so_far, A, action, B):
return cost_so_far + (self.graph.get(A,B) or infinity)
def h(self, node):
"h function is straight-line distance from a node's state to goal."
locs = getattr(self.graph, 'locations', None)
if locs:
return int(distance(locs[node.state], locs[self.goal]))
else:
return infinity
#______________________________________________________________________________
class NQueensProblem(Problem):
"""The problem of placing N queens on an NxN board with none attacking
each other. A state is represented as an N-element array, where
a value of r in the c-th entry means there is a queen at column c,
row r, and a value of None means that the c-th column has not been
filled in yet. We fill in columns left to right.
>>> depth_first_tree_search(NQueensProblem(8))
<Node [7, 3, 0, 2, 5, 1, 6, 4]>
"""
def __init__(self, N):
self.N = N
self.initial = [None] * N
def actions(self, state):
"In the leftmost empty column, try all non-conflicting rows."
if state[-1] is not None:
return [] # All columns filled; no successors
else:
col = state.index(None)
return [row for row in range(self.N)
if not self.conflicted(state, row, col)]
def result(self, state, row):
"Place the next queen at the given row."
col = state.index(None)
new = state[:]
new[col] = row
return new
def conflicted(self, state, row, col):
"Would placing a queen at (row, col) conflict with anything?"
return any(self.conflict(row, col, state[c], c)
for c in range(col))
def conflict(self, row1, col1, row2, col2):
"Would putting two queens in (row1, col1) and (row2, col2) conflict?"
return (row1 == row2 ## same row
or col1 == col2 ## same column
or row1-col1 == row2-col2 ## same \ diagonal
or row1+col1 == row2+col2) ## same / diagonal
def goal_test(self, state):
"Check if all columns filled, no conflicts."
if state[-1] is None:
return False
return not any(self.conflicted(state, state[col], col)
for col in range(len(state)))
#______________________________________________________________________________
# Inverse Boggle: Search for a high-scoring Boggle board. A good domain for
# iterative-repair and related search techniques, as suggested by Justin Boyan.
ALPHABET = 'ABCDEFGHIJKLMNOPQRSTUVWXYZ'
cubes16 = ['FORIXB', 'MOQABJ', 'GURILW', 'SETUPL',
'CMPDAE', 'ACITAO', 'SLCRAE', 'ROMASH',
'NODESW', 'HEFIYE', 'ONUDTK', 'TEVIGN',
'ANEDVZ', 'PINESH', 'ABILYT', 'GKYLEU']
def random_boggle(n=4):
"""Return a random Boggle board of size n x n.
We represent a board as a linear list of letters."""
cubes = [cubes16[i % 16] for i in range(n*n)]
random.shuffle(cubes)
return map(random.choice, cubes)
# The best 5x5 board found by Boyan, with our word list this board scores
# 2274 words, for a score of 9837
boyan_best = list('RSTCSDEIAEGNLRPEATESMSSID')
def print_boggle(board):
"Print the board in a 2-d array."
n2 = len(board); n = exact_sqrt(n2)
for i in range(n2):
if i % n == 0 and i > 0: print
if board[i] == 'Q': print 'Qu',
else: print str(board[i]) + ' ',
print
def boggle_neighbors(n2, cache={}):
"""Return a list of lists, where the i-th element is the list of indexes
for the neighbors of square i."""
if cache.get(n2):
return cache.get(n2)
n = exact_sqrt(n2)
neighbors = [None] * n2
for i in range(n2):
neighbors[i] = []
on_top = i < n
on_bottom = i >= n2 - n
on_left = i % n == 0
on_right = (i+1) % n == 0
if not on_top:
neighbors[i].append(i - n)
if not on_left: neighbors[i].append(i - n - 1)
if not on_right: neighbors[i].append(i - n + 1)
if not on_bottom:
neighbors[i].append(i + n)
if not on_left: neighbors[i].append(i + n - 1)
if not on_right: neighbors[i].append(i + n + 1)
if not on_left: neighbors[i].append(i - 1)
if not on_right: neighbors[i].append(i + 1)
cache[n2] = neighbors
return neighbors
def exact_sqrt(n2):
"If n2 is a perfect square, return its square root, else raise error."
n = int(math.sqrt(n2))
assert n * n == n2
return n
#_____________________________________________________________________________
class Wordlist:
"""This class holds a list of words. You can use (word in wordlist)
to check if a word is in the list, or wordlist.lookup(prefix)
to see if prefix starts any of the words in the list."""
def __init__(self, filename, min_len=3):
lines = open(filename).read().upper().split()
self.words = [word for word in lines if len(word) >= min_len]
self.words.sort()
self.bounds = {}
for c in ALPHABET:
c2 = chr(ord(c) + 1)
self.bounds[c] = (bisect.bisect(self.words, c),
bisect.bisect(self.words, c2))
def lookup(self, prefix, lo=0, hi=None):
"""See if prefix is in dictionary, as a full word or as a prefix.
Return two values: the first is the lowest i such that
words[i].startswith(prefix), or is None; the second is
True iff prefix itself is in the Wordlist."""
words = self.words
if hi is None: hi = len(words)
i = bisect.bisect_left(words, prefix, lo, hi)
if i < len(words) and words[i].startswith(prefix):
return i, (words[i] == prefix)
else:
return None, False
def __contains__(self, word):
return self.lookup(word)[1]
def __len__(self):
return len(self.words)
#_____________________________________________________________________________
class BoggleFinder:
"""A class that allows you to find all the words in a Boggle board. """
wordlist = None ## A class variable, holding a wordlist
def __init__(self, board=None):
if BoggleFinder.wordlist is None:
BoggleFinder.wordlist = Wordlist("../data/EN-text/wordlist")
self.found = {}
if board:
self.set_board(board)
def set_board(self, board=None):
"Set the board, and find all the words in it."
if board is None:
board = random_boggle()
self.board = board
self.neighbors = boggle_neighbors(len(board))
self.found = {}
for i in range(len(board)):
lo, hi = self.wordlist.bounds[board[i]]
self.find(lo, hi, i, [], '')
return self
def find(self, lo, hi, i, visited, prefix):
"""Looking in square i, find the words that continue the prefix,
considering the entries in self.wordlist.words[lo:hi], and not
revisiting the squares in visited."""
if i in visited:
return
wordpos, is_word = self.wordlist.lookup(prefix, lo, hi)
if wordpos is not None:
if is_word:
self.found[prefix] = True
visited.append(i)
c = self.board[i]
if c == 'Q': c = 'QU'
prefix += c
for j in self.neighbors[i]:
self.find(wordpos, hi, j, visited, prefix)
visited.pop()
def words(self):
"The words found."
return self.found.keys()
scores = [0, 0, 0, 0, 1, 2, 3, 5] + [11] * 100
def score(self):
"The total score for the words found, according to the rules."
return sum([self.scores[len(w)] for w in self.words()])
def __len__(self):
"The number of words found."
return len(self.found)
#_____________________________________________________________________________
def boggle_hill_climbing(board=None, ntimes=100, verbose=True):
"""Solve inverse Boggle by hill-climbing: find a high-scoring board by
starting with a random one and changing it."""
finder = BoggleFinder()
if board is None:
board = random_boggle()
best = len(finder.set_board(board))
for _ in range(ntimes):
i, oldc = mutate_boggle(board)
new = len(finder.set_board(board))
if new > best:
best = new
if verbose: print best, _, board
else:
board[i] = oldc ## Change back
if verbose:
print_boggle(board)
return board, best
def mutate_boggle(board):
i = random.randrange(len(board))
oldc = board[i]
board[i] = random.choice(random.choice(cubes16)) ##random.choice(boyan_best)
return i, oldc
#______________________________________________________________________________
# Code to compare searchers on various problems.
class InstrumentedProblem(Problem):
"""Delegates to a problem, and keeps statistics."""
def __init__(self, problem):
self.problem = problem
self.succs = self.goal_tests = self.states = 0
self.found = None
def actions(self, state):
self.succs += 1
return self.problem.actions(state)
def result(self, state, action):
self.states += 1
return self.problem.result(state, action)
def goal_test(self, state):
self.goal_tests += 1
result = self.problem.goal_test(state)
if result:
self.found = state
return result
def path_cost(self, c, state1, action, state2):
return self.problem.path_cost(c, state1, action, state2)
def value(self, state):
return self.problem.value(state)
def __getattr__(self, attr):
return getattr(self.problem, attr)
def __repr__(self):
return '<%4d/%4d/%4d/%s>' % (self.succs, self.goal_tests,
self.states, str(self.found)[:4])
def compare_searchers(problems, header,
searchers=[breadth_first_tree_search,
breadth_first_search, depth_first_graph_search,
iterative_deepening_search,
depth_limited_search,
recursive_best_first_search]):
def do(searcher, problem):
p = InstrumentedProblem(problem)
searcher(p)
return p
table = [[name(s)] + [do(s, p) for p in problems] for s in searchers]
print_table(table, header)
def compare_graph_searchers():
"""Prints a table of results like this:
>>> compare_graph_searchers()
Searcher Romania(A, B) Romania(O, N) Australia
breadth_first_tree_search < 21/ 22/ 59/B> <1158/1159/3288/N> < 7/ 8/ 22/WA>
breadth_first_search < 7/ 11/ 18/B> < 19/ 20/ 45/N> < 2/ 6/ 8/WA>
depth_first_graph_search < 8/ 9/ 20/B> < 16/ 17/ 38/N> < 4/ 5/ 11/WA>
iterative_deepening_search < 11/ 33/ 31/B> < 656/1815/1812/N> < 3/ 11/ 11/WA>
depth_limited_search < 54/ 65/ 185/B> < 387/1012/1125/N> < 50/ 54/ 200/WA>
recursive_best_first_search < 5/ 6/ 15/B> <5887/5888/16532/N> < 11/ 12/ 43/WA>"""
compare_searchers(problems=[GraphProblem('A', 'B', romania),
GraphProblem('O', 'N', romania),
GraphProblem('Q', 'WA', australia)],
header=['Searcher', 'Romania(A, B)', 'Romania(O, N)', 'Australia'])
#______________________________________________________________________________
__doc__ += """
>>> ab = GraphProblem('A', 'B', romania)
>>> breadth_first_tree_search(ab).solution()
['S', 'F', 'B']
>>> breadth_first_search(ab).solution()
['S', 'F', 'B']
>>> uniform_cost_search(ab).solution()
['S', 'R', 'P', 'B']
>>> depth_first_graph_search(ab).solution()
['T', 'L', 'M', 'D', 'C', 'P', 'B']
>>> iterative_deepening_search(ab).solution()
['S', 'F', 'B']
>>> len(depth_limited_search(ab).solution())
50
>>> astar_search(ab).solution()
['S', 'R', 'P', 'B']
>>> recursive_best_first_search(ab).solution()
['S', 'R', 'P', 'B']
>>> board = list('SARTELNID')
>>> print_boggle(board)
S A R
T E L
N I D
>>> f = BoggleFinder(board)
>>> len(f)
206
"""
__doc__ += random_tests("""
>>> ' '.join(f.words())
'LID LARES DEAL LIE DIETS LIN LINT TIL TIN RATED ERAS LATEN DEAR TIE LINE INTER STEAL LATED LAST TAR SAL DITES RALES SAE RETS TAE RAT RAS SAT IDLE TILDES LEAST IDEAS LITE SATED TINED LEST LIT RASE RENTS TINEA EDIT EDITS NITES ALES LATE LETS RELIT TINES LEI LAT ELINT LATI SENT TARED DINE STAR SEAR NEST LITAS TIED SEAT SERAL RATE DINT DEL DEN SEAL TIER TIES NET SALINE DILATE EAST TIDES LINTER NEAR LITS ELINTS DENI RASED SERA TILE NEAT DERAT IDLEST NIDE LIEN STARED LIER LIES SETA NITS TINE DITAS ALINE SATIN TAS ASTER LEAS TSAR LAR NITE RALE LAS REAL NITER ATE RES RATEL IDEA RET IDEAL REI RATS STALE DENT RED IDES ALIEN SET TEL SER TEN TEA TED SALE TALE STILE ARES SEA TILDE SEN SEL ALINES SEI LASE DINES ILEA LINES ELD TIDE RENT DIEL STELA TAEL STALED EARL LEA TILES TILER LED ETA TALI ALE LASED TELA LET IDLER REIN ALIT ITS NIDES DIN DIE DENTS STIED LINER LASTED RATINE ERA IDLES DIT RENTAL DINER SENTI TINEAL DEIL TEAR LITER LINTS TEAL DIES EAR EAT ARLES SATE STARE DITS DELI DENTAL REST DITE DENTIL DINTS DITA DIET LENT NETS NIL NIT SETAL LATS TARE ARE SATI'
>>> boggle_hill_climbing(list('ABCDEFGHI'), verbose=False)
(['E', 'P', 'R', 'D', 'O', 'A', 'G', 'S', 'T'], 123)
""")