"""Provide some widely useful functions and objects."""

infinity = float('inf')

argmin = min

argmax = max

def ignore(x): None

def identity(x): 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
    """
    result=1
    for i in numbers:
        result=result*i
    return result


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



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_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 x: (x[1],x[0]), 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 is 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 weighted_sample_with_replacement(seq, weights, n):
    """Pick n samples from seq at random, with replacement, with the
    probability of each element in proportion to its corresponding
    weight."""
    sample = weighted_sampler(seq, weights)
    return [sample() for s in range(n)]

def weighted_sampler(seq, weights):
    "Return a random-sample function that picks from seq weighted by weights."
    totals = []
    for w in weights:
        totals.append(w + totals[-1] if totals else w)
    return lambda: seq[bisect.bisect(totals, random.uniform(0, totals[-1]))]

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

def clip(x, lowest, highest):
    """Return x clipped to the range [lowest..highest].
    >>> [clip(x, 0, 1) for x in [-1, 0.5, 10]]
    [0, 0.5, 1]
    """
    return max(lowest, min(x, highest))

#______________________________________________________________________________
## 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_heading(heading, inc, headings=orientations):
    return headings[(headings.index(heading) + inc) % len(headings)]

def turn_right(heading):
    return turn_heading(heading, -1)

def turn_left(heading):
    return turn_heading(heading, +1)

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 vector_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.
    >>> vector_clip((-1, 10), (0, 0), (9, 9))
    (0, 9)
    """
    return type(vector)(map(clip, 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, lambda: args[-1], lambda: format)

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 name(object):
    "Try to find some reasonable name for the object."
    return (getattr(object, 'name', False) or
            getattr(object, '__name__', False) or
            getattr(getattr(object, '__class__', None), '__name__', False) or
            str(object))

def isnumber(x):
    "Is x a number? We say it is if it is a float, int, or complex."
    return isinstance(x, (int, float, complex))

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 different 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, lambda: 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:
        print sep.join(getattr(str(x), j)(size)
                       for (j, size, x) in zip(justs, sizes, row))

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(order, f): Queue in sorted order (default min-first).
    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())
        item in q       -- does q contain item?
    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
    def __contains__(self, item):
        return item in self.A[self.start:]

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).
    Also supports dict-like lookup."""
    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]
    def __contains__(self, item):
        return some(lambda (_, x): x == item, self.A)
    def __getitem__(self, key):
        for _, item in self.A:
            if item == key:
                return item
    def __delitem__(self, key):
        for i, (value, item) in enumerate(self.A):
            if item == key:
                self.A.pop(i)
                return

## 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 = {}

#______________________________________________________________________________
# Support for doctest



def random_tests(text):
    """Some functions are stochastic. We want to be able to write a test
    with random output.  We do that by ignoring the output."""
    def fixup(test):
        if " = " in test:
            return ">>> " + test
        else:
            return ">>> ignore(" + test + ")"
    tests =  re.findall(">>> (.*)", text)
    return '\n'.join(map(fixup, tests))

#______________________________________________________________________________

__doc__ += """
>>> d = DefaultDict(0)
>>> d['x'] += 1
>>> d['x']
1

>>> d = DefaultDict([])
>>> d['x'] += [1]
>>> d['y'] += [2]
>>> d['x']
[1]

>>> s = Struct(a=1, b=2)
>>> s.a
1
>>> s.a = 3
>>> s
Struct(a=3, b=2)

>>> def is_even(x):
...     return x % 2 == 0
>>> sorted([1, 2, -3])
[-3, 1, 2]
>>> sorted(range(10), key=is_even)
[1, 3, 5, 7, 9, 0, 2, 4, 6, 8]
>>> sorted(range(10), lambda x,y: y-x)
[9, 8, 7, 6, 5, 4, 3, 2, 1, 0]

>>> removeall(4, [])
[]
>>> removeall('s', 'This is a test. Was a test.')
'Thi i a tet. Wa a tet.'
>>> removeall('s', 'Something')
'Something'
>>> removeall('s', '')
''

>>> list(reversed([]))
[]

>>> count_if(is_even, [1, 2, 3, 4])
2
>>> count_if(is_even, [])
0

>>> argmax([1], lambda x: x*x)
1
>>> argmin([1], lambda x: x*x)
1


# Test of memoize with slots in structures
>>> countries = [Struct(name='united states'), Struct(name='canada')]

# Pretend that 'gnp' was some big hairy operation:
>>> def gnp(country):
...     print 'calculating gnp ...'
...     return len(country.name) * 1e10

>>> gnp = memoize(gnp, '_gnp')
>>> map(gnp, countries)
calculating gnp ...
calculating gnp ...
[130000000000.0, 60000000000.0]
>>> countries
[Struct(_gnp=130000000000.0, name='united states'), Struct(_gnp=60000000000.0, name='canada')]

# This time we avoid re-doing the calculation
>>> map(gnp, countries)
[130000000000.0, 60000000000.0]

# Test Queues:
>>> nums = [1, 8, 2, 7, 5, 6, -99, 99, 4, 3, 0]
>>> def qtest(q):
...     q.extend(nums)
...     for num in nums: assert num in q
...     assert 42 not in q
...     return [q.pop() for i in range(len(q))]
>>> qtest(Stack())
[0, 3, 4, 99, -99, 6, 5, 7, 2, 8, 1]

>>> qtest(FIFOQueue())
[1, 8, 2, 7, 5, 6, -99, 99, 4, 3, 0]

>>> qtest(PriorityQueue(min))
[-99, 0, 1, 2, 3, 4, 5, 6, 7, 8, 99]

>>> qtest(PriorityQueue(max))
[99, 8, 7, 6, 5, 4, 3, 2, 1, 0, -99]

>>> qtest(PriorityQueue(min, abs))
[0, 1, 2, 3, 4, 5, 6, 7, 8, -99, 99]

>>> qtest(PriorityQueue(max, abs))
[99, -99, 8, 7, 6, 5, 4, 3, 2, 1, 0]

>>> vals = [100, 110, 160, 200, 160, 110, 200, 200, 220]
>>> histogram(vals)
[(100, 1), (110, 2), (160, 2), (200, 3), (220, 1)]
>>> histogram(vals, 1)
[(200, 3), (160, 2), (110, 2), (220, 1), (100, 1)]
>>> histogram(vals, 1, lambda v: round(v, -2))
[(200.0, 6), (100.0, 3)]

>>> log2(1.0)
0.0

>>> def fib(n):
...     return (n<=1 and 1) or (fib(n-1) + fib(n-2))

>>> fib(9)
55

# Now we make it faster:
>>> fib = memoize(fib)
>>> fib(9)
55

>>> q = Stack()
>>> q.append(1)
>>> q.append(2)
>>> q.pop(), q.pop()
(2, 1)

>>> q = FIFOQueue()
>>> q.append(1)
>>> q.append(2)
>>> q.pop(), q.pop()
(1, 2)


>>> abc = set('abc')
>>> bcd = set('bcd')
>>> 'a' in abc
True
>>> 'a' in bcd
False
>>> list(abc.intersection(bcd))
['c', 'b']
>>> list(abc.union(bcd))
['a', 'c', 'b', 'd']

## From "What's new in Python 2.4", but I added calls to sl

>>> def sl(x):
...     return sorted(list(x))


>>> a = set('abracadabra')                  # form a set from a string
>>> 'z' in a                                # fast membership testing
False
>>> sl(a)                                   # unique letters in a
['a', 'b', 'c', 'd', 'r']

>>> b = set('alacazam')                     # form a second set
>>> sl(a - b)                               # letters in a but not in b
['b', 'd', 'r']
>>> sl(a | b)                               # letters in either a or b
['a', 'b', 'c', 'd', 'l', 'm', 'r', 'z']
>>> sl(a & b)                               # letters in both a and b
['a', 'c']
>>> sl(a ^ b)                               # letters in a or b but not both
['b', 'd', 'l', 'm', 'r', 'z']


>>> a.add('z')                              # add a new element
>>> a.update('wxy')                         # add multiple new elements
>>> sl(a)
['a', 'b', 'c', 'd', 'r', 'w', 'x', 'y', 'z']
>>> a.remove('x')                           # take one element out
>>> sl(a)
['a', 'b', 'c', 'd', 'r', 'w', 'y', 'z']

>>> weighted_sample_with_replacement([], [], 0)
[]
>>> weighted_sample_with_replacement('a', [3], 2)
['a', 'a']
>>> weighted_sample_with_replacement('ab', [0, 3], 3)
['b', 'b', 'b']
"""

__doc__ += random_tests("""
>>> weighted_sample_with_replacement(range(10), [x*x for x in range(10)], 3)
[8, 9, 6]
""")