def extrapolate(x, y, t, mode="forward"):
# if sum(np.diff(x, n=2)) != 0:
# return None #check if the x spacing is constant
#let's assume this is correct for computational quickness
bino = lambda n, k: fact(n)/(fact(k)*fact(n-k))
if len(x) == 1:
return x[0]
h = float(x[1]-x[0])
derivatives = [0]*(len(y))
if mode == "forward":
f = lambda n, i, y: (-1)**i*bino(n,i)*y[n-i]
x0 = x[0]
derivatives[0]=y[0]
else:
f = lambda n, i, y: (-1)**i*bino(n,i)*y[-i-1]
x0 = x[-1]
derivatives[0] = y[-1]
for n in range(1,len(y)):
for i in range(0, n+1):
# print(n, i, f(n, i, y, bino))
derivatives[n] += f(n, i, y)
derivatives[n] /= h**n
return sum([derivatives[n]/fact(n)*(t-x0)**n for n in range(len(y))])
def problem_53():
from math import factorial as fact
c=0
for n in range(1,101):
for r in range(1,n):
if fact(n)/(fact(r)*fact(n-r))>1000000:c+=1
return c
def __ecMatch__(self, seq, ref):
if len(ref)==0: # shitty lines
return -100,0
oneago = None
thisrow = range(1, len(ref) + 1) + [0]
for x in xrange(len(seq)):
twoago, oneago, thisrow = oneago, thisrow, [0] * len(ref) + [x + 1]
for y in xrange(len(ref)):
delcost = oneago[y] + 1
addcost = thisrow[y - 1] + 1
subcost = oneago[y - 1] + (seq[x] != ref[y])
thisrow[y] = min(delcost, addcost, subcost)
# return thisrow[len(ref) - 1],len(ref)
thisrow.pop() # eliminate last element
n = thisrow.index(min(thisrow))+1
#n = len(thisrow)-thisrow[-1::-1].index(min(thisrow))
d = thisrow[n-1]
# print seq
# print ref
# print thisrow
# print d,n
d = min(d,n)
#n=max(d,len(seq))
#print d,n
err_lsc = d*log(self.err_p) + (n-d)*log(1.0-self.err_p) + log(fact(n))-(log(fact(d))+log(fact(n-d)))
return err_lsc,n
def GetChanceOfDominantTraits(organisms): totalOutcomes = 4.0 * fact(len(organisms)) / (2*fact(len(organisms)-2)) totalDominantOutcomes = 0.0 for i in range(0, len(organisms)-1): for j in range(i+1, len(organisms)): totalDominantOutcomes += CountDominantAleleCombos(organisms[i], organisms[j]) return totalDominantOutcomes / totalOutcomes
def findFactorialSum():
factorials = [fact(x) for x in range(0, 10)] # pre-calculate products
total_sum = 0
for k in range(10, fact(9) * 7): # 9999999 is way more than its fact-sum
if sum([factorials[int(x)] for x in str(k)]) == k:
total_sum += k
return total_sum
def main():
from sys import stdin,stdout
from math import factorial as fact
from collections import Counter
k = int(stdin.readline().strip())
s = stdin.readline().strip()
c = Counter(s)
stdout.write(str(fact(k)/fact(len(filter(lambda x: x>1,c.values())))))
def Enum(x):
res = 1
for i in xrange(1,x+1):
res += fact(x)/(fact(x-i)*fact(i))
return res % 1000000
def comb(n, k):
if (k > n):
return 0
else:
if (k == n):
return 1
else:
#print(n)
#print(k)
return ((fact(n))/((fact(k))*(fact(n-k))))
def run():
count = 0
for n in xrange(23, 101):
r = 1
fn = fact(n)
while fn / fact(r) / fact(n - r) < 10**6:
r += 1
o = 2 * (int(n / 2) + 1 - r) - (1 if n % 2 == 0 else 0)
count += o
return count
def sph_harm_large(m, n, az, el):
"""Compute spherical harmonics for large orders > 84
Parameters
----------
m : (int)
Order of the spherical harmonic. abs(m) <= n
n : (int)
Degree of the harmonic, sometimes called l. n >= 0
az: (float)
Azimuthal (longitudinal) coordinate [0, 2pi], also called Theta.
el : (float)
Elevation (colatitudinal) coordinate [0, pi], also called Phi.
Returns
-------
y_mn : (complex float)
Complex spherical harmonic of order m and degree n,
sampled at theta = az, phi = el
Y_n,m (theta, phi) = ((n - m)! * (2l + 1)) / (4pi * (l + m))^0.5 * exp(i m phi) * P_n^m(cos(theta))
as per http://dlmf.nist.gov/14.30
Pmn(z) is the associated Legendre function of the first kind, like scipy.special.lpmv
scipy.special.lpmn calculates P(0...m 0...n) and its derivative but won't return +inf at high orders
"""
if _np.all(_np.abs(m) < 84):
return scy.sph_harm(m, n, az, el)
else:
# TODO: confirm that this uses the correct SH definition
mAbs = _np.abs(m)
if isinstance(el, _np.ndarray):
P = _np.empty(el.size)
for k in range(0, el.size):
P[k] = scy.lpmn(mAbs, n, _np.cos(el[k]))[0][-1][-1]
else:
P = scy.lpmn(mAbs, n, _np.cos(el))[0][-1][-1]
preFactor1 = _np.sqrt((2 * n + 1) / (4 * _np.pi))
try:
preFactor2 = _np.sqrt(fact(n - mAbs) / fact(n + mAbs))
except OverflowError: # integer division for very large orders
preFactor2 = _np.sqrt(fact(n - mAbs) // fact(n + mAbs))
Y = preFactor1 * preFactor2 * _np.exp(1j * m * az) * P
if m < 0:
return _np.conj(Y)
else:
return Y
def S(n):
N = n+1
numbers = [ i for i in range(N) ]
r = ''
p = 1000000-1
for i in range(1, N):
j = p // fact(N-i)
p %= fact(N-i)
r += str(numbers.pop(j))
if p == 0:
break
for n in numbers:
r += str(n)
return r
def count_pairs(a):
a.sort()
cnt = 0
repeat = 1
for i in range(1, len(a)):
if a[i-1] == a[i]:
repeat += 1
else:
if repeat > 1:
cnt += fact(repeat) / fact(repeat-2) # permutation (n 2)
repeat = 1
if repeat > 1:
cnt += fact(repeat) / fact(repeat-2)
return int(cnt)
def problem_74():
from math import factorial as fact
cnt = 0
c=0
for i in xrange(1000000):
c+= 1
if not c%10000: print c,cnt
l = []
while i not in l:
l.append(i)
reduce(lambda a,b: a + fact(int(n)),string(i))
i = sum([fact(int(n)) for n in str(i)])
if len(l)==60:cnt+=1
return cnt
def p0(self,Pb,Pj):
xi_ = self.xi(Pb)
eta_ = self.eta(Pj)
t1 = self.S1(Pb)+self.S2(Pb)
t2 = ((self.c**self.c/fact(self.c))*xi_**(self.ns)
*(1-eta_**(self.n-1-self.ns))/(1-eta_))
return float(((t1+t2)**(-1)))
def get_random_ranks(permsize, samplesize):
perms = fact(permsize)
ranks = set()
while len(ranks) < samplesize:
ranks |= set( randrange(perms)
for r in range(samplesize - len(ranks)) )
return ranks
def S5(self, Pb, Pj):
t1 = (
(self.c ** self.c / fact(self.c))
* (self.xi(Pb) ** self.ns)
* sum([self.eta(Pj) ** (k - self.ns) for k in range(self.ns, self.n)])
)
return float(t1)
def __searchNbestNodeMatchRestricted__(self, segm_s, segm_best, valid_nodes, is_prefix):
# TODO:
segm = " ".join(segm_s).strip()
n = len(segm)
# max_lsc = float("-inf")
# max_node = None
nbest_nodes = []
for n_idx in valid_nodes:
covered_sent = self.__nodes__[n_idx].getCoveredString().strip()
if not is_prefix or (is_prefix and covered_sent[0:3] == "<s>"):
covered_sent = covered_sent.replace("|UNK|UNK|UNK","").replace("<s>","").replace("</s>","").strip()
d = Levenshtein.distance(segm,covered_sent)
d = min(d,n)
err_lsc = d*log(self.err_p) + (n-d)*log(1.0-self.err_p) + log(fact(n))-(log(fact(d))+log(fact(n-d)))
itp_lsc = self.__nodes__[n_idx].getInsideLogScore()+self.__nodes__[n_idx].getOutsideLogScore()
cur_lsc = itp_lsc+self.err_w*err_lsc #inside x outside x err**err_w
# if cur_lsc > max_lsc:
# max_lsc = cur_lsc
# max_itp_lsc = itp_lsc
# max_node = n_idx
if len(nbest_nodes)<=segm_best or cur_lsc>nbest_nodes[0][0]:
nbest_nodes.append((cur_lsc,itp_lsc,n_idx))
nbest_nodes = sorted(nbest_nodes)[-segm_best:]
#print nbest_nodes
#return max_lsc,max_itp_lsc,max_node
still_more_options = True
if len(nbest_nodes)<segm_best:
still_more_options = False
return nbest_nodes[0],still_more_options
def __searchBestNodeMatch__(self, pref_s):
if len(pref_s)==0:
node=self.__nodes__[self.__init_node__]
ec_lsc = node.getInsideLogScore()+node.getOutsideLogScore()
return self.__init_node__,ec_lsc,ec_lsc
pref = " ".join(pref_s).strip()
n = len(pref)
max_lsc = float("-inf")
max_node = None
ordered_keys = sorted(self.__nodes__)
#inside x outside x err
for n_idx in ordered_keys:
covered_sent = self.__nodes__[n_idx].getCoveredString().strip()
if covered_sent[0:3] == "<s>": #consider only nodes covering a prefix
covered_sent = covered_sent.replace("|UNK|UNK|UNK","").replace("<s>","").replace("</s>","").strip()
d = Levenshtein.distance(pref,covered_sent)
d = min(d,n)
err_lsc = d*log(self.err_p) + (n-d)*log(1.0-self.err_p) + log(fact(n))-(log(fact(d))+log(fact(n-d)))
itp_lsc = self.__nodes__[n_idx].getInsideLogScore()+self.__nodes__[n_idx].getOutsideLogScore()
cur_lsc = itp_lsc+self.err_w*err_lsc
if cur_lsc > max_lsc:
max_lsc = cur_lsc
max_itp_lsc = itp_lsc
max_node = n_idx
# print "\n-----------------------"
# print pref,"#",covered_sent,"#",n,"->",d
# print max_lsc, max_itp_lsc, err_lsc
# print self.__nodes__[max_node]
# print "-----------------------\n"
# else:
# print " -->","#"+covered_sent+"#",d,cur_lsc,itp_lsc,err_lsc
return max_node,max_lsc,max_itp_lsc
def calc_loss_combinations(n, prob_down):
total_loss = 0
prob_up = 1.0 - prob_down
total_probs = 0
for i in xrange(1, n+1):
combs = fact(n * 2) / (fact(n+i) * fact(n-i))
prob = prob_up ** (n+i) * prob_down ** (n-i)
single_loss = (i*2) * combs * (prob * 2)
total_loss += single_loss
print "combs: {}".format(combs)
if i > 0:
total_probs += (prob * 2 * combs)
else:
total_probs += (prob * combs)
return total_loss, total_probs
def unranker2(n, r, pi):
while n > 0:
n1 = n-1
s, rmodf = divmod(r, fact(n1))
pi[n1], pi[s] = pi[s], pi[n1]
n = n1
r = rmodf
return pi
def ranker2(n, pi, pi1):
if n == 1:
return 0
n1 = n-1
s = pi[n1]
pi[n1], pi[pi1[n1]] = pi[pi1[n1]], pi[n1]
pi1[s], pi1[n1] = pi1[n1], pi1[s]
return s * fact(n1) + ranker2(n1, pi, pi1)
def __searchNbestNodeMatchRestricted__(self, segm_s, segm_best, valid_nodes, first_isle):
segm = " ".join(segm_s).strip()
n = len(segm)
#print "SN:",segm_s, segm_best, len(valid_nodes), first_isle
nbest_nodes = []
for n_idx in valid_nodes:
covered_sent_s,inside_lsc = valid_nodes[n_idx]
#print n_idx,covered_sent_s,inside_lsc
# all nodes represent prefixes
# "|||" symbol represents previous matching
# search for node whith best EC score on the unmatched suffix
if first_isle:
covered_sent = " ".join(covered_sent_s).replace("|UNK|UNK|UNK","").replace("</s>","").strip()
d = Levenshtein.distance(segm,covered_sent)
d = min(d,n)
err_lsc = d*log(self.err_p) + (n-d)*log(1.0-self.err_p) + log(fact(n))-(log(fact(d))+log(fact(n-d)))
itp_lsc = self.__nodes__[n_idx].getInsideLogScore()+self.__nodes__[n_idx].getOutsideLogScore()
cur_lsc = itp_lsc+self.err_w*err_lsc #inside x outside x err**err_w
if len(nbest_nodes)<=segm_best or cur_lsc>nbest_nodes[0][0]:
nbest_nodes.append((cur_lsc,itp_lsc,n_idx,segm_s))
nbest_nodes = sorted(nbest_nodes)[-segm_best:]
#print "P",covered_sent,d,err_lsc,itp_lsc,cur_lsc
#print "P",nbest_nodes
else:
max_suffix_size = len(covered_sent_s)-covered_sent_s.index("|||")
for suffix_size in range(1,max_suffix_size):
covered_sent = " ".join(covered_sent_s[-suffix_size:]).replace("|UNK|UNK|UNK","").replace("</s>","").strip()
d = Levenshtein.distance(segm,covered_sent)
d = min(d,n)
err_lsc = d*log(self.err_p) + (n-d)*log(1.0-self.err_p) + log(fact(n))-(log(fact(d))+log(fact(n-d)))
itp_lsc = self.__nodes__[n_idx].getInsideLogScore()+self.__nodes__[n_idx].getOutsideLogScore()
cur_lsc = itp_lsc+self.err_w*err_lsc #inside x outside x err**err_w
if len(nbest_nodes)<=segm_best or cur_lsc>nbest_nodes[0][0]:
out_str = covered_sent_s[:-suffix_size]+tuple(segm_s)
nbest_nodes.append((cur_lsc,itp_lsc,n_idx,out_str))
nbest_nodes = sorted(nbest_nodes)[-segm_best:]
#print "I",covered_sent,d,err_lsc,itp_lsc,cur_lsc
#print "I", nbest_nodes
#print nbest_nodes
#return max_lsc,max_itp_lsc,max_node
#sys.exit()
still_more_options = True
if len(nbest_nodes)<segm_best:
still_more_options = False
return nbest_nodes[0],still_more_options
def pieinsky():
c1 = Decimal(4)
c2 = Decimal(1103)
c3 = Decimal(26390)
c4 = Decimal(396)
c5 = Decimal(9801)
# code formatted for readability (make it be one line)
root8 = Decimal('2.82842712474619009760337744841939615'
'7139343750753896146353359475981464956'
'9242140777007750686552831454700276')
i = Decimal(0)
thesum = Decimal(0)
while True:
term = (fact(c1*i)*(c2 + c3*i))/(pow(fact(i),4)*pow(c4,4*i))
thesum = thesum + term
yield 1/((root8/c5)*thesum)
i += 1
def test_binomial():
from operator import __eq__
from math import factorial as fact
assert isinstance(real_binomial(1, 1), float)
for f, eq in ((binomial, __eq__), (real_binomial, approx_eq)):
for n in xrange(20):
for k in xrange(n + 10):
if k > n:
assert eq(f(n, k), 0)
else:
assert eq(f(n, k), fact(n) / fact(k) / fact(n - k))
if k > 0 :
assert eq(f(n, -k), 0)
# To prove correct our implementation of the binomial coefficient
# C(r, k) for real r, int k, we only need one non-integer test
# case beyond our tests for r = integer n above. This case shows
# that we're not using floor division.
assert approx_eq(real_binomial(-5.5, 2), 17.875)
def main():
N = readInt()
if N <= 12:
der = countDer(N)
f = fact(N)
res = (f - der) / f
print('%.8f' % res)
else:
print('0.63212056')
def ev(n, l, a):
"""Evaluate zernike polynomial (n,l)
:param a: The array over which to evaluate, of form [ [x,y] ]
Example: evalZern(2,0, numpy.moveaxis(numpy.mgrid[-1:1:64j, -1:1:64j], 0, -1) )
"""
m=abs(l)
nradterms= 1+ (n-m)//2
radpowers= n - 2*numpy.arange(nradterms)
radcoeffs= numpy.array(list(map(lambda s: (-1)**s * fact(n-s) / ( fact(s) * fact ( (n+m)/2 -s ) * fact( (n-m)/2 -s )),
numpy.arange(nradterms))))
r=numpy.hypot(a[...,0], a[...,1])
phi=numpy.arctan2(a[...,1], a[...,0])
v=numpy.zeros_like(r)
for i in range(nradterms):
v+=radcoeffs[i]*r**radpowers[i]
if l>0:
v*=numpy.cos(l*phi);
elif l<0:
v*=numpy.sin(-l*phi)
return v
def test1(comment, unranker, ranker):
n, samplesize, n2 = 3, 4, 12
print(comment)
perms = []
for r in range(fact(n)):
pi = identity_perm(n)
perm = unranker(n, r, pi)
perms.append((r, perm))
for r, pi in perms:
pi1 = init_pi1(n, pi)
print(' From rank %2i to %r back to %2i' % (r, pi, ranker(n, pi[:], pi1)))
print('\n %i random individual samples of %i items:' % (samplesize, n2))
for r in get_random_ranks(n2, samplesize):
pi = identity_perm(n2)
print(' ' + ' '.join('%2i' % i for i in unranker(n2, r, pi)))
print('')
def analyse(sLast, s, terms, power=0):
"""Recursive function to analyse the series."""
# we are done if s is all zeros
if set(s) == {0}:
return prettyTerms(terms)
# differences have not converged yet
elif len(s) > 1 and not len(set(s)) == 1:
return analyse(sLast, difference(s), terms, power + 1)
# differences have converged
elif len(set(s)) == 1 and not (terms and terms[-1][1] == power):
coeff = s[0]/fact(power)
terms.append((coeff,power))
s = [x - coeff * i ** power for i, x in enumerate(sLast,1)]
return analyse(s, s, terms)
# failure
else:
return "Failed to analyse sequence."
def chain(n):
l = [n]
while True:
tot = 0
for d in str(n):
tot += fact(int(d))
if v.has_key(tot):
for j in range( len( l ) ):
v[ l[j] ] = len(l)-j+v[tot]
return len(l)+v[tot]
if l.count(tot):
for j in range( len( l ) ):
v[ l[j] ] = len(l)-j
return len(l)
else:
l.append(tot)
n=tot
def w3j_000(L, l, lp):
J = L + l + lp
if J % 2 == 1:
#print 'odd J\n'
return 0.
if l + lp < L:
#print 'l + lp < L'
return 0.
if np.abs(l - lp) > L:
#print 'abs(l - lp) > L'
return 0.
#lnfact1 = stirling(J-2.*L) + stirling(J-2.*l) + stirling(J-2.*lp) - stirling(J+1.)
#lnfact2 = stirling(J/2.) - stirling(J/2.-L) - stirling(J/2.-l) - stirling(J/2.-lp)
#res = (-1.)**(J/2.) * np.exp(0.5*lnfact1 + lnfact2)
fact1 = fact(J-2*L) * fact(J-2*l) * fact(J-2*lp) / fact(J+1)
fact2 = fact(J/2) / (fact(J/2-L) * fact(J/2-l) * fact(J/2-lp))
res = (-1)**(J/2) * fact1**0.5 * fact2
return res
def n_choose_r(n, r):
return fact(n) / (fact(r) * fact(n - r))
def factorial(n):
from math import factorial as fact
return fact(n)
from math import factorial as fact
tc = int(input())
for i in range(tc):
m, n = [int(j) for j in input().split(" ")]
print((fact(m + n) // (fact(m) * fact(n))) % 1000000007)
while True:
''' print('1. Fibo Series')
print('2. Odd Series')
print('3. Even or Odd')
print('4. Factorial')
print('5. Exit') '''
print('1. Fibo Series', '2. Odd Series', '3. Even or Odd', '4. Factorial', '5. Exit', sep='\n')
choice = int(input('Please enter ur choice: '))
if choice == 1 or choice == 2 or choice == 3 or choice == 4:
n = int(input('Enter n: '))
if choice == 1:
# fibo series till n
# print(com.abc.lib.series.fibo_series(n=n))
print(series.fibo_series(n=n))
elif choice == 2:
# odd series till n
# print(com.abc.lib.series.odd_series(n=n))
print(series.odd_series(n=n))
elif choice == 3:
# even or odd -> n
print(even_odd(n=n))
elif choice == 4:
# factorial of number n
# print(factorial(n))
print(fact(n))
else:
# print(n) # this will not work if at the start the user chooses the option 5
break # breaks out forcibly from the closest loop
""" To find the number of combinations to choose k items from n items"""
from math import factorial as fact # or use import math
""" n:
Total number of items
k:
Number of items to choose
c:
Number of combinations = n!/(k!*(n-k)!) """
n = int(input("Enter the total number of items: "))
k = int(input("Enter the number of items to choose: "))
c = (
fact(n) / (fact(k) * fact(n - k))
) # or use c = (math.factorial(n)/(math.factorial(k)*math.factorial(n-k)))
print(
"The total number of combinations to choose {0} items from {1} items is {2}"
.format(k, n, c))
def generate_spherical_coeff(l, m, lx, ly, lz):
j = (lx + ly - abs(m))
if j % 2 == 0:
j = int(j / 2)
else:
return 0.0
prefactor = fact(2. * lx) * fact(2. * ly) * fact(2. * lz) * fact(l)
prefactor = prefactor * fact(l - abs(m))
prefactor = prefactor / (fact(2. * l) * fact(lx) * fact(ly) * fact(lz))
prefactor = prefactor / fact(l + abs(m))
prefactor = math.sqrt(prefactor)
term1 = 0.0
for i in range(int((l - abs(m)) / 2) + 1):
term1 = term1 + binomial(l,i) * binomial(i,j) * \
math.pow(-1,i) * fact( 2*l - 2*i ) / \
fact( l - abs(m) - 2*i )
term1 = term1 / math.pow(2, l) / fact(l)
m_fact = 1.
if m < 0:
m_fact = -1.
term2 = 0.0 + 0.0j
for k in range(j + 1):
z = cmath.exp(m_fact * math.pi / 2. * (abs(m) - lx + 2 * k) * 1.j)
term2 = term2 + binomial(j, k) * binomial(abs(m), lx - 2 * k) * z
val = prefactor * term1 * term2
if abs(val.real) < 1e-10:
val = 0.0 + val.imag * 1j
if abs(val.imag) < 1e-10:
val = val.real
return val
def Comb(n, p):
from math import factorial as fact
return fact(n) // fact(p) // fact(n - p)
def number_of_permuations(lst, n):
'''gets the number of permutations of the type corresponding to a partition. E.g. a partition [1,2] means
"swap 2 numbers, leave one alone"'''
res = 1
for i in range(1, n + 1):
a = lst.count(i) #how many times is the number there?
if a > 0:
res = res * (i**a) * fact(a)
return fact(n) // res
h = 12
w = 12
s = 2
total = 0
n = 0
for p in partitions(h):
for q in partitions(w):
nh = number_of_permuations(p, h)
nw = number_of_permuations(q, w)
exponent = 0
for i in p:
for j in q:
exponent += gcd(i, j)
total = total + nh * nw * s**exponent
print(p, q)
total = total // fact(h) // fact(w)
print(total)
def Solve():
return (sum([int(x) for x in str(fact(100))]))
def get_domain_matrix(start_time, fname="", **kwas):
'''
:param start_time: int indicating the earliest query the window should include
:param **kwas: keyword arguments for vv.get_svl()
:return: (m) matrix of client pairs vs domains,
(fmt) list of domains
other outputs:
-> csv with pairs vs domains matrix (m)
-> csv with list of domain pair correlations (corrs)
-> csv with list of mean Jaccard for each domain (means)
'''
kwas['start_time'] = start_time
kwas['return_ccache'] = False
svl, fmt, anssets = vv.get_svl(**kwas)
print "svl len", len(svl)
combs = fact(len(svl)) / (fact(2) * fact(len(svl) - 2))
m = np.zeros((combs, len(fmt)))
p = 0
for i in xrange(0, len(svl) - 1):
a = svl[i]
logger.warning(str(i) + ", " + str(a.get_id()))
aset = dict()
for dom in a:
aset[dom] = set(a[dom])
for j in xrange(i + 1, len(svl)):
b = svl[j]
for k in xrange(0, len(fmt)):
dom = fmt[k]
domtotal = sum([a[dom][z] for z in a[dom]]) + sum(
[b[dom][z] for z in b[dom]])
overlap = aset[dom].intersection(b[dom])
weight = 0
for z in overlap:
weight += (a[dom][z] + b[dom][z])
m[p, k] = weight / domtotal
p += 1
df.overwrite(plotsdir + "dommatrix" + fname + ".csv",
df.list2line(fmt) + "\n")
df.append(plotsdir + "dommatrix" + fname + ".csv", df.list2col(m))
C = np.corrcoef(m, rowvar=False)
corrs = list()
for i in xrange(0, len(fmt) - 1):
for j in xrange(i + 1, len(fmt)):
corrs.append((fmt[i] + "_" + fmt[j], C[i, j]))
corrs = sorted([y for y in corrs if not math.isnan(y[1])],
key=lambda z: z[1])
means = sorted(zip(fmt, np.mean(m, axis=0)), key=lambda z: z[1])
df.overwrite(plotsdir + "domcorr" + fname + ".csv", df.list2col(corrs))
df.overwrite(plotsdir + "dommean" + fname + ".csv", df.list2col(means))
meand = dict(means)
# get mean jaccard vs # IPs seen
mj_ni = [(meand[dom], len(anssets[dom])) for dom in meand]
d_mj_ni = sorted([(dom, meand[dom], len(anssets[dom])) for dom in meand],
key=lambda z: z[1])
df.overwrite(plotsdir + "jaccard_vs_ipspace" + fname + ".csv",
df.list2col(d_mj_ni))
fig, ax = plt.subplots(1, 1)
colors = iter(cm.rainbow(np.linspace(0, 1, len(mj_ni))))
for x, y in mj_ni:
ax.scatter(x, y, color=next(colors))
plt.xlabel("mean jaccard")
plt.ylabel("# IPs observed")
ax.grid(b=True, which='major', color='b', linestyle='-')
ps.set_dim(fig, ax, ylog=True)
filename = plotsdir + "jaccard_vs_ipspace" + fname
fig.savefig(filename + '.png', bbox_inches='tight')
fig.savefig(filename + '.pdf', bbox_inches='tight')
plt.show()
plt.close(fig)
return m, fmt
from math import factorial as fact n = 5 o = 3 x = fact(n)/fact(o) print(x) y=5/3 print(x)
def ways(n, r):
return fact(n) / (fact(r) * fact(n - r))
def combination(self, n, r):
return (fact(n) / (fact(n - r) * fact(r)))
def nCr_rep(n, r):
return fact(n + r - 1) // (fact(r) * fact(n - 1))
def binomial(x, n, p=0.5):
coef = fact(n) / (fact(x) * fact(n - x))
binom = coef * (p**x) * (1 - p)**(n - x)
return binom
def coef(i, j, z):
if i < j: return 0
return fact(i) * z**(i - j) / fact(i - j)
tree.insert(15)
tree.insert(13)
print(tree.find(1))
print(tree.find(12))
''' Following tree is getting created:
10
/ \
5 12
/ \ \
4 8 20
/ /
7 15
/
13
'''
tree.preorder()
tree.inorder()
tree.postorder()
print('\n\nAfter deleting 20')
tree.delete(20)
tree.inorder()
tree.preorder()
print('\n\nAfter deleting 10')
tree.delete(10)
tree.inorder()
tree.preorder()
elem = int(input("\nHow many elements you want to enter in a binary tree : "))
result = fact(2 * elem) // (fact(elem + 1) * fact(elem))
print("There are {} possible structure for {} elements".format(result, elem))
from math import factorial as fact
n, i = (int(i) for i in input().strip().split(' '))
groups = list()
for _ in range(i):
a, b = (int(i) for i in input().strip().split(' '))
new = True
for group in groups:
if a in group or b in group:
group.add(a)
group.add(b)
new = False
break
if new:
group = set()
group.add(a)
group.add(b)
groups.append(group)
if n == 1:
total = 1
else:
total = fact(n) / (fact(2) * fact(n - 2))
for group in groups:
ng = len(group)
total -= fact(ng) / (fact(2) * fact(ng - 2))
print(int(total))
def c(n, x):
return fact(n) / (fact(n - x) * fact(x))
max_time = 10000 #2000 / µ
debug_interval = max_time / 200
Ntr = 3 # number of simulations to run
# RUN SIMULATIONS
simulations = []
for i in range(Ntr):
print(f"Running simulation {i}")
sim = Simulation(max_time, λ, µ, c, debug_interval)
sim.run()
simulations.append(sim)
print(f'Finished simulating')
# 9: show average number of packets in system over time
ρ = λ / (c * µ)
pi_0 = 1 / (sum([(c * ρ)**k / fact(k)
for k in range(0, c)]) + (c * ρ)**c / (fact(c) * (1 - ρ)))
pi_c_plus = (c * ρ)**c / (fact(c) * (1 - ρ)) * pi_0
theor_avg_load = c * ρ + ρ / (1 - ρ) * pi_c_plus
plt.plot([0, max_time], [theor_avg_load] * 2, 'k-', linewidth=1)
for sim in simulations:
debug_times = [ds.event_time for ds in sim.debugStats]
cum_avg_loads = [ds.cum_avg_load for ds in sim.debugStats]
plt.plot(debug_times,
cum_avg_loads,
'-',
c=np.random.rand(3, ),
linewidth=1)
plt.show()
# -*- coding:utf-8 -*-
"""Project Euler problem 15"""
from math import factorial as fact
w = 20
h = 20
print("Answer: " + str(int(fact(w + h) / (fact(w) * fact(h)))))
->a single python file containing set functions packages --> sub packages --> modules ---> function ---> statements # In[18]: import math math.floor(123.45) # In[20]: from math import factorial as fact fact(5) # In[21]: from math import gcd as fact gcd(10,15) # In[ ]: ### standard libraries - file i/o - regular expressions
def nCr(n, r):
return fact(n) / (fact(r) * fact(n - r))
def calculate_odds(white_bc, red_bc):
product = red_bc * fact(white_bc) / fact(white_bc - 5) / fact(5)
return product
def estimate_state(p, m, ghk):
p_list = [p[:, :, i] + c * (p[:, :, 0] - m) / fact(i) for i, c in enumerate(ghk)]
res = torch.stack(p_list).permute((1, 2, 0, 3))
return res
import math
from math import factorial as fact
print(math.sqrt(4))
# help(math)
# help(math.factorial)
print(math.factorial(5))
print(fact(5) // fact(2) * fact(3))
print(fact(100))
print(0b10)
print(0o10)
print(0x10)
print(int("10000", 3))
print(3e8)
print(1.616e-35)
print(float("nan"))
print(float("-inf"))
x = """This is
a
multiline string"""
print(x)
from math import factorial as fact
c = int(input())
for i in range(c):
m, n = map(int, input().split())
print(fact(n) // fact(m) // fact(n - m))
import math from functools import reduce from math import factorial as fact import mates.mates from mates.mates import factorial from mates.mates import gcd from mates.mates import to_square print(fact(4)) print(math.factorial(5)) print(reduce(lambda n1, n2: n1 + n2, [1, 2, 3, 4, 5])) print(factorial(5)) print(gcd(8, 19)) print(to_square(10)) print(mates.mates.gcd(8, 18))
def coef(P, i, j):
from math import factorial as fact
if i >= len(P) or j > i: return 0
return P[i] * (fact(i) // fact(j) // fact(i - j))
# Starting in the top left corner of a 2×2 grid, and only being able to move to the right and down, there are exactly
# 6 routes to the bottom right corner.
#
# How many such routes are there through a 20×20 grid?
# question rephrased: how many different combinations of 20 units can fill 40 spots?
# answer: 40 choose 20
########################################################################################################################
# simple method using equation of n!/k!(n-k)! with n = 40, k = 20
from math import factorial as fact
print(int(fact(40) / (fact(20) * fact(40 - 20))))
########################################################################################################################
# outputting pascal's triangle, max of a given row gives result of above equation
n = 41 # needed to get answer: 2^40, need middle term so 41 since odd
new_list = []
for i in range(1, n + 1):
old_list = new_list
new_list = []
for _ in range(i):
new_list.append(0)