def find_optimal_path_n(zumy_pos, final_dest): if zumy_pos.ndim == 2: zumy_number = np.shape(zumy_pos)[0] else: zumy_number = 1 return final_dest pair_list = range(zumy_number) possible_pairs_iter = permutations(pair_list) possible_pairs = np.asarray([np.asarray(elem) for elem in possible_pairs_iter]) pair_for_cross_iter = combinations(pair_list, 2) pair_for_cross = np.asarray([np.asarray(elem) for elem in pair_for_cross_iter]) possible_total_distance = np.zeros(math.factorial(zumy_number)) possible_cross = np.zeros(math.factorial(zumy_number)) for ii in range(math.factorial(zumy_number)): current_pair = possible_pairs[ii] for jj in range(zumy_number): possible_total_distance[ii] = possible_total_distance[ii] + \ get_distance(zumy_pos[jj], final_dest[current_pair[jj]]) for curr_pair_for_cross in pair_for_cross: possible_cross[ii] = possible_cross[ii] + \ check_crossing(zumy_pos[curr_pair_for_cross[0]], final_dest[current_pair[curr_pair_for_cross[0]]], zumy_pos[curr_pair_for_cross[1]], final_dest[current_pair[curr_pair_for_cross[1]]]) possible_total_penalty = 1000*possible_cross + possible_total_distance minimum_index = np.argmin(possible_total_penalty) best_pair = possible_pairs[minimum_index] new_final_dest_tuple = tuple(final_dest[order] for order in best_pair) new_final_dest = np.vstack(new_final_dest_tuple) return new_final_dest
def testSmall(data, repeat1, repeat2):
# Check that the shuffling is along the first axis.
# The order of the elements in each subarray must not change.
# This takes long time so `repeat1` need to be small.
for i in range(repeat1):
ret = mx.nd.random.shuffle(data)
check_first_axis_shuffle(ret)
# Count the number of each different outcome.
# The sequence composed of the first elements of the subarrays is enough to discriminate
# the outcomes as long as the order of the elements in each subarray does not change.
count = {}
stride = int(data.size / data.shape[0])
for i in range(repeat2):
ret = mx.nd.random.shuffle(data)
h = str(ret.reshape((ret.size,))[::stride])
c = count.get(h, 0)
count[h] = c + 1
# Check the total number of possible outcomes.
# If `repeat2` is not large enough, this could fail with high probability.
assert len(count) == math.factorial(data.shape[0])
# The outcomes must be uniformly distributed.
# If `repeat2` is not large enough, this could fail with high probability.
for p in itertools.permutations(range(0, data.size - stride + 1, stride)):
err = abs(1. * count[str(mx.nd.array(p))] / repeat2 - 1. / math.factorial(data.shape[0]))
assert err < 0.01, "The absolute error {} is larger than the tolerance.".format(err)
# Check symbol interface
a = mx.sym.Variable('a')
b = mx.sym.random.shuffle(a)
c = mx.sym.random.shuffle(data=b, name='c')
d = mx.sym.sort(c, axis=0)
assert (d.eval(a=data, ctx=mx.current_context())[0] == data).prod() == 1
def binomial_factorial(self,n,k):
"""Calculate binomial coefficient using math.factorial, for testing against binomial
coefficients generated by other means."""
if n >= k:
return int( round( math.factorial(n) / ( math.factorial(k) * math.factorial(n - k) ) ) )
else:
return 0
def f_f(j):
n=2*j
r=n//2
num=math.factorial(n)
den=math.factorial(n-r) * math.factorial(r)
return num//den
def keyspace(n,m,k):
lastterm = factorial(k) / (factorial(k - m))
result = int(n * comb(n,m,exact=True) * lastterm)
return result
def __init__(self, f_center, samplerate, order=4, bw_factor=1.0):
self.f_center = f_center
self.samplerate = samplerate
self.order = order
self.bw_factor = bw_factor
fc_erb = (GFB_L + self.f_center / GFB_Q) * self.bw_factor
# equation (14), line 3 [Hohmann 2002]:
a = np.pi * math.factorial(2.*order - 2.) * 2.**-(2.*order - 2.)
b = math.factorial(order - 1.)**2
a_gamma = a / b
# equation (14), line 2 [Hohmann 2002]:
b = fc_erb / a_gamma
# equation (14), line 1 [Hohmann 2002]:
lamda = np.exp(-2*np.pi*b / samplerate)
# equation (10) [Hohmann 2002]:
beta = 2 * np.pi * f_center / samplerate
# equation (1), line 2 [Hohmann 2002]:
self.coef = lamda * np.exp(0 + 1j*beta)
# normalization factor from section 2.2 (text) [Hohmann 2002]:
self.normalization_factor = 2. * (1 - np.abs(self.coef)) ** order
self.state = np.zeros(order, dtype=np.complex, order='c')
def n_choose_k(n, k):
"""Computes n choose k."""
if n < k:
return 0
else:
return factorial(n) / factorial(k) / factorial(n - k)
def __ClassShape(self, w, x, N1, N2, dz):
# Class function; taking input of N1 and N2
C = np.zeros(len(x), dtype=complex)
for i in range(len(x)):
C[i] = x[i]**N1*((1-x[i])**N2)
# Shape function; using Bernstein Polynomials
n = len(w) - 1 # Order of Bernstein polynomials
K = np.zeros(n+1, dtype=complex)
for i in range(0, n+1):
K[i] = factorial(n)/(factorial(i)*(factorial((n)-(i))))
S = np.zeros(len(x), dtype=complex)
for i in range(len(x)):
S[i] = 0
for j in range(0, n+1):
S[i] += w[j]*K[j]*x[i]**(j) * ((1-x[i])**(n-(j)))
# Calculate y output
y = np.zeros(len(x), dtype=complex)
for i in range(len(y)):
y[i] = C[i] * S[i] + x[i] * dz
return y
def choose(a, b):
if b == 0 or a == b:
return 1
else:
numer = factorial(a)
denom = factorial(b) * factorial(a-b)
return numer//denom
def expand_power(u, n):
if n < Number(0):
return Number(1) / expand_power(_expand(u), abs(n))
if isinstance(n, Rational):
largest_int = Number(int(floor(n.value)))
m = n - largest_int
return expand_product(u ** m, expand_power(u, largest_int))
if not isinstance(n, Integer):
raise ValueError('n must be an integer, not {}'.format(repr(type(n))))
elif n < Number(0):
raise ValueError('n must be > 0, not {}'.format(n))
if isinstance(u, Add):
f = u.args[0]
r = u - f
s = Number(0)
for k in range(n.value+1):
c = Number(factorial(n.value)/(factorial(k) * factorial(n.value - k)))
s = s + expand_product(c * f**Number(n.value-k), expand_power(r, Number(k)))
return s
else:
return u**n
def probabilityOfKeepSet(keep_set): probability = math.factorial(len(keep_set)) for value in range(1,7): num_value_in_set = sum([1 for x in keep_set if x == value]) probability /= math.factorial(num_value_in_set) probability = float(probability)/6**len(keep_set) # Divide by all possible choices return probability
def naiveBayesMultinomial(value,frequency,adjustment = 1):
if not value: return 0
lim = 80
if frequency > 92:
return math.log(math.pow(value*adjustment,lim)/math.factorial(lim))
else:
return math.log(math.pow(value*adjustment,frequency)/math.factorial(frequency))
def multCoeff(x):
a = 0
b = 0
c = 0
d = 0
e = 0
f = 0
g = 0
h = 0
i = 0
for j in str(x):
if j == '1':
a += 1
elif j == '2':
b += 1
elif j == '3':
c += 1
elif j == '4':
d += 1
elif j == '5':
e += 1
elif j == '6':
f += 1
elif j == '7':
g += 1
elif j == '8':
h += 1
elif j == '9':
i += 1
num = factorial(a+b+c+d+e+f+g+h+i)
den = factorial(a)*factorial(b)*factorial(c)*factorial(d)*factorial(e)\
*factorial(f)*factorial(g)*factorial(h)*factorial(i)
return num/den
def fast_nth_perm(digits, n):
#temporary storage variables
curr_num = n - 1
result = ""
#go through the digits from the biggest down (i.e. 9 to 0)
for i in reversed(range(len(digits))):
#do integer division to get the quotient of curr_num / i!
quotient = curr_num / math.factorial(int(i))
#also get the remainder with mod
remainder = curr_num % math.factorial(int(i))
#the quotient is the index of the current digit in the desired
#permutation. Add it to the result.
result += (digits[quotient])
# and remove it from the list of digits (each digit can only
# appear once)
digits = "%s%s" % (digits[:quotient], digits[quotient+1:])
#update curr num to be the remainder of the previous
#curr_num's division.
curr_num = remainder
return result
def solve(self, cipher):
"""
Labeled permutation variants
:param cipher: the cipher
"""
N, M = cipher
return math.factorial(N+M-1)/math.factorial(N)/math.factorial(M-1)%MOD
def combsel(): i = 0 for n in range(1, 101): for r in range(1, n+1): if (math.factorial(n)/((math.factorial(r)*(math.factorial(n-r))))) > 1000000: i+=1 return i
def get_score(self, subtract_cards):
same_form = 0
form_larger = 0
if self.straight:
for i in range(0, 12 - len(self.cards)):
and_cards = True
for j in range(len(self.cards)):
and_cards = and_cards and subtract_cards[(i + j)* 4 + self.cards[j].suit]
if and_cards:
same_form += 1
if self.cards[0].rank > i:
form_larger += 1
else:
for i in range(0, 12):
and_cards = True
for j in range(len(self.cards)):
and_cards = and_cards and subtract_cards[i* 4 + self.cards[j].suit]
if and_cards:
same_form += 1
if self.cards[0].rank > i:
form_larger += 1
count_rank_2 = 0
for j in range(12*4, len(subtract_cards)):
if subtract_cards[j]:
count_rank_2 += 1
if count_rank_2 >= len(self.cards):
same_form += math.factorial(count_rank_2)/(math.factorial(count_rank_2 - len(self.cards)) * math.factorial(len(self.cards)))
return same_form if same_form == 0 else form_larger * 1.0/same_form
def digitFactorials():
sum = 0
for i in range(0, 10):
for j in range(0, 10):
for k in range(0, 10):
for l in range(0, 10):
for m in range(0, 10):
for n in range(0, 10):
for o in range(0, 10):
digitSum = math.factorial(i) + math.factorial(j) + math.factorial(k) + math.factorial(l) + math.factorial(m) + math.factorial(n) + math.factorial(o)
if i == 0:
digitSum -= 1
if i == 0 and j == 0:
digitSum -= 1
if i == 0 and j == 0 and k == 0:
digitSum -= 1
if i == 0 and j == 0 and k == 0 and l == 0:
digitSum -= 1
if i == 0 and j == 0 and k == 0 and l == 0 and m == 0:
digitSum -= 1
if i == 0 and j == 0 and k == 0 and l == 0 and m == 0 and n == 0:
digitSum -= 1
num = i*1000000 + j*100000 + k*10000 + l*1000 + m*100 + n*10 + o
if num == digitSum and num != 1 and num != 2:
print num
sum += num
def count(self, N):
# Is amazing easy the algoritm when understand. Is essential visualize
# the structure of data, in this case, you should imagine than the SMN
# is a line path that cross all points, without returning to one, after
# having gone through.
#Assume that N = 4 . Then there exists an MTF that follows the path ABCD,
# with distance 2, 2 , 2, where A, B , C , D are the vertices. There is
# also an MTF which follows the route ABDC with 2-2-2 away . These two
# SMN share the same structure , the only thing that varies is the
# order of the points. If you look , all combinations with 1-1-1 equals
# the number of combination between two points is calculated as the
# permutation of 4 points, must be reduced by half because the lines
# connecting the vertices are unidirectional.
numerodecombinaciones = math.factorial(N) / 2
SMNs = list(itertools.product(reversed(range(1, 3)), repeat = (N - 1)))
waystotal = 0
for SMN in SMNs:
waysSMN = 1
for i in range(N):
for j in range(i +2, N):
ways = 2
for k in range(i, j):
if SMN[k] == 2:
ways = 1
waysSMN *= ways
waysSMN %= 1000000007
waystotal += waysSMN
waystotal %= 1000000007
waystotal *= math.factorial(N) / 2
waystotal %= 1000000007
return waystotal
def nSphereVolume(n):
'''
Calculate the volume of a unit n-sphere.
TYPICAL USAGE
=============
>>> nSphereVolume(0)
1
>>> nSphereVolume(1)
2
>>> nSphereVolume(2)/pi
1.0
>>> nSphereVolume(3)/(pi**2)
0.5
REFERENCES
==========
Equation 5.19.4, NIST Digital Library of Mathematical Functions. http://dlmf.nist.gov/, Release 1.0.6 of 2013-05-06.
@param n: dimension of the n-sphere
@type n: int
@return: volume of the unit n-sphere
@rtype:
'''
if n%2 == 0:
d = n/2
return(pi**d/factorial(d))
else:
d = (n-1)/2
return((2*((4*pi)**d)*factorial(d))/(factorial(2*d+1)))
def numtobasef(num,l): # computes the l-"digit" "base" factorial representation of num
# there's probably a real name for this
basef=[0]*l
for i in range(l):
basef[i]=num/factorial(l-i)
num-=basef[i]*factorial(l-i)
return basef
def GetWaveFunction(n,l,m,x,y,z):
r = lambda x,y,z: numpy.sqrt(x**2+y**2+z**2)
theta = lambda x,y,z: numpy.arccos(z/r(x,y,z))
phi = lambda x,y,z: numpy.arctan2(y,x)
#phi = lambda x,y,z: numpy.arctan(y/x)
a0 = 1.
R = lambda r,n,l: numpy.sqrt(((2.0/n/a0)**3)*(math.factorial(n-l-1))/(math.factorial(n+l))/2/n)*(2*r/n/a0)**l * numpy.exp(-r/n/a0) * scipy.special.genlaguerre(n-l-1,2*l+1)(2*r/n/a0)
#R = lambda r,n,l: (2*r/n/a0)**l * numpy.exp(-r/n/a0) * scipy.special.genlaguerre(n-l-1,2*l+1)(2*r/n/a0)
WF = lambda r,theta,phi,n,l,m: R(r,n,l) * scipy.special.sph_harm(m,l,phi,theta)
absWF = lambda r,theta,phi,n,l,m: abs((WF(r,theta,phi,n,l,m))**2)
wf = WF(r(x,y,z),theta(x,y,z),phi(x,y,z),n,l,m)
w = absWF(r(x,y,z),theta(x,y,z),phi(x,y,z),n,l,m)
w[numpy.isnan(w)]=0
#wf[numpy.isnan(wf)]=0
phase = numpy.angle(wf)
realwf = numpy.imag(wf)*10
#realwf = numpy.fabs(numpy.real(wf)*10)# need to by 10 because of the pg.isosurface() function
#phase = numpy.array(w)
#xsize = w.size/w[0].size
#ysize = w[0].size/w[0][0].size
#zsize = w[0][0].size
#for i in range(0,xsize):
# for j in range(0,ysize):
# for k in range(0,zsize):
# #angular = numpy.arctan2(wf[i][j][k].imag,wf[i][j][k].real)
# #if angular < 0:
# # phase[i][j][k] = angular+2*numpy.pi
# #else:
# # phase[i][j][k] = angular
# phase[i][j][k] = numpy.arctan2(wf[i][j][k].imag,wf[i][j][k].real)
phase[numpy.isnan(phase)]=0
realwf[numpy.isnan(realwf)]=0
return w,phase, realwf
def test_factorial():
""" Tests the factorial function. """
# DONE: 3a. Implement this function, using it to test the NEXT
# function. Write the two functions in whichever order you prefer.
# Include at least 4 tests.
#
# ** Use the math.factorial function as an ORACLE for testing. **
print()
print('--------------------------------------------------')
print('Testing the factorial function:')
print('--------------------------------------------------')
actual_answer = factorial(5)
oracle_answer = math.factorial(5)
test_case = 'factorial(5). Actual, Oracle answers:'
print(' Called ', test_case, actual_answer, oracle_answer)
actual_answer = factorial(8)
oracle_answer = math.factorial(8)
test_case = 'factorial(8). Actual, Oracle answers:'
print(' Called ', test_case, actual_answer, oracle_answer)
actual_answer = factorial(11)
oracle_answer = math.factorial(11)
test_case = 'factorial(11). Actual, Oracle answers:'
print(' Called ', test_case, actual_answer, oracle_answer)
actual_answer = factorial(14)
oracle_answer = math.factorial(14)
test_case = 'factorial(14). Actual, Oracle answers:'
print(' Called ', test_case, actual_answer, oracle_answer)
def check_topological_embedding_brute(self, verbose=False):
'''
Brute-force combinatoric method to check topological embedding
'''
# Clear table and nodemap:
self.T = { superN:{ subN:None for subN in self.subD.nodes }
for superN in self.superD.nodes }
self.AB_nodemap = None
N = len(self.subD.nodes) # number of subdesign nodes
if len(self.superD.nodes) < N:
# shortcut - fewer nodes in superdesign
self.AB_nodemap = None
return False
# compute number of matchings:
num_matchings = math.factorial(len(self.subD.nodes))*math.factorial(len(self.superD.nodes))
count = 0
for sub_perm in permutations(self.subD.nodes):
for super_perm in permutations(self.superD.nodes, N):
#sys.stdout.write("%d \r" % count )
#sys.stdout.flush() # carriage returns don't work in Eclipse :-(
if verbose:
print str(count) + " / " + str(num_matchings)
count += 1
self.AB_nodemap = dict (zip(sub_perm, super_perm))
if self.check_vertex2vertex():
if self.check_edge2path():
if self.check_vertex_disjointness():
return True
# no embedding found.
self.AB_nodemap = None
return False
def odf_sh(self):
r""" Calculates the real analytical ODF in terms of Spherical
Harmonics.
"""
# Number of Spherical Harmonics involved in the estimation
J = (self.radial_order + 1) * (self.radial_order + 2) // 2
# Compute the Spherical Harmonics Coefficients
c_sh = np.zeros(J)
counter = 0
for l in range(0, self.radial_order + 1, 2):
for n in range(l, int((self.radial_order + l) / 2) + 1):
for m in range(-l, l + 1):
j = int(l + m + (2 * np.array(range(0, l, 2)) + 1).sum())
Cnl = (
((-1) ** (n - l / 2)) /
(2.0 * (4.0 * np.pi ** 2 * self.zeta) ** (3.0 / 2.0)) *
((2.0 * (4.0 * np.pi ** 2 * self.zeta) ** (3.0 / 2.0) *
factorial(n - l)) /
(gamma(n + 3.0 / 2.0))) ** (1.0 / 2.0)
)
Gnl = (gamma(l / 2 + 3.0 / 2.0) * gamma(3.0 / 2.0 + n)) / \
(gamma(l + 3.0 / 2.0) * factorial(n - l)) * \
(1.0 / 2.0) ** (-l / 2 - 3.0 / 2.0)
Fnl = hyp2f1(-n + l, l / 2 + 3.0 / 2.0, l + 3.0 / 2.0, 2.0)
c_sh[j] += self._shore_coef[counter] * Cnl * Gnl * Fnl
counter += 1
return c_sh
def n_choose_k(n: int, k: int) -> int:
""" Return the binomial coefficient for n choose k.
The binomial coefficient is defined as:
n choose k = n! / (k!(n-k)!)
For a number of objects n, which k choices allowed, this function reports
the number of ways to make the selection if order is disregarded.
We define n choose k == 0 for k > n.
Args:
n (int): A positive integer indicating the possible number of items to
select.
k (int): A positive integer indicating the number of items selected.
Returns:
int: The result of n choose k.
Raises:
ValueError: if n or k are not non-negative integers.
"""
# Check that n and k are allowed
if not countable.is_nonnegative_integer(n):
raise ValueError("n is a not a non-negative integer")
if not countable.is_nonnegative_integer(k):
raise ValueError("k is a not a non-negative integer")
# We define n choose k for k > n as 0, that is, there are no way
# to choose more items than exist in a set.
if k > n:
return 0
# Compute and return
return math.factorial(n) // (math.factorial(k) * math.factorial(n - k))
def basis(coords,b1,b2,nmax):
hermites = np.loadtxt('hermite_coeffs.txt')
xrot = coords[:,0]/b1
yrot = coords[:,1]/b2
npix = coords.shape[0]
all_basis = np.zeros((npix,nmax+1,nmax+1))
gauss = np.exp(-0.5*(np.array(xrot)**2+np.array(yrot)**2))
n1 = 0
n2 = 0
for n1 in range(0,nmax):
n2 = 0
while (n1+n2) <= nmax:
norm = m.sqrt(m.pow(2,n1+n2)*m.pi*b1*b2*m.factorial(n1)*m.factorial(n2))
k=0
h1=0.
h2=0.
while (k <= n1):
h1 = h1+hermites[n1, k]*(np.array(xrot))**(n1-k)
k=k+1
k=0
while (k <= n2):
h2 = h2+hermites[n2, k]*(np.array(yrot))**(n2-k)
k=k+1
all_basis[:, n1, n2] = gauss/norm*h1*h2;
n2 = n2+1
return all_basis
def dig_fact():
# import timeit and start timer to measure time of function
import timeit
start = timeit.default_timer()
import math # import math package for factorial function
sum_total = 0 # initialize sum variable to hold sum of digit factorials
list = [] # initalize list to hold all numbers which are equal to the sum of the factorial of their digits
for i in range(3,math.factorial(9)*7): # iterate through range and check conditions per problem
sum_total = 0 # reset sum variable for each number in range above
for j in range(0,len(str(i))): # iterate through each digit of number in range above
sum_total += math.factorial(int(str(i)[j])) # add factorial of each digit of number to "sum" variable for checking problem condition below
if i == sum_total: # append number to list if it is equal to the sum of the factorial of its digits
list.append(i)
print sum(list) # return solution
# stop timer and print total elapsed time
stop = timeit.default_timer()
print "Total time:", stop - start, "seconds"
def g_statistic(X, p=None, idx=None):
"""
return g statistic and p value
arguments:
X - the periodicity profile (e.g. DFT magnitudes, autocorrelation etc)
X needs to contain only those period values being considered,
i.e. only periods in the range [llim, ulim]
"""
# X should be real
X = abs(numpy.array(X))
if p is None:
power = X.max(0)
idx = X.argmax(0)
else:
assert idx is not None
power = X[idx]
g_obs = power/X.sum()
M = numpy.floor(1/g_obs)
pmax = len(X)
result = numpy.zeros((int(M+1),), float)
pmax_fact = factorial(pmax)
for index in xrange(1, min(pmax, int(M))+1):
v = (-1)**(index-1)*pmax_fact/factorial(pmax-index)/factorial(index)
v *= (1-index*g_obs)**(pmax-1)
result[index] = v
p_val = result.sum()
return g_obs, p_val
def tabela(n):
somatorio = lambda termo: sum(termo(float(i)) for i in xrange(n))
mysin = lambda x: somatorio(lambda i: (x ** (2 * i + 1)) * (-1) ** i / factorial(2 * i + 1))
mycos = lambda x: somatorio(lambda i: (x ** (2 * i)) * (-1) ** i / factorial(2 * i))
mytan = lambda x: mysin(x) / mycos(x)
mypi = somatorio(lambda k: 4 * (-1) ** k / (2 * k + 1))
mye = somatorio(lambda k: 1.0 / factorial(k))
mypie = mypi / mye
# calcular valores
valores = [
['n={0}'.format(n), 'Ve', 'Va', 'Eabs', 'Erel'],
['pi', pi, mypi],
['e', e, mye],
['pi/e', pie, mypie],
['sen(pi/e)', sin(pie), mysin(mypie)],
['cos(pi/e)', cos(pie), mycos(mypie)],
['tg(pi/e)', tan(pie), mytan(mypie)],
]
# calcular erros
for v in valores[1:]:
ve, va = v[1], v[2]
eabs = ve - va
erel = eabs / ve
v.append(eabs)
v.append(erel)
# imprimir tabela e uma linha em branco
print_table(valores)
print
def comb(n, r):
if n == r:
return 1
elif n < r:
return 0
return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
def __init__(self, n):
self.n = n
self.search_space_size = math.factorial(n)
self.solution_size = n
self.max_leave_out = self.solution_size - 1
(lunches == 'no food truck').all(axis=1).mean()
# How likely is it that a food truck will show up sometime this week?
1 - (3 * .3**7)
((np.random.random((trials, 3)) > travis_park_food_truck).sum(axis=1) == 0).sum()/trials
(lunches == 'food truck').any(axis=1).mean()
# 8. If 23 people are in the same room, what are the odds that two of them
# share a birthday? What if it's 20 people? 40?
# (365! / (365 - 23)!) / (365^23)
import math
1 - ((math.factorial(365) / math.factorial(365-23)) / 365**23)
1 - ((math.factorial(365) / math.factorial(365-20)) / 365**20)
1 - ((math.factorial(365) / math.factorial(365-40)) / 365**40)
birthdays = pd.DataFrame(np.random.randint(1, 365, (10_000, 23)))
birthdays.count(axis=1)
birthdays
birthdays.iterrows()
birthdays.iloc[0, :]
birthdays[birthdays.nunique(axis=1) == birthdays.count(axis=1)].count()/trials
#or
(birthdays.nunique(axis=1) == birthdays.count(axis=1)).mean()
# with numpy
birthdays = (np.random.randint(1, 365, (10_000, 23)))
people = 23
import math
r_func = list(range(10**7)) # lets just check a ton of numbers lol
for i in r_func:
if i == int(sum([math.factorial(int(k)) for k in str(i)])):
print(i)
n = int(input())
time = []
mod = 1000000007
from collections import Counter
from math import factorial
for _ in range(n):
t = int(input())
time.append(t)
c = Counter(time)
ans = 1
for v in list(c.values()):
ans *= factorial(v)
ans %= mod
t = 0
time.sort()
for i in range(1, n):
time[i] += time[i - 1]
for j in range(n):
t += time[j]
print(t)
print(ans)
import math
# Questão 1
count = 0
for i in range(1, 5000001, 1):
if i % 49 == 0 and i % 37 == 0 and i % 2 == 0:
count += 1
print(count)
# Questão 2
x = []
for i in range(10):
if i % 2 == 0:
X = 3**i + 7 * (math.factorial(i))
else:
X = 2**i + 4 * math.log(i)
x.append(X)
num = 0
soma = 0
posicao = 0
count = 0
for a in x:
soma += a
if a > num:
num = a
posicao = count
count += 1
media = soma / 10
print('o maior número está na posição {0}'.format(posicao))
print('a média é {0:.2f}'.format(media))
def n_choose(self, n, k):
n_choose = (math.factorial(n)) / (math.factorial(k) *
math.factorial(n - k))
return n_choose
# Project Euler - Question 15
# Starting in the top left corner of a 2×2 grid, and only being able to move to the right and down, how many routes
# are there to the bottotm right corner through a 20x20 grid?
import time
from math import factorial
n = 20
ans = factorial(2*n)/(factorial(n)**2)
print(int(ans))
print('Time Elapsed:', time.perf_counter(), 'seconds')
def combinations_count(n, r):
return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
def factorial(num):
print(math.factorial(num))
def lattice_paths(n):
"Returns the total number of possible paths in an n-by-n grid from one corner to the opposite corner."
routes = (math.factorial(2*n)/pow(math.factorial(n),2))
return int(routes)
# 1 <= N <= 10**5 import math N = int(input()) ans = math.factorial(N) # for i in range(1, N+1): # ans = ans*i print(ans % (10**9 + 7))
def fact(request, n):
n = int(n)
return HttpResponse("<h2>factorial is {}</h2>".format(factorial(n)))
def gridMovingCountByBinomial(x, y):
# use explict // for true division, otherwise, a estimation will be given for classic division /
return math.factorial(x + y) // (math.factorial(x) * math.factorial(y))
import math print(math.ceil(3.90)) # This will return 4 print(math.floor(3.90)) # This will print 3 print(math.factorial(5)) # Print factorial of 5 ie- 120 print(math.gcd(36, 92)) # This will print greatest common divisor of two nos print(math.sqrt(64)) # This will result the square root of the function
def fact(x, y):
return math.factorial(x)
import math
n = int(input())
if n % 2 == 1:
print(0)
else:
print((math.factorial(n) // math.factorial(n // 2)**2) // (n // 2 + 1))
alp.append(chr(ord('A') + i))
print(alp)
print("------------------------")
a = [[1, 3], [2, 6], [15, 18], [8, 10], [3, 10]]
a.sort()
print(a)
import bisect
b = [2, 4]
bisect.insort(a, b)
print(a)
print("------------------------")
b = [[5, 8], [9, 11], [12, 15], [15, 22]]
n = [1, 13]
l = len(b)
x = bisect.bisect(b, n)
if (b[x - 1] > n) and (n < b[x]):
bisect.insort(b, n)
print(b)
print("------------------------")
import math
print(math.factorial(200))
print("------------------------")
print(1 / 2)
def get_r(x, n):
return get_der(x + 1, n + 1) * (x ** (n + 1)) / math.factorial(n + 1)
import math
n = eval(input('Introduceti n: '))
s = 0
for i in range(1, n + 1):
s += math.factorial(i)
print('Suma = ', s)
def combination(n, k):
return int(
(math.factorial(n)) / ((math.factorial(k)) * (math.factorial(n - k))))
def get_der(x, n):
if n == 0:
return np.log(x)
else:
return ((-1) ** (n + 1)) * 1.0 * math.factorial(n - 1) / (x ** n)
def _factorial(num):
# sleep 2 seconds because it takes very less time
# so that you can see the actual difference
time.sleep(2)
print(math.factorial(num))
import math
n = int(input("Kitne line chahiye bhiaya "))
for i in range(0, n + 1):
print(" " * (n - i), end="")
for j in range(0, i + 1):
print(int(
math.factorial(i) / (math.factorial(i - j) * math.factorial(j))),
end=" 15")
if j == i:
print()
def permutation_formula(n, r):
return factorial(n) // factorial(n-r)
def savitzky_golay(y,
window_size,
order,
deriv=0,
rate=1,
returnScoreList=False):
'''
Smooths over data using a Savitzky Golay filter
This can either return a list of scores, or a list of peaks
y : array-like, score list
window_size : int, how big of a window to smooth
order : what order polynomial
returnScoreList : bool
'''
from math import factorial
y = np.array(y)
try:
window_size = np.abs(np.int(window_size))
order = np.abs(np.int(order))
except ValueError:
raise ValueError("window_size and order have to be of type int")
if window_size % 2 != 1 or window_size < 1:
raise TypeError("window_size size must be a positive odd number")
if window_size < order + 2:
raise TypeError("window_size is too small for the polynomials order")
order_range = range(order + 1)
half = (window_size - 1) // 2
# precompute coefficients
b = np.mat([[k**i for i in order_range] for k in range(-half, half + 1)])
m = np.linalg.pinv(b).A[deriv] * rate**deriv * factorial(deriv)
# pad the signal at the extremes with values taken from the signal itself
firstvals = y[0] - np.abs(y[1:half + 1][::-1] - y[0])
lastvals = y[-1] + np.abs(y[-half - 1:-1][::-1] - y[-1])
y = np.concatenate((firstvals, y, lastvals))
filtered = np.convolve(m[::-1], y, mode='valid')
if returnScoreList:
return np.convolve(m[::-1], y, mode='valid')
# set everything between 1 and -inf to 1
posFiltered = []
for i in range(len(filtered)):
if 1 > filtered[i] >= -np.inf:
posFiltered.append(1)
else:
posFiltered.append(filtered[i])
# use slopes to determine peaks
peaks = []
slopes = np.diff(posFiltered)
la = 45 # how far in sequence to look ahead
for i in range(len(slopes) - 50):
if i > len(slopes) - la: # probably irrelevant now
dec = all(slopes[i + x] < 0 for x in range(1, 50))
if slopes[i] > 0 and dec:
if i not in peaks:
peaks.append(i)
else:
dec = all(slopes[i + x] < 0 for x in range(1, la))
if slopes[i] > 0 and dec:
peaks.append(i)
return peaks
import math a, b = map(int, input().split()) print(int(math.factorial(a) / (math.factorial(b) * math.factorial(a - b))))
def combination_formula(n, r):
return factorial(n) // (factorial(r)*factorial(n-r))
# Project Euler --> https://projecteuler.net/problem=24
# Problem 24 : Lexicographic permutations
from math import factorial
digits = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
result = []
index = 999999
for j in range(9, -1, -1):
n = int(index / factorial(j))
result.append(str(digits[n]))
index -= n * factorial(j)
del digits[n]
print(''.join(result))
import math
n = int(input("Enter the value of n in Euler's formula: "))
sum1 = 1
for i in range(1, n + 1):
sum1 = sum1 + (1 / math.factorial(i))
print("value of e is :", round(sum1, 2))
#Lucciffer
