Artificial Intelligence: A Modern Approach

AIMA Python file:

"""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, 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" 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[0]; 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[0]), [] 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[0]); 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[1], 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)[0][0] 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][3] 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[0]] 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)[1] else: return self.A.pop()[1] ## 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 NorvigModified: Jul 18, 2005