from __future__ import absolute_import, division

import __builtin__
import math
import random
import time

def median(x, use_float=True):
    # there exist better algorithms...
    y = sorted(x)
    if not y:
        raise ValueError('empty sequence!')
    left = (len(y) - 1)//2
    right = len(y)//2
    sum = y[left] + y[right]
    if use_float:
        return sum/2
    else:
        return sum//2

def mean(x):
    total = 0
    count = 0
    for y in x:
        total += y
        count += 1
    return total/count

def shuffled(x):
    x = list(x)
    random.shuffle(x)
    return x

def shift_left(n, m):
    # python: :(
    if m >= 0:
        return n << m
    return n >> -m

def clip(x, (low, high)):
    if x < low:
        return low
    elif x > high:
        return high
    else:
        return x

add_to_range = lambda x, (low, high): (min(low, x), max(high, x))

def nth(i, n=0):
    i = iter(i)
    for _ in xrange(n):
        i.next()
    return i.next()

def geometric(p):
    if p <= 0 or p > 1:
        raise ValueError('p must be in the interval (0.0, 1.0]')
    if p == 1:
        return 1
    return int(math.log1p(-random.random()) / math.log1p(-p)) + 1

def add_dicts_ext(add_func=lambda a, b: a+b, zero=0):
    def add_dicts(*dicts):
        res = {}
        for d in dicts:
            for k, v in d.iteritems():
                res[k] = add_func(res.get(k, zero), v)
        return dict((k, v) for k, v in res.iteritems() if v != zero)
    return add_dicts
add_dicts = add_dicts_ext()

mult_dict = lambda c, x: dict((k, c*v) for k, v in x.iteritems())

def format(x):
    prefixes = 'kMGTPEZY'
    count = 0
    while x >= 100000 and count < len(prefixes) - 2:
        x = x//1000
        count += 1
    s = '' if count == 0 else prefixes[count - 1]
    return '%i' % (x,) + s

def format_dt(dt):
    for value, name in [(365.2425*60*60*24, 'years'), (60*60*24, 'days'), (60*60, 'hours'), (60, 'minutes'), (1, 'seconds')]:
        if dt > value:
            break
    return '%.01f %s' % (dt/value, name)

perfect_round = lambda x: int(x + random.random())

def erf(x):
    # save the sign of x
    sign = 1
    if x < 0:
        sign = -1
    x = abs(x)
    
    # constants
    a1 =  0.254829592
    a2 = -0.284496736
    a3 =  1.421413741
    a4 = -1.453152027
    a5 =  1.061405429
    p  =  0.3275911
    
    # A&S formula 7.1.26
    t = 1.0/(1.0 + p*x)
    y = 1.0 - (((((a5*t + a4)*t) + a3)*t + a2)*t + a1)*t*math.exp(-x*x)
    return sign*y # erf(-x) = -erf(x)

def find_root(y_over_dy, start, steps=10, bounds=(None, None)):
    guess = start
    for i in xrange(steps):
        prev, guess = guess, guess - y_over_dy(guess)
        if bounds[0] is not None and guess < bounds[0]: guess = bounds[0]
        if bounds[1] is not None and guess > bounds[1]: guess = bounds[1]
        if guess == prev:
            break
    return guess

def ierf(z):
    return find_root(lambda x: (erf(x) - z)/(2*math.e**(-x**2)/math.sqrt(math.pi)), 0)

def binomial_conf_interval(x, n, conf=0.95):
    assert 0 <= x <= n and 0 <= conf < 1
    if n == 0:
        left = random.random()*(1 - conf)
        return left, left + conf
    # approximate - Wilson score interval
    z = math.sqrt(2)*ierf(conf)
    p = x/n
    topa = p + z**2/2/n
    topb = z * math.sqrt(p*(1-p)/n + z**2/4/n**2)
    bottom = 1 + z**2/n
    return [clip(x, (0, 1)) for x in add_to_range(x/n, [(topa - topb)/bottom, (topa + topb)/bottom])]

minmax = lambda x: (min(x), max(x))

def format_binomial_conf(x, n, conf=0.95, f=lambda x: x):
    if n == 0:
        return '???'
    left, right = minmax(map(f, binomial_conf_interval(x, n, conf)))
    return '~%.1f%% (%.f-%.f%%)' % (100*f(x/n), math.floor(100*left), math.ceil(100*right))

def reversed(x):
    try:
        return __builtin__.reversed(x)
    except TypeError:
        return reversed(list(x))

class Object(object):
    def __init__(self, **kwargs):
        for k, v in kwargs.iteritems():
            setattr(self, k, v)

def add_tuples(res, *tuples):
    for t in tuples:
        if len(t) != len(res):
            raise ValueError('tuples must all be the same length')
        res = tuple(a + b for a, b in zip(res, t))
    return res

def flatten_linked_list(x):
    while x is not None:
        x, cur = x
        yield cur

def weighted_choice(choices):
    choices = list((item, weight) for item, weight in choices)
    target = random.randrange(sum(weight for item, weight in choices))
    for item, weight in choices:
        if weight > target:
            return item
        target -= weight
    raise AssertionError()

def natural_to_string(n, alphabet=None):
    if n < 0:
        raise TypeError('n must be a natural')
    if alphabet is None:
        s = ('%x' % (n,)).lstrip('0')
        if len(s) % 2:
            s = '0' + s
        return s.decode('hex')
    else:
        assert len(set(alphabet)) == len(alphabet)
        res = []
        while n:
            n, x = divmod(n, len(alphabet))
            res.append(alphabet[x])
        res.reverse()
        return ''.join(res)

def string_to_natural(s, alphabet=None):
    if alphabet is None:
        assert not s.startswith('\x00')
        return int(s.encode('hex'), 16) if s else 0
    else:
        assert len(set(alphabet)) == len(alphabet)
        assert not s.startswith(alphabet[0])
        return sum(alphabet.index(char) * len(alphabet)**i for i, char in enumerate(reversed(s)))

class RateMonitor(object):
    def __init__(self, max_lookback_time):
        self.max_lookback_time = max_lookback_time
        
        self.datums = []
        self.first_timestamp = None
    
    def _prune(self):
        start_time = time.time() - self.max_lookback_time
        for i, (ts, datum) in enumerate(self.datums):
            if ts > start_time:
                self.datums[:] = self.datums[i:]
                return
    
    def get_datums_in_last(self, dt=None):
        if dt is None:
            dt = self.max_lookback_time
        assert dt <= self.max_lookback_time
        self._prune()
        now = time.time()
        return [datum for ts, datum in self.datums if ts > now - dt], min(dt, now - self.first_timestamp) if self.first_timestamp is not None else 0
    
    def add_datum(self, datum):
        self._prune()
        t = time.time()
        if self.first_timestamp is None:
            self.first_timestamp = t
        else:
            self.datums.append((t, datum))