Artificial Intelligence: A Modern Approach

# AIMA Python file: utils.py

"""Provide some widely useful utilities. Safe for "from utils import *".

"""

from __future__ import generators
import operator, math, random, copy, sys,  os.path, bisect

# Compatibility with Python 2.2 and 2.3

# The AIMA code is designed to run in Python 2.2 and up (at some point,
# support for 2.2 may go away; 2.2 was released in 2001, and so is over
# 3 years old). The first part of this file brings you up to 2.4
# compatibility if you are running in Python 2.2 or 2.3:

try: bool, True, False ## Introduced in 2.3
except NameError:
class bool(int):
"Simple implementation of Booleans, as in PEP 285"
def __init__(self, val): self.val = val
def __int__(self): return self.val
def __repr__(self): return ('False', 'True')[self.val]

True, False = bool(1), bool(0)

try: sum ## Introduced in 2.3
except NameError:
def sum(seq, start=0):
"""Sum the elements of seq.
>>> sum([1, 2, 3])
6
"""
return reduce(operator.add, seq, start)

try: enumerate  ## Introduced in 2.3
except NameError:
def enumerate(collection):
"""Return an iterator that enumerates pairs of (i, c[i]). PEP 279.
>>> list(enumerate('abc'))
[(0, 'a'), (1, 'b'), (2, 'c')]
"""
## Copied from PEP 279
i = 0
it = iter(collection)
while 1:
yield (i, it.next())
i += 1

try: reversed ## Introduced in 2.4
except NameError:
def reversed(seq):
"""Iterate over x in reverse order.
>>> list(reversed([1,2,3]))
[3, 2, 1]
"""
if hasattr(seq, 'keys'):
raise ValueError("mappings do not support reverse iteration")
i = len(seq)
while i > 0:
i -= 1
yield seq[i]

try: sorted ## Introduced in 2.4
except NameError:
def sorted(seq, cmp=None, key=None, reverse=False):
"""Copy seq and sort and return it.
>>> sorted([3, 1, 2])
[1, 2, 3]
"""
seq2 = copy.copy(seq)
if key:
if cmp == None:
cmp = __builtins__.cmp
seq2.sort(lambda x,y: cmp(key(x), key(y)))
else:
if cmp == None:
seq2.sort()
else:
seq2.sort(cmp)
if reverse:
seq2.reverse()
return seq2

try:
set, frozenset ## set builtin introduced in 2.4
except NameError:
try:
import sets ## sets module introduced in 2.3
set, frozenset = sets.Set, sets.ImmutableSet
except (NameError, ImportError):
class BaseSet:
"set type (see http://docs.python.org/lib/types-set.html)"

def __init__(self, elements=[]):
self.dict = {}
for e in elements:
self.dict[e] = 1

def __len__(self):
return len(self.dict)

def __iter__(self):
for e in self.dict:
yield e

def __contains__(self, element):
return element in self.dict

def issubset(self, other):
for e in self.dict.keys():
if e not in other:
return False
return True

def issuperset(self, other):
for e in other:
if e not in self:
return False
return True

def union(self, other):
return type(self)(list(self) + list(other))

def intersection(self, other):
return type(self)([e for e in self.dict if e in other])

def difference(self, other):
return type(self)([e for e in self.dict if e not in other])

def symmetric_difference(self, other):
return type(self)([e for e in self.dict if e not in other] +
[e for e in other if e not in self.dict])

def copy(self):
return type(self)(self.dict)

def __repr__(self):
elements = ", ".join(map(str, self.dict))
return "%s([%s])" % (type(self).__name__, elements)

__le__ = issubset
__ge__ = issuperset
__or__ = union
__and__ = intersection
__sub__ = difference
__xor__ = symmetric_difference

class frozenset(BaseSet):
"A frozenset is a BaseSet that has a hash value and is immutable."

def __init__(self, elements=[]):
BaseSet.__init__(elements)
self.hash = 0
for e in self:
self.hash |= hash(e)

def __hash__(self):
return self.hash

class set(BaseSet):
"A set is a BaseSet that does not have a hash, but is mutable."

def update(self, other):
for e in other:
self.add(e)
return self

def intersection_update(self, other):
for e in self.dict.keys():
if e not in other:
self.remove(e)
return self

def difference_update(self, other):
for e in self.dict.keys():
if e in other:
self.remove(e)
return self

def symmetric_difference_update(self, other):
to_remove1 = [e for e in self.dict if e in other]
to_remove2 = [e for e in other if e in self.dict]
self.difference_update(to_remove1)
self.difference_update(to_remove2)
return self

def add(self, element):
self.dict[element] = 1

def remove(self, element):
del self.dict[element]

def discard(self, element):
if element in self.dict:
del self.dict[element]

def pop(self):
key, val = self.dict.popitem()
return key

def clear(self):
self.dict.clear()

__ior__ = update
__iand__ = intersection_update
__isub__ = difference_update
__ixor__ = symmetric_difference_update

# Simple Data Structures: infinity, Dict, Struct

infinity = 1.0e400

def Dict(**entries):
"""Create a dict out of the argument=value arguments.
>>> Dict(a=1, b=2, c=3)
{'a': 1, 'c': 3, 'b': 2}
"""
return entries

class DefaultDict(dict):
"""Dictionary with a default value for unknown keys."""
def __init__(self, default):
self.default = default

def __getitem__(self, key):
if key in self: return self.get(key)
return self.setdefault(key, copy.deepcopy(self.default))

def __copy__(self):
copy = DefaultDict(self.default)
copy.update(self)
return copy

class Struct:
"""Create an instance with argument=value slots.
This is for making a lightweight object whose class doesn't matter."""
def __init__(self, **entries):
self.__dict__.update(entries)

def __cmp__(self, other):
if isinstance(other, Struct):
return cmp(self.__dict__, other.__dict__)
else:
return cmp(self.__dict__, other)

def __repr__(self):
args = ['%s=%s' % (k, repr(v)) for (k, v) in vars(self).items()]
return 'Struct(%s)' % ', '.join(args)

def update(x, **entries):
"""Update a dict; or an object with slots; according to entries.
>>> update({'a': 1}, a=10, b=20)
{'a': 10, 'b': 20}
>>> update(Struct(a=1), a=10, b=20)
Struct(a=10, b=20)
"""
if isinstance(x, dict):
x.update(entries)
else:
x.__dict__.update(entries)
return x

# Functions on Sequences (mostly inspired by Common Lisp)
# NOTE: Sequence functions (count_if, find_if, every, some) take function
# argument first (like reduce, filter, and map).

def removeall(item, seq):
"""Return a copy of seq (or string) with all occurences of item removed.
>>> removeall(3, [1, 2, 3, 3, 2, 1, 3])
[1, 2, 2, 1]
>>> removeall(4, [1, 2, 3])
[1, 2, 3]
"""
if isinstance(seq, str):
return seq.replace(item, '')
else:
return [x for x in seq if x != item]

def unique(seq):
"""Remove duplicate elements from seq. Assumes hashable elements.
>>> unique([1, 2, 3, 2, 1])
[1, 2, 3]
"""
return list(set(seq))

def product(numbers):
"""Return the product of the numbers.
>>> product([1,2,3,4])
24
"""
return reduce(operator.mul, numbers, 1)

def count_if(predicate, seq):
"""Count the number of elements of seq for which the predicate is true.
>>> count_if(callable, [42, None, max, min])
2
"""
f = lambda count, x: count + (not not predicate(x))
return reduce(f, seq, 0)

def find_if(predicate, seq):
"""If there is an element of seq that satisfies predicate; return it.
>>> find_if(callable, [3, min, max])
<built-in function min>
>>> find_if(callable, [1, 2, 3])
"""
for x in seq:
if predicate(x): return x
return None

def every(predicate, seq):
"""True if every element of seq satisfies predicate.
>>> every(callable, [min, max])
1
>>> every(callable, [min, 3])
0
"""
for x in seq:
if not predicate(x): return False
return True

def some(predicate, seq):
"""If some element x of seq satisfies predicate(x), return predicate(x).
>>> some(callable, [min, 3])
1
>>> some(callable, [2, 3])
0
"""
for x in seq:
px = predicate(x)
if  px: return px
return False

def isin(elt, seq):
"""Like (elt in seq), but compares with is, not ==.
>>> e = []; isin(e, [1, e, 3])
True
>>> isin(e, [1, [], 3])
False
"""
for x in seq:
if elt is x: return True
return False

# Functions on sequences of numbers
# NOTE: these take the sequence argument first, like min and max,
# and like standard math notation: \sigma (i = 1..n) fn(i)
# A lot of programing is finding the best value that satisfies some condition;
# so there are three versions of argmin/argmax, depending on what you want to
# do with ties: return the first one, return them all, or pick at random.

def argmin(seq, fn):
"""Return an element with lowest fn(seq[i]) score; tie goes to first one.
>>> argmin(['one', 'to', 'three'], len)
'to'
"""
best = seq; best_score = fn(best)
for x in seq:
x_score = fn(x)
if x_score < best_score:
best, best_score = x, x_score
return best

def argmin_list(seq, fn):
"""Return a list of elements of seq[i] with the lowest fn(seq[i]) scores.
>>> argmin_list(['one', 'to', 'three', 'or'], len)
['to', 'or']
"""
best_score, best = fn(seq), []
for x in seq:
x_score = fn(x)
if x_score < best_score:
best, best_score = [x], x_score
elif x_score == best_score:
best.append(x)
return best

def argmin_random_tie(seq, fn):
"""Return an element with lowest fn(seq[i]) score; break ties at random.
Thus, for all s,f: argmin_random_tie(s, f) in argmin_list(s, f)"""
best_score = fn(seq); n = 0
for x in seq:
x_score = fn(x)
if x_score < best_score:
best, best_score = x, x_score; n = 1
elif x_score == best_score:
n += 1
if random.randrange(n) == 0:
best = x
return best

def argmax(seq, fn):
"""Return an element with highest fn(seq[i]) score; tie goes to first one.
>>> argmax(['one', 'to', 'three'], len)
'three'
"""
return argmin(seq, lambda x: -fn(x))

def argmax_list(seq, fn):
"""Return a list of elements of seq[i] with the highest fn(seq[i]) scores.
>>> argmax_list(['one', 'three', 'seven'], len)
['three', 'seven']
"""
return argmin_list(seq, lambda x: -fn(x))

def argmax_random_tie(seq, fn):
"Return an element with highest fn(seq[i]) score; break ties at random."
return argmin_random_tie(seq, lambda x: -fn(x))
# Statistical and mathematical functions

def histogram(values, mode=0, bin_function=None):
"""Return a list of (value, count) pairs, summarizing the input values.
Sorted by increasing value, or if mode=1, by decreasing count.
If bin_function is given, map it over values first."""
if bin_function: values = map(bin_function, values)
bins = {}
for val in values:
bins[val] = bins.get(val, 0) + 1
if mode:
return sorted(bins.items(), key=lambda v: v, reverse=True)
else:
return sorted(bins.items())

def log2(x):
"""Base 2 logarithm.
>>> log2(1024)
10.0
"""
return math.log10(x) / math.log10(2)

def mode(values):
"""Return the most common value in the list of values.
>>> mode([1, 2, 3, 2])
2
"""
return histogram(values, mode=1)

def median(values):
"""Return the middle value, when the values are sorted.
If there are an odd number of elements, try to average the middle two.
If they can't be averaged (e.g. they are strings), choose one at random.
>>> median([10, 100, 11])
11
>>> median([1, 2, 3, 4])
2.5
"""
n = len(values)
values = sorted(values)
if n % 2 == 1:
return values[n/2]
else:
middle2 = values[(n/2)-1:(n/2)+1]
try:
return mean(middle2)
except TypeError:
return random.choice(middle2)

def mean(values):
"""Return the arithmetic average of the values."""
return sum(values) / float(len(values))

def stddev(values, meanval=None):
"""The standard deviation of a set of values.
Pass in the mean if you already know it."""
if meanval == None: meanval = mean(values)
return math.sqrt(sum([(x - meanval)**2 for x in values]) / (len(values)-1))

def dotproduct(X, Y):
"""Return the sum of the element-wise product of vectors x and y.
>>> dotproduct([1, 2, 3], [1000, 100, 10])
1230
"""
return sum([x * y for x, y in zip(X, Y)])

def vector_add(a, b):
"""Component-wise addition of two vectors.
>>> vector_add((0, 1), (8, 9))
(8, 10)
"""
return tuple(map(operator.add, a, b))

def probability(p):
"Return true with probability p."
return p > random.uniform(0.0, 1.0)

def num_or_str(x):
"""The argument is a string; convert to a number if possible, or strip it.
>>> num_or_str('42')
42
>>> num_or_str(' 42x ')
'42x'
"""
if isnumber(x): return x
try:
return int(x)
except ValueError:
try:
return float(x)
except ValueError:
return str(x).strip()

def normalize(numbers, total=1.0):
"""Multiply each number by a constant such that the sum is 1.0 (or total).
>>> normalize([1,2,1])
[0.25, 0.5, 0.25]
"""
k = total / sum(numbers)
return [k * n for n in numbers]

## OK, the following are not as widely useful utilities as some of the other
## functions here, but they do show up wherever we have 2D grids: Wumpus and
## Vacuum worlds, TicTacToe and Checkers, and markov decision Processes.

orientations = [(1,0), (0, 1), (-1, 0), (0, -1)]

def turn_right(orientation):
return orientations[orientations.index(orientation)-1]

def turn_left(orientation):
return orientations[(orientations.index(orientation)+1) % len(orientations)]

def distance((ax, ay), (bx, by)):
"The distance between two (x, y) points."
return math.hypot((ax - bx), (ay - by))

def distance2((ax, ay), (bx, by)):
"The square of the distance between two (x, y) points."
return (ax - bx)**2 + (ay - by)**2

def clip(vector, lowest, highest):
"""Return vector, except if any element is less than the corresponding
value of lowest or more than the corresponding value of highest, clip to
those values.
>>> clip((-1, 10), (0, 0), (9, 9))
(0, 9)
"""
return type(vector)(map(min, map(max, vector, lowest), highest))
# Misc Functions

def printf(format, *args):
"""Format args with the first argument as format string, and write.
Return the last arg, or format itself if there are no args."""
sys.stdout.write(str(format) % args)
return if_(args, args[-1], format)

def caller(n=1):
"""Return the name of the calling function n levels up in the frame stack.
>>> caller(0)
'caller'
>>> def f():
...     return caller()
>>> f()
'f'
"""
import inspect
return  inspect.getouterframes(inspect.currentframe())[n]

def memoize(fn, slot=None):
"""Memoize fn: make it remember the computed value for any argument list.
If slot is specified, store result in that slot of first argument.
If slot is false, store results in a dictionary."""
if slot:
def memoized_fn(obj, *args):
if hasattr(obj, slot):
return getattr(obj, slot)
else:
val = fn(obj, *args)
setattr(obj, slot, val)
return val
else:
def memoized_fn(*args):
if not memoized_fn.cache.has_key(args):
memoized_fn.cache[args] = fn(*args)
return memoized_fn.cache[args]
memoized_fn.cache = {}
return memoized_fn

def if_(test, result, alternative):
"""Like C++ and Java's (test ? result : alternative), except
both result and alternative are always evaluated. However, if
either evaluates to a function, it is applied to the empty arglist,
so you can delay execution by putting it in a lambda.
>>> if_(2 + 2 == 4, 'ok', lambda: expensive_computation())
'ok'
"""
if test:
if callable(result): return result()
return result
else:
if callable(alternative): return alternative()
return alternative

def name(object):
"Try to find some reasonable name for the object."
return (getattr(object, 'name', 0) or getattr(object, '__name__', 0)
or getattr(getattr(object, '__class__', 0), '__name__', 0)
or str(object))

def isnumber(x):
"Is x a number? We say it is if it has a __int__ method."
return hasattr(x, '__int__')

def issequence(x):
"Is x a sequence? We say it is if it has a __getitem__ method."
return hasattr(x, '__getitem__')

def print_table(table, header=None, sep=' ', numfmt='%g'):
"""Print a list of lists as a table, so that columns line up nicely.
header, if specified, will be printed as the first row.
numfmt is the format for all numbers; you might want e.g. '%6.2f'.
(If you want different formats in differnt columns, don't use print_table.)
sep is the separator between columns."""
justs = [if_(isnumber(x), 'rjust', 'ljust') for x in table]
if header:
table = [header] + table
table = [[if_(isnumber(x), lambda: numfmt % x, x)  for x in row]
for row in table]
maxlen = lambda seq: max(map(len, seq))
sizes = map(maxlen, zip(*[map(str, row) for row in table]))
for row in table:
for (j, size, x) in zip(justs, sizes, row):
print getattr(str(x), j)(size), sep,
print

def AIMAFile(components, mode='r'):
"Open a file based at the AIMA root directory."
import utils
dir = os.path.dirname(utils.__file__)
return open(apply(os.path.join, [dir] + components), mode)

def DataFile(name, mode='r'):
"Return a file in the AIMA /data directory."
return AIMAFile(['..', 'data', name], mode)

# Queues: Stack, FIFOQueue, PriorityQueue

class Queue:
"""Queue is an abstract class/interface. There are three types:
Stack(): A Last In First Out Queue.
FIFOQueue(): A First In First Out Queue.
PriorityQueue(lt): Queue where items are sorted by lt, (default <).
Each type supports the following methods and functions:
q.append(item)  -- add an item to the queue
q.extend(items) -- equivalent to: for item in items: q.append(item)
q.pop()         -- return the top item from the queue
len(q)          -- number of items in q (also q.__len())
Note that isinstance(Stack(), Queue) is false, because we implement stacks
as lists.  If Python ever gets interfaces, Queue will be an interface."""

def __init__(self):
abstract

def extend(self, items):
for item in items: self.append(item)

def Stack():
"""Return an empty list, suitable as a Last-In-First-Out Queue."""
return []

class FIFOQueue(Queue):
"""A First-In-First-Out Queue."""
def __init__(self):
self.A = []; self.start = 0
def append(self, item):
self.A.append(item)
def __len__(self):
return len(self.A) - self.start
def extend(self, items):
self.A.extend(items)
def pop(self):
e = self.A[self.start]
self.start += 1
if self.start > 5 and self.start > len(self.A)/2:
self.A = self.A[self.start:]
self.start = 0
return e

class PriorityQueue(Queue):
"""A queue in which the minimum (or maximum) element (as determined by f and
order) is returned first. If order is min, the item with minimum f(x) is
returned first; if order is max, then it is the item with maximum f(x)."""
def __init__(self, order=min, f=lambda x: x):
update(self, A=[], order=order, f=f)
def append(self, item):
bisect.insort(self.A, (self.f(item), item))
def __len__(self):
return len(self.A)
def pop(self):
if self.order == min:
return self.A.pop(0)
else:
return self.A.pop()

## Fig: The idea is we can define things like Fig[3,10] later.
## Alas, it is Fig[3,10] not Fig[3.10], because that would be the same as Fig[3.1]
Fig = {}



 AI: A Modern Approach by Stuart Russell and Peter Norvig Modified: Jul 18, 2005