aima-python/search.py at master · sofmonk/aima-python · GitHub

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"""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 (

is_in, argmin, argmax, argmax_random_tie, probability,

weighted_sample_with_replacement, memoize, print_table, DataFile, Stack,

FIFOQueue, PriorityQueue, name

)

from grid import distance

from collections import defaultdict

import math

import random

import sys

import bisect

infinity = float('inf')

# ______________________________________________________________________________

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."""

raise NotImplementedError

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)."""

raise NotImplementedError

def goal_test(self, state):

"""Return True if the state is a goal. The default method compares the

state to self.goal or checks for state in self.goal if it is a

list, as specified in the constructor. Override this method if

checking against a single self.goal is not enough."""

if isinstance(self.goal, list):

return is_in(state, self.goal)

else:

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."""

raise NotImplementedError

# ______________________________________________________________________________

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."""

self.state = state

self.parent = parent

self.action = action

self.path_cost = path_cost

self.depth = 0

if parent:

self.depth = parent.depth + 1

def __repr__(self):

return "<Node {}>".format(self.state)

def __lt__(self, node):

return self.state < node.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):

"""[Figure 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. [Figure 3.1]"""

def __init__(self, initial_state=None):

"""State is an sbstract representation of the state

of the world, and seq is the list of actions required

to get to a particular state from the initial state(root)."""

self.state = initial_state

self.seq = []

def __call__(self, percept):

"""[Figure 3.1] Formulate a goal and problem, then

search for a sequence of actions to solve it."""

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):

raise NotImplementedError

def formulate_goal(self, state):

raise NotImplementedError

def formulate_problem(self, state, goal):

raise NotImplementedError

def search(self, problem):

raise NotImplementedError

# ______________________________________________________________________________

# 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. [Figure 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. [Figure 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):

"""[Figure 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):

"""[Figure 3.14]"""

return best_first_graph_search(problem, lambda node: node.path_cost)

def depth_limited_search(problem, limit=50):

"""[Figure 3.17]"""

def recursive_dls(node, problem, limit):

if problem.goal_test(node.state):

return node

elif limit == 0:

return 'cutoff'

else:

cutoff_occurred = False

for child in node.expand(problem):

result = recursive_dls(child, problem, limit - 1)

if result == 'cutoff':

cutoff_occurred = True

elif result is not None:

return result

return 'cutoff' if cutoff_occurred else None

# Body of depth_limited_search:

return recursive_dls(Node(problem.initial), problem, limit)

def iterative_deepening_search(problem):

"""[Figure 3.18]"""

for depth in range(sys.maxsize):

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):

"""[Figure 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:

# Order by lowest f value

successors.sort(key=lambda x: x.f)

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. [Figure 4.2]"""

current = Node(problem.initial)

while True:

neighbors = current.expand(problem)

if not neighbors:

break

neighbor = argmax_random_tie(neighbors,

key=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: (k * math.exp(-lam * t) if t < limit else 0)

def simulated_annealing(problem, schedule=exp_schedule()):

"""[Figure 4.5] CAUTION: This differs from the pseudocode as it

returns a state instead of a Node."""

current = Node(problem.initial)

for t in range(sys.maxsize):

T = schedule(t)

if T == 0:

return current.state

neighbors = current.expand(problem)

if not neighbors:

return current.state

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):

"""[Figure 4.11]Used when the environment is nondeterministic and completely observable.

Contains OR nodes where the agent is free to choose any action.

After every action there is an AND node which contains all possible states

the agent may reach due to stochastic nature of environment.

The agent must be able to handle all possible states of the AND node (as it

may end up in any of them).

Returns a conditional plan to reach goal state,

or failure if the former is not possible."""

# functions used by and_or_search

def or_search(state, problem, path):

"""returns a plan as a list of actions"""

if problem.goal_test(state):

return []

if state in path:

return None

for action in problem.actions(state):

plan = and_search(problem.result(state, action),

problem, path + [state, ])

if plan is not None:

return [action, plan]

def and_search(states, problem, path):

"""Returns plan in form of dictionary where we take action plan[s] if we reach state s.""" # noqa

plan = {}

for s in states:

plan[s] = or_search(s, problem, path)

if plan[s] is None:

return None

return plan

# body of and or search

return or_search(problem.initial, problem, [])

class OnlineDFSAgent:

"""[Figure 4.21] The abstract class for an OnlineDFSAgent. Override

update_state method to convert percept to state. While initializing

the subclass a problem needs to be provided which is an instance of

a subclass of the Problem class."""

def __init__(self, problem):

self.problem = problem

self.s = None

self.a = None

self.untried = defaultdict(list)

self.unbacktracked = defaultdict(list)

self.result = {}

def __call__(self, percept):

s1 = self.update_state(percept)

if self.problem.goal_test(s1):

self.a = None

else:

if s1 not in self.untried.keys():

self.untried[s1] = self.problem.actions(s1)

if self.s is not None:

if s1 != self.result[(self.s, self.a)]:

self.result[(self.s, self.a)] = s1

self.unbacktracked[s1].insert(0, self.s)

if len(self.untried[s1]) == 0:

if len(self.unbacktracked[s1]) == 0:

self.a = None

else:

# else a <- an action b such that result[s', b] = POP(unbacktracked[s']) # noqa

unbacktracked_pop = self.unbacktracked[s1].pop(0) # noqa

for (s, b) in self.result.keys():

if self.result[(s, b)] == unbacktracked_pop:

self.a = b

break

else:

self.a = self.untried[s1].pop(0)

self.s = s1

return self.a

def update_state(self, percept):

"""To be overridden in most cases. The default case

assumes the percept to be of type state."""

return percept

# ______________________________________________________________________________

class OnlineSearchProblem(Problem):

"""

A problem which is solved by an agent executing

actions, rather than by just computation.

Carried in a deterministic and a fully observable environment."""

def __init__(self, initial, goal, graph):

self.initial = initial

self.goal = goal

self.graph = graph

def actions(self, state):

return self.graph.dict[state].keys()

def output(self, state, action):

return self.graph.dict[state][action]

def h(self, state):

"""Returns least possible cost to reach a goal for the given state."""

return self.graph.least_costs[state]

def c(self, s, a, s1):

"""Returns a cost estimate for an agent to move from state 's' to state 's1'."""

return 1

def update_state(self, percept):

raise NotImplementedError

def goal_test(self, state):

if state == self.goal:

return True

return False

class LRTAStarAgent:

""" [Figure 4.24]

Abstract class for LRTA*-Agent. A problem needs to be

provided which is an instanace of a subclass of Problem Class.

Takes a OnlineSearchProblem [Figure 4.23] as a problem.

"""

def __init__(self, problem):

self.problem = problem

# self.result = {} # no need as we are using problem.result

self.H = {}

self.s = None

self.a = None

def __call__(self, s1): # as of now s1 is a state rather than a percept

if self.problem.goal_test(s1):

self.a = None

return self.a

else:

if s1 not in self.H:

self.H[s1] = self.problem.h(s1)

if self.s is not None:

# self.result[(self.s, self.a)] = s1 # no need as we are using problem.output

# minimum cost for action b in problem.actions(s)

self.H[self.s] = min(self.LRTA_cost(self.s, b, self.problem.output(self.s, b),

self.H) for b in self.problem.actions(self.s))

# costs for action b in problem.actions(s1)

costs = [self.LRTA_cost(s1, b, self.problem.output(s1, b), self.H)

for b in self.problem.actions(s1)]

# an action b in problem.actions(s1) that minimizes costs

self.a = list(self.problem.actions(s1))[costs.index(min(costs))]

self.s = s1

return self.a

def LRTA_cost(self, s, a, s1, H):

"""Returns cost to move from state 's' to state 's1' plus

estimated cost to get to goal from s1."""

print(s, a, s1)

if s1 is None:

return self.problem.h(s)

else:

# sometimes we need to get H[s1] which we haven't yet added to H

# to replace this try, except: we can initialize H with values from problem.h

try:

return self.problem.c(s, a, s1) + self.H[s1]

except:

return self.problem.c(s, a, s1) + self.problem.h(s1)

# ______________________________________________________________________________

# 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):

"""[Figure 4.8]"""

for i in range(ngen):

new_population = []

for i in range(len(population)):

fitnesses = map(fitness_fn, population)

p1, p2 = weighted_sample_with_replacement(2, population, fitnesses)

child = p1.mate(p2)

if random.uniform(0, 1) < pmut:

child.mutate()

new_population.append(child)

population = new_population

return argmax(population, key=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."""

raise NotImplementedError

# _____________________________________________________________________________

# 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 list(self.dict.keys()):

for (b, dist) in self.dict[a].items():

self.connect1(b, a, dist)

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 list(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=list(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, key=distance_to_node)

d = distance(g.locations[neighbor], here) * curvature()

g.connect(node, neighbor, int(d))

return g

""" [Figure 3.2]

Simplified road map of Romania

"""

romania_map = UndirectedGraph(dict(

Arad=dict(Zerind=75, Sibiu=140, Timisoara=118),

Bucharest=dict(Urziceni=85, Pitesti=101, Giurgiu=90, Fagaras=211),

Craiova=dict(Drobeta=120, Rimnicu=146, Pitesti=138),

Drobeta=dict(Mehadia=75),

Eforie=dict(Hirsova=86),

Fagaras=dict(Sibiu=99),

Hirsova=dict(Urziceni=98),

Iasi=dict(Vaslui=92, Neamt=87),

Lugoj=dict(Timisoara=111, Mehadia=70),

Oradea=dict(Zerind=71, Sibiu=151),

Pitesti=dict(Rimnicu=97),

Rimnicu=dict(Sibiu=80),

Urziceni=dict(Vaslui=142)))

romania_map.locations = dict(

Arad=(91, 492), Bucharest=(400, 327), Craiova=(253, 288),

Drobeta=(165, 299), Eforie=(562, 293), Fagaras=(305, 449),

Giurgiu=(375, 270), Hirsova=(534, 350), Iasi=(473, 506),

Lugoj=(165, 379), Mehadia=(168, 339), Neamt=(406, 537),

Oradea=(131, 571), Pitesti=(320, 368), Rimnicu=(233, 410),

Sibiu=(207, 457), Timisoara=(94, 410), Urziceni=(456, 350),

Vaslui=(509, 444), Zerind=(108, 531))

""" [Figure 4.9]

Eight possible states of the vacumm world

Each state is represented as

* "State of the left room" "State of the right room" "Room in which the agent

is present"

1 - DDL Dirty Dirty Left

2 - DDR Dirty Dirty Right

3 - DCL Dirty Clean Left

4 - DCR Dirty Clean Right

5 - CDL Clean Dirty Left

6 - CDR Clean Dirty Right

7 - CCL Clean Clean Left

8 - CCR Clean Clean Right

"""

vacumm_world = Graph(dict(

State_1=dict(Suck=['State_7', 'State_5'], Right=['State_2']),

State_2=dict(Suck=['State_8', 'State_4'], Left=['State_2']),

State_3=dict(Suck=['State_7'], Right=['State_4']),

State_4=dict(Suck=['State_4', 'State_2'], Left=['State_3']),

State_5=dict(Suck=['State_5', 'State_1'], Right=['State_6']),

State_6=dict(Suck=['State_8'], Left=['State_5']),

State_7=dict(Suck=['State_7', 'State_3'], Right=['State_8']),

State_8=dict(Suck=['State_8', 'State_6'], Left=['State_7'])

))

""" [Figure 4.23]

One-dimensional state space Graph

"""

one_dim_state_space = Graph(dict(

State_1=dict(Right='State_2'),

State_2=dict(Right='State_3', Left='State_1'),

State_3=dict(Right='State_4', Left='State_2'),

State_4=dict(Right='State_5', Left='State_3'),

State_5=dict(Right='State_6', Left='State_4'),

State_6=dict(Left='State_5')

))

one_dim_state_space.least_costs = dict(

State_1=8,

State_2=9,

State_3=2,

State_4=2,

State_5=4,

State_6=3)

""" [Figure 6.1]

Principal states and territories of Australia

"""

australia_map = 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_map.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 list(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 GraphProblemStochastic(GraphProblem):

"""

A version of GraphProblem where an action can lead to

nondeterministic output i.e. multiple possible states.

Define the graph as dict(A = dict(Action = [[<Result 1>, <Result 2>, ...], <cost>], ...), ...)

A the dictionary format is different, make sure the graph is created as a directed graph.

"""

def result(self, state, action):

return self.graph.get(state, action)

def path_cost(self):

raise NotImplementedError

# ______________________________________________________________________________

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))

"""

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 or # same row

col1 == col2 or # same column

row1 - col1 == row2 - col2 or # same \ diagonal

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 list(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', end=' ')

else:

print(str(board[i]) + ' ', end=' ')

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, file, min_len=3):

lines = file.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:

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