from __future__ import absolute_import, division

import __builtin__
import math
import random

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

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(*dicts):
    res = {}
    for d in dicts:
        for k, v in d.iteritems():
            res[k] = res.get(k, 0) + v
    return dict((k, v) for k, v in res.iteritems() if v)

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

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)

try:
    from scipy import special
except ImportError:
    print 'Install SciPy for more accurate confidence intervals!'
    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)
        # 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 (topa - topb)/bottom, (topa + topb)/bottom
else:
    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
        b = special.beta(x+1, n-x+1)
        def f(left_a):
            left, right = max(1e-8, special.betaincinv(x+1, n-x+1, left_a)), min(1-1e-8, special.betaincinv(x+1, n-x+1, left_a + conf))
            top = right**(x+1) * (1-right)**(n-x+1) * left*(1-left) - left**(x+1) * (1-left)**(n-x+1) * right * (1-right)
            bottom = (x - n*right)*left*(1-left) - (x - n*left)*right*(1-right)
            return top/bottom/b
        left_a = find_root(f, (1-conf)/2, bounds=(0, 1-conf))
        return special.betaincinv(x+1, n-x+1, left_a), special.betaincinv(x+1, n-x+1, left_a + conf)

def binomial_conf_center_radius(x, n, conf=0.95):
    assert 0 <= x <= n and 0 <= conf < 1
    left, right = binomial_conf_interval(x, n, conf)
    if n == 0:
        return (left+right)/2, (right-left)/2
    p = x/n
    return p, max(p - left, right - p)

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), left-1/2, right+1/2)

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,)
        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)))

if __name__ == '__main__':
    import random
    a = 1
    while True:
        print a, format(a) + 'H/s'
        a = a * random.randrange(2, 5)