def wangdomain(own_ship_xy, length, vown, cog=0, k_shape=2, r_static=0.5):
"""
Parameters
----------
own_ship_xy : (float, float)
xy coordinates of ellipse centre.
cog : scalar, optional
Rotation in degrees anti-clockwise.
vown: is the own ship speed represented in knots
k_shape :shape index
"""
# Constant
r0 = 0.5
# L is the own ship length,
# k_AD and k_DT represent gains of the advance, AD ,
# and the tactical diameter, D T ,
k_ad = 10**(0.359 * lg(vown) + 0.0952)
k_dt = 10**(0.541 * lg(vown) - 0.0795)
R_fore = (1 + 1.34 * sqrt((k_ad)**2 + (k_dt / 2)**2)) * length
R_aft = (1 + 0.67 * sqrt((k_ad)**2 + (k_dt / 2)**2)) * length
R_starb = (0.2 + k_dt) * length
R_port = (0.2 + 0.75 * k_dt) * length
R = np.array((R_fore, R_aft, R_starb, R_port))
r_fuzzy = ((ln(1 / r_static)) / (ln(1 / r0)))**(1 / k_shape)
R_fuzzy = r_fuzzy * R
# y_1: first quadrant x >= 0 y >= 0
x_max = R_fuzzy[0]
x_min = -R_fuzzy[1]
x_serises_plus = np.linspace(0, x_max, 80)
x_serises_minus = np.linspace(x_min, -0.01, 80)
# x>=0, y>=0
y_1 = R_fuzzy[2] * pow(
(1 - (x_serises_plus / R_fuzzy[0])**k_shape), 1 / k_shape)
y_4 = R_fuzzy[3] * -pow(
(1 - (x_serises_plus / R_fuzzy[0])**k_shape), 1 / k_shape)
y_2 = R_fuzzy[2] * pow(
(1 - (-x_serises_minus / R_fuzzy[1])**k_shape), 1 / k_shape)
y_3 = R_fuzzy[3] * -pow(
(1 - (-x_serises_minus / R_fuzzy[1])**k_shape), 1 / k_shape)
# stack the column
curve1 = np.column_stack((x_serises_plus, y_1))
curve2 = np.column_stack((x_serises_minus, y_2))
curve3 = np.column_stack((x_serises_minus, y_3))
curve4 = np.column_stack((x_serises_plus, y_4))
# Primacy connection
curve4 = np.flipud(curve4)
curve3 = np.flipud(curve3)
# cat the data series to one curve.
curves = np.row_stack((curve1, curve4, curve3, curve2)).T
curves[0, :] += own_ship_xy[0]
curves[1, :] += own_ship_xy[1]
#
t_rot = pi * cog / 180 - pi / 2
R_rot = np.array([[cos(t_rot), sin(t_rot)], [-sin(t_rot), cos(t_rot)]])
for i in range(curves.shape[1]):
curves[:, i] = np.dot(R_rot, curves[:, i])
return curves
def print_rates(E):
from math import log as lg
print '%.4e - %.4e - ' \
%(E[0][0], E[0][1])
for i in range(1, len(E)):
r1 = lg(E[i-1][0]/E[i][0], 2)
r2 = lg(E[i-1][1]/E[i][1], 2)
print '%.4e %.2f %.4e %.2f' \
%(E[i][0], r1, E[i][1], r2)
print '\n'
def get_L(data, num_clusters, mean_li, cov_li, phi_matrix, pi_vect):
L_func_value= 0
#print(pi_vect)
#print(phi_matrix)
for i in range(len(data)):
for j in range(num_clusters):
L_func_value += phi_matrix[i][j] * ( lg(pi_vect[j]) + lg(ss.multivariate_normal.pdf(data[i], mean_li[j], cov_li[j], allow_singular=True) ) )
print(L_func_value)
return L_func_value
def expg( a, b ):
"""
Returns the largest ( base, exponent ) tuple from a, b.
This solution utilizes logarithmic properties to simplify the calculations.
Consider two base-exponent pairs that we want to compare, say a**b and c**d:
a**b > c**d
( 10**loga )**b > ( 10**logc )**d
10**( loga * b ) > 10**( logc * d )
Now we have the same base, and we can simplify our comparison:
loga * b > logc * d
"""
return a if lg( a[ 0 ] ) * a[ 1 ] > lg( b[ 0 ] ) * b[ 1 ] else b
def get_public_tags_cloud(force_reload=False):
"""
return tags cloud: list of tuples-pairs ("tag", "tag_weight"), tag_weight - is a number divisible by 5,
0 <= tag_weight <= 100
Only for published articles.
"""
value = cache.get_value('tags_cloud')
if value is None or force_reload:
dbsession = DBSession()
q = dbsession.query(func.count(Tag.id), Tag.tag).join(Article).filter(Article.is_draft==False).group_by(Tag.tag)
items = list()
counts = list()
total = 0
for rec in q.all():
if rec[0] <= 0:
continue
total += rec[0]
items.append((rec[1], int(rec[0])))
counts.append(int(rec[0]))
if len(counts) != 0:
min_count = min(counts)
max_counts = max(counts)
if min_count == max_counts:
# i.e. all tags counts are the same, so they have the same weight
weights = [(x[0], 50) for x in items]
else:
lmm = lg(max_counts) - lg(min_count)
weights = [(x[0], (lg(x[1])-lg(min_count)) / lmm) for x in items]
weights = [(x[0], int(5*(int(100*x[1])/5))) for x in weights]
value = weights
else:
value = []
cache.set_value('tags_cloud', value)
return value
def pearson_criterion(sample, distribution, mean, var):
a = 0.05
n = len(sample)
# k = int(1.72 * n ** (1 / 3))
k = int(1 + 3.3 * lg(n))
xsi = get_xsi(k - 1, 1 - a)
ns, deltas = divide_sample(sample, k, mean, 0.3)
print(f"ni: {str(ns)}")
ps = count_pi(deltas, distribution)
print(f"pi: {str(ps)}")
xsi_b = count_xsi_b(ns, ps, n)
if xsi_b < xsi:
return True
return False
class Func:
n,p,s,v = map(float,input().split())
sq2 = sqrt(2)
lgn = lg(n)
a = (n/(p*10**9))
b = s/v
@staticmethod
def f(c):
return Func.a * (Func.lgn)**(c*Func.sq2) + Func.b * (1+1/c)
@staticmethod
def g(c):
return 1/(Func.a * (Func.lgn)**(c*Func.sq2) + Func.b * (1+1/c))
def pre_process():
years_to_bits = {
y: 2**(i + 2)
for i, y in enumerate(range(1960, 2170, 10))
}
years_to_n = {}
s, n, year = 0, 2, 1960
while year < 2170:
s += lg(n)
if s > years_to_bits[year]:
years_to_n[year] = n - 1
year += 10
n += 1
return years_to_n
def check_n_selfnum(num):
temp=[num]
k=9
while(k>1):
k =int(lg(num+0.1))
t =int(num//pow(10, k ))
num =int(num%pow(10, k))
temp.append(t)
# print('k:', k ,' num: ',num)
temp.append(num%10)
# print('temp : ', temp, 'remove : ',sum(temp))
try:
self_num_list.remove(sum(temp))
except:
pass
def getAuxInfo(logFileName, profileFileName):
logFile = open(logFileName, 'r')
csv_reader = csv.reader(logFile, delimiter='\t')
log = [tuple(x) for x in csv_reader]
log = log[1:]
logFile.close()
# MSn_Scan -- 0
# Parent_Scan -- 2
# Mono_Intensity -- 10
if log[7] == ('MSn_Scan', 'MSn_Level', 'Parent_Scan', 'Parent_Scan_Level',
'Parent_Mz', 'Mono_Mz', 'Charge_State', 'Monoisotopic_Mass',
'Isotopic_Fit', 'Parent_Intensity', 'Mono_Intensity'):
log = log[8:]
else:
raise Exception
profileFile = open(profileFileName, 'r')
csv_reader = csv.reader(profileFile, delimiter='\t')
profile = [tuple(x) for x in csv_reader]
profileFile.close()
# AGC_accumulation_time -- 2
# TIC -- 3
if profile[0] == ('MSn_Scan', 'Parent_Scan', 'AGC_accumulation_time',
'TIC'):
profile = profile[1:]
else:
raise Exception
dictAuxInfo = {}
# len(log) should be equal to len(profile) now
for i in range(len(log)):
dictAuxInfo[log[i][0]] = (log[i][2],
lg(
float(log[i][10]) *
float(profile[i][2]) / 1000,
10), float(profile[i][3]) *
float(profile[i][2]) / 1000)
# returns key:ms2 values:(ms1, log10IntensityInTheTrap, TIC_InTheTrap)
return dictAuxInfo
def decrypt(self, e):
"""e is an encrypted message encoded as a polynomial"""
if self._f is None or self._g is None:
raise Exception("Private key not found.")
if e._N <= self._P.get_N():
if not self._fp:
self._fp = invert_in_p(self._f, self._P.get_N())
if not self._fq:
self._fq = invert_in2tor(self._f, self._P.get_N(),
int(lg(self._P.get_q())))
assert (self._h == self._fq * self._g)
a = (self._f * e) % self._P.get_q()
b = (self._fp * a) % self._P.get_p()
return b # decrypted message
else:
raise Exception("e is too large, must be equal or under size %d" %
self._P.get_N())
def rel(val: float, peak: float, digs: int = 0) -> str:
if val == 0:
return '-inf'
return str(round(20 * lg(abs(val) / peak), digs))
#! /usr/bin/env python
from functools import partial
import sys
if sys.version_info > (3, 5):
# python 3.5 or above
from math import log2
log = log2
str_utf8 = lambda x: str(x, 'utf-8')
else:
from math import log as lg
log = lambda x: lg(x, 2) if x > 0 else 0
str_utf8 = lambda x: str(x).encode('utf-8')
import click
attrs = [
"edibility",
"cap-shape",
"cap-surface",
"cap-color",
"bruises?",
"odor",
"grill-attachment",
"grill-spacing",
"grill-size",
"grill-color",
"stalk-shape",
"stalk-root",
"stalk-surface-above-ring",
def sharing_chromosomes(n, k):
return lg(sum(c(n, i) for i in range(k, n + 1))) - (n * lg(2))
def l2(num):
"""
log base 2
:rtype real
"""
return lg(num, 2)
from math import log as lg
if __name__=='__main__':
n,b,p=map(int,input().split())
bottle= 0
k = pow(2,int(lg(n,2)))
towel = n*p
while k>=2:
bottle += (k*b+int(k/2))
n = int(k/2)+n-k #winners + rem
if n>0:
k = pow(2,int(lg(n,2)))
print (bottle,towel)
#else
#print ((n-1)*(2*b+1),n*p)
'''
A. Tennis Tournament
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output
A tennis tournament with n participants is running. The participants are playing by an olympic system, so the winners move on and the losers drop out.
The tournament takes place in the following way (below, m is the number of the participants of the current round):
#difficulty calculator from math import log as lg rate = 100 #hash/sec idealreward = 1.0/60.0 #block/sec """ idealreward = 1-(1-difficulty)**rate lg(id - 1)/lg(rate) = 1 - difficulty 1- lg(id - 1)/lg(rate) = difficulty """ difficulty = lg(1-idealreward**rate,.5) print difficulty print (2**(160-difficulty))/(2**160)
157185040413215530975165633061, 178617532837899776787217832941,
96368378329569366965481375161, 41702562059995270288416739123,
234425024443044792063543979349, 147325628837781527224761907889,
89981271475268439210802711349, 216948066429127138241721468529,
118962322543851674548159048321
]
#for p in TIMEOUTS:
# print(p)
from math import log2 as lg
import random
semiprimes = set([p * q for p in FIFTEEN_DIGIT for q in FIFTEEN_DIGIT])
#semiprimes = set([p*q for p in TEN_DIGIT for q in TWENTY_DIGIT])
suitable = [n for n in semiprimes if 96 <= lg(n) < 97]
#suitable = [n for n in semiprimes if lg(n) < 97]
#print (format(max(suitable), "02x"))
#print (format(min(suitable), "02x"))
#print (len(suitable))
random.shuffle(suitable)
#for n in suitable:
for n in suitable[:200]:
#for n in sorted(suitable)[-10:]:
#pass
print("0x{:02x}".format(n))
147325628837781527224761907889,
89981271475268439210802711349,
216948066429127138241721468529,
118962322543851674548159048321
]
#for p in TIMEOUTS:
# print(p)
from math import log2 as lg
import random
semiprimes = set([p*q for p in FIFTEEN_DIGIT for q in FIFTEEN_DIGIT])
#semiprimes = set([p*q for p in TEN_DIGIT for q in TWENTY_DIGIT])
suitable = [n for n in semiprimes if 96 <= lg(n) < 97]
#suitable = [n for n in semiprimes if lg(n) < 97]
#print (format(max(suitable), "02x"))
#print (format(min(suitable), "02x"))
#print (len(suitable))
random.shuffle(suitable)
#for n in suitable:
for n in suitable[:200]:
#for n in sorted(suitable)[-10:]:
#pass
print("0x{:02x}".format(n))
s = s1 = s2 = a1 = a2 = x = f = eps = i = 0
while not ((0 < eps < 1) and (-1 < x < 1)):
eps = float(input("Введите точность eps, (0 ;1) << "))
x = float(input("Введите значение x, (-1;1) << "))
s1 = s2 = a1 = a2 = x
i = 2
while (abs(a1 + a2) >= eps) and (i < 300):
a1 *= ((-x) * (i-1) / i)
a2 *= ((-x) / i)
s1 += a1
s2 += a2
i += 1
s = s1 + s2
f = ln(x) - exp(-x) + 1
eOut = trunc(lg(round(1/eps))) + 1
print(\
"\n"*2,\
f"Сумма ряда S >> %1.{eOut}f"%s, "\n",\
f"Контрольная формула F >> %1.{eOut}f"%f, "\n",\
"Количество итераций i >> ", i, "\n",\
f"S - F >> %1.{eOut}f"%(s-f),\
sep="")
def log0(x):
return 0 if x == 0 else lg(x)
def main():
n, k = map(int, input().split())
if k >= lg(n):
print('Your wish is granted!')
else:
print('You will become a flying monkey!')
def walther(temp_1, nu_1, temp_2, nu_2, temp_3):
"""
Calculate the kinematic viscosity at temperature `temp_3` based on the
kinematic viscosities at temperatures `temp_1` and `temp_2`. The
implementation follows standard ASTM D341.
Parameters
----------
temp_1: scalar
The temperature in :math:`^{\\circ}\\text{C}` that corresponds to the
kinematic viscosity :code:`nu_1`.
nu_1: scalar
The kinematic viscosity in cSt at temperature :code:`temp_1`.
temp_2: scalar
The temperature in :math:`^{\\circ}\\text{C}` that corresponds to the
kinematic viscosity :code:`nu_2`.
nu_2: scalar
The kinematic viscosity in cSt at temperature :code:`temp_2`.
temp_3: ndarray
The temperature in :math:`^{\\circ}\\text{C}` for which to calculate
the kinematic viscosity.
Returns
-------
nu_3: ndarray
The kinematic viscosity in cSt at temperature :code:`temp_3`.
"""
abs_zero = -273.15
viscs = [nu_1, nu_2]
thetas = [temp_1 - abs_zero, temp_2 - abs_zero, temp_3 - abs_zero]
zed = [__zedwalther(nu) for nu in viscs]
const_a = (lg(lg(zed[0])) - lg(lg(zed[1])) *
lg(thetas[0]) / lg(thetas[1])) / \
(1 - lg(thetas[0]) / lg(thetas[1]))
const_b = (const_a - lg(lg(zed[1]))) / lg(thetas[1])
nu_3 = __nuwalther(10**10**(const_a - const_b * np.log10(thetas[2])))
return nu_3
def h(distribution):
return sum(p * lg(1 / p) for p in distribution)
#difficulty calculator from math import log as lg rate = 100 #hash/sec idealreward = 1.0 / 60.0 #block/sec """ idealreward = 1-(1-difficulty)**rate lg(id - 1)/lg(rate) = 1 - difficulty 1- lg(id - 1)/lg(rate) = difficulty """ difficulty = lg(1 - idealreward**rate, .5) print difficulty print(2**(160 - difficulty)) / (2**160)