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search.py
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search.py
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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_sampler,
memoize, print_table, open_data, Stack, FIFOQueue, PriorityQueue, name,
distance, vector_add
)
from collections import defaultdict
import math
import random
import sys
import bisect
from operator import itemgetter
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
# ______________________________________________________________________________
# Bidirectional Search
# Pseudocode from https://webdocs.cs.ualberta.ca/%7Eholte/Publications/MM-AAAI2016.pdf
def bidirectional_search(problem):
e = problem.find_min_edge()
gF, gB = {problem.initial : 0}, {problem.goal : 0}
openF, openB = [problem.initial], [problem.goal]
closedF, closedB = [], []
U = infinity
def extend(U, open_dir, open_other, g_dir, g_other, closed_dir):
"""Extend search in given direction"""
n = find_key(C, open_dir, g_dir)
open_dir.remove(n)
closed_dir.append(n)
for c in problem.actions(n):
if c in open_dir or c in closed_dir:
if g_dir[c] <= problem.path_cost(g_dir[n], n, None, c):
continue
open_dir.remove(c)
g_dir[c] = problem.path_cost(g_dir[n], n, None, c)
open_dir.append(c)
if c in open_other:
U = min(U, g_dir[c] + g_other[c])
return U, open_dir, closed_dir, g_dir
def find_min(open_dir, g):
"""Finds minimum priority, g and f values in open_dir"""
m, m_f = infinity, infinity
for n in open_dir:
f = g[n] + problem.h(n)
pr = max(f, 2*g[n])
m = min(m, pr)
m_f = min(m_f, f)
return m, m_f, min(g.values())
def find_key(pr_min, open_dir, g):
"""Finds key in open_dir with value equal to pr_min
and minimum g value."""
m = infinity
state = -1
for n in open_dir:
pr = max(g[n] + problem.h(n), 2*g[n])
if pr == pr_min:
if g[n] < m:
m = g[n]
state = n
return state
while openF and openB:
pr_min_f, f_min_f, g_min_f = find_min(openF, gF)
pr_min_b, f_min_b, g_min_b = find_min(openB, gB)
C = min(pr_min_f, pr_min_b)
if U <= max(C, f_min_f, f_min_b, g_min_f + g_min_b + e):
return U
if C == pr_min_f:
# Extend forward
U, openF, closedF, gF = extend(U, openF, openB, gF, gB, closedF)
else:
# Extend backward
U, openB, closedB, gB = extend(U, openB, openF, gB, gF, closedB)
return infinity
# ______________________________________________________________________________
# 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))
# ______________________________________________________________________________
# A* heuristics
class EightPuzzle():
def __init__(self):
self.path = []
self.final = []
def checkSolvability(self, state):
inversion = 0
for i in range(len(state)):
for j in range(i,len(state)):
if (state[i]>state[j] and state[j]!=0):
inversion += 1
check = True
if inversion%2 != 0:
check = False
print(check)
def getPossibleMoves(self,state,heuristic,goal,moves):
move = {0:[1,3], 1:[0,2,4], 2:[1,5], 3:[0,6,4], 4:[1,3,5,7], 5:[2,4,8], 6:[3,7], 7:[6,8], 8:[7,5]} # create a dictionary of moves
index = state[0].index(0)
possible_moves = []
for i in range(len(move[index])):
conf = list(state[0][:])
a = conf[index]
b = conf[move[index][i]]
conf[move[index][i]] = a
conf[index] = b
possible_moves.append(conf)
scores = []
for i in possible_moves:
scores.append(heuristic(i,goal))
scores = [x+moves for x in scores]
allowed_state = []
for i in range(len(possible_moves)):
node = []
node.append(possible_moves[i])
node.append(scores[i])
node.append(state[0])
allowed_state.append(node)
return allowed_state
def create_path(self,goal,initial):
node = goal[0]
self.final.append(goal[0])
if goal[2] == initial:
return reversed(self.final)
else:
parent = goal[2]
for i in self.path:
if i[0] == parent:
parent = i
self.create_path(parent,initial)
def show_path(self,initial):
move = []
for i in range(0,len(self.path)):
move.append(''.join(str(x) for x in self.path[i][0]))
print("Number of explored nodes by the following heuristic are: ", len(set(move)))
print(initial)
for i in reversed(self.final):
print(i)
del self.path[:]
del self.final[:]
return
def solve(self,initial,goal,heuristic):
root = [initial,heuristic(initial,goal),'']
nodes = [] # nodes is a priority Queue based on the state score
nodes.append(root)
moves = 0
while len(nodes) != 0:
node = nodes[0]
del nodes[0]
self.path.append(node)
if node[0] == goal:
soln = self.create_path(self.path[-1],initial )
self.show_path(initial)
return
moves +=1
opened_nodes = self.getPossibleMoves(node,heuristic,goal,moves)
nodes = sorted(opened_nodes+nodes, key=itemgetter(1))
# ______________________________________________________________________________
# 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 simulated_annealing_full(problem, schedule=exp_schedule()):
""" This version returns all the states encountered in reaching
the goal state."""
states = []
current = Node(problem.initial)
for t in range(sys.maxsize):
states.append(current.state)
T = schedule(t)
if T == 0:
return states
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."""
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, [])
# Pre-defined actions for PeakFindingProblem
directions4 = { 'W':(-1, 0), 'N':(0, 1), 'E':(1, 0), 'S':(0, -1) }
directions8 = dict(directions4)
directions8.update({'NW':(-1, 1), 'NE':(1, 1), 'SE':(1, -1), 'SW':(-1, -1) })
class PeakFindingProblem(Problem):
"""Problem of finding the highest peak in a limited grid"""
def __init__(self, initial, grid, defined_actions=directions4):
"""The grid is a 2 dimensional array/list whose state is specified by tuple of indices"""
Problem.__init__(self, initial)
self.grid = grid
self.defined_actions = defined_actions
self.n = len(grid)
assert self.n > 0
self.m = len(grid[0])
assert self.m > 0
def actions(self, state):
"""Returns the list of actions which are allowed to be taken from the given state"""
allowed_actions = []
for action in self.defined_actions:
next_state = vector_add(state, self.defined_actions[action])
if next_state[0] >= 0 and next_state[1] >= 0 and next_state[0] <= self.n - 1 and next_state[1] <= self.m - 1:
allowed_actions.append(action)
return allowed_actions
def result(self, state, action):
"""Moves in the direction specified by action"""
return vector_add(state, self.defined_actions[action])
def value(self, state):
"""Value of a state is the value it is the index to"""
x, y = state
assert 0 <= x < self.n
assert 0 <= y < self.m
return self.grid[x][y]
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'])
unbacktracked_pop = self.unbacktracked[s1].pop(0)
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 instance 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))
# an action b in problem.actions(s1) that minimizes costs
self.a = argmin(self.problem.actions(s1),
key=lambda b: self.LRTA_cost(s1, b, self.problem.output(s1, b), self.H))
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."""
# NOTE: This is not tested and might not work.
# TODO: Use this function to make Problems work with genetic_algorithm.
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, gene_pool=[0, 1], f_thres=None, ngen=1000, pmut=0.1):
"""[Figure 4.8]"""
for i in range(ngen):
population = [mutate(recombine(*select(2, population, fitness_fn)), gene_pool, pmut)
for i in range(len(population))]
fittest_individual = fitness_threshold(fitness_fn, f_thres, population)
if fittest_individual:
return fittest_individual
return argmax(population, key=fitness_fn)
def fitness_threshold(fitness_fn, f_thres, population):
if not f_thres:
return None
fittest_individual = argmax(population, key=fitness_fn)
if fitness_fn(fittest_individual) >= f_thres:
return fittest_individual
return None
def init_population(pop_number, gene_pool, state_length):
"""Initializes population for genetic algorithm
pop_number : Number of individuals in population
gene_pool : List of possible values for individuals
state_length: The length of each individual"""
g = len(gene_pool)
population = []
for i in range(pop_number):
new_individual = [gene_pool[random.randrange(0, g)] for j in range(state_length)]
population.append(new_individual)
return population
def select(r, population, fitness_fn):
fitnesses = map(fitness_fn, population)
sampler = weighted_sampler(population, fitnesses)
return [sampler() for i in range(r)]
def recombine(x, y):
n = len(x)
c = random.randrange(0, n)
return x[:c] + y[c:]
def mutate(x, gene_pool, pmut):
if random.uniform(0, 1) >= pmut:
return x
n = len(x)
g = len(gene_pool)
c = random.randrange(0, n)
r = random.randrange(0, g)
new_gene = gene_pool[r]
return x[:c] + [new_gene] + x[c+1:]
# _____________________________________________________________________________
# 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