def mean_time_system(self):
Lsys = self.mean_system()
a5 = self.pr_infinitesimal_generator()
p0 = a5[0]
if (self.M >= self.N + self.r) and (self.M >= self.N
and self.M < self.N + self.r):
sum1 = sum([
p0 * (self.M - n) * self.eps * math.perm(self.M, n) *
((self.eps * self.theta / self.C)**n)
for n in range(self.N + 1)
])
sum2 = sum([
p0 * (self.M - n) * self.eps * math.perm(self.M, n) *
((self.theta / self.C)**self.N) * ((self.eps**n) / math.prod([
self.C / self.theta + i * self.gama
for i in range(1, n - self.N + 1)
])) for n in range(self.N + 1, self.M)
])
dominator1 = sum1 + sum2
Wsys1 = Lsys / dominator1
return Wsys1
else:
dominator2 = sum([
p0 * (self.M - n) * self.eps * math.perm(self.M, n) *
((self.eps * self.theta / self.C)**n) for n in range(self.M)
])
Wsys2 = Lsys / dominator2
return Wsys2
def birthdayParadoxNoCollisionProbability(tValue):
# result = 1
# for i in range(tValue):
# result *= 1 - (i/365)
# print(result)
print("Probability that there is no birthday collision",
perm(365, tValue) / pow(365, tValue))
print("Probability that there is at least 1 birthday collision",
1 - (perm(365, tValue) / pow(365, tValue)))
def nPr(n: int, r: int) -> int:
"""
Equivalent to:
math.factorial(n) // math.factorial(n - r)
"""
return math.perm(n, r)
def random_perm_generator(
cards_set: List[Card],
num_opponent_unknown_cards: int,
num_permutations_requested: Optional[int],
seed: Optional[Any] = None) -> List[Permutation[Card]]:
"""
A simple implementation of a PermutationsGenerator. It generates permutations
randomly where the first num_opponent_unknown_cards are sorted until it
manages to generate num_permutations_requested unique examples.
Advantages: High dispersion. Fast for a small number of permutations.
Disadvantages: Slow for a high number of permutations requested (e.g., 1000).
"""
assert num_opponent_unknown_cards <= len(cards_set)
rng = random.Random(seed)
permutations = set()
if num_permutations_requested is None:
num_unknown_cards = len(cards_set)
num_permutations_requested = \
math.comb(num_unknown_cards, num_opponent_unknown_cards) * \
math.perm(num_unknown_cards - num_opponent_unknown_cards)
while len(permutations) < num_permutations_requested:
permutation = [card.copy() for card in cards_set]
rng.shuffle(permutation)
# noinspection PyTypeChecker
permutation = sorted(permutation[:num_opponent_unknown_cards]) + \
permutation[num_opponent_unknown_cards:]
permutations.add(tuple(permutation))
permutations = list(list(p) for p in permutations)
return permutations
def permutations(self, arg_list):
"""wrapper of math package - return permutation of two number
"""
if len(arg_list) > 2:
raise bad_args
result = math.perm(arg_list[0], arg_list[1])
return self.convert_int(result)
def math_solution(nth: int):
perm = [0] * 10
digits = list(range(0, 10))
nth -= 1 # convert to zero-indexed base
for i in range(0, 10):
p = math.perm(10 - i - 1) # number of permutations from n items
perm[i] = digits[nth // p]
nth = nth % p
digits.remove(perm[i])
return perm
def find(solution, elements, n, k):
# print(solution, elements, n, k)
if not elements:
return solution
s = 0
cnt_p = math.perm(len(elements) - 1)
for e in elements:
if s + cnt_p >= k:
elements.remove(e)
return find(solution + str(e), elements, n, k - s)
s += cnt_p
def pont41(label):
print(label)
kiiratas("math.ceil(0)", math.ceil(0))
kiiratas("math.ceil(-8)", math.ceil(-8))
kiiratas("math.ceil(13.58)", math.ceil(13.58))
kiiratas("math.ceil(-13.58)", math.ceil(-13.58))
print()
kiiratas("math.comb(90, 5)", math.comb(90, 5)) #3.8. verziótól
kiiratas("math.comb(45, 6)", math.comb(45, 6))
kiiratas("math.comb(35, 7)", math.comb(35, 7))
print()
kiiratas("math.perm(5, 2)", math.perm(5, 2)) #3.8. verziótól
kiiratas("math.perm(10, 3)", math.perm(10, 3))
kiiratas("math.perm(5, 1)", math.perm(5, 1))
print()
kiiratas("math.copysign(15, 0.0)", math.copysign(15, 0.0))
kiiratas("math.copysign(15, -0.0)", math.copysign(15, -0.0))
kiiratas("math.copysign(13.62, 3.0)", math.copysign(13.62, 3.0))
kiiratas("math.copysign(13.62, -1.0)", math.copysign(13.62, -1.0))
print()
kiiratas("math.fabs(0)", math.fabs(0))
kiiratas("math.fabs(58)", math.fabs(58))
kiiratas("math.fabs(-13)", math.fabs(-13))
kiiratas("math.fabs(-13.5878)", math.fabs(-13.5878))
print()
kiiratas("math.factorial(0)", math.factorial(0))
kiiratas("math.factorial(1)", math.factorial(1))
kiiratas("math.factorial(5)", math.factorial(5))
print()
kiiratas("math.floor(0)", math.floor(0))
kiiratas("math.floor(-8)", math.floor(-8))
kiiratas("math.floor(13.58)", math.floor(13.58))
kiiratas("math.floor(-13.58)", math.floor(-13.58))
print()
kiiratas("math.gcd(120, 25)", math.gcd(120, 25))
kiiratas("math.gcd(24, 60)", math.gcd(24, 60))
print()
kiiratas("math.isqrt(68)", math.isqrt(68)) #3.8. verziótól
kiiratas("math.isqrt(125)", math.isqrt(125))
print()
def mean_service(self):
a3 = self.pr_infinitesimal_generator()
p0 = a3[0]
if (self.M >= self.N + self.r):
sum1_1 = sum([
p0 * i * math.perm(self.M, i) *
((self.eps * self.theta / self.C)**i)
for i in range(self.N + 1)
])
sum1_2 = self.N * sum([
p0 * math.perm(self.M, i) * ((self.theta / self.C)**self.N) *
((self.eps)**i / math.prod([
self.C / self.theta + j * self.gama
for j in range(1, i - self.N + 1)
])) for i in range(self.N + 1, self.N + self.r + 1)
])
Lser_1 = sum1_1 + sum1_2
return Lser_1
elif (self.M >= self.N and self.M < self.N + self.r):
sum2_1 = sum([
p0 * i * ((self.eps * self.theta / self.C)**i) *
math.perm(self.M, i) for i in range(self.N + 1)
])
sum2_2 = self.N * sum([
p0 * math.perm(self.M, i) * ((self.theta / self.C)**self.N) *
((self.eps)**i / math.prod([
self.C / self.theta + j * self.gama
for j in range(1, i - self.N + 1)
])) for i in range(self.N + 1, self.M + 1)
])
Lser_2 = sum2_1 + sum2_2
return Lser_2
else:
Lser_3 = sum([
p0 * i * ((self.eps * self.theta / self.C)**i) *
math.perm(self.M, i) for i in range(self.M + 1)
])
return Lser_3
def _math38_():
prior = 0.8
likelihoods = [0.625, 0.84, 0.30]
r = 650320427
s = r**2
print("3.8 math")
print(math.dist([3], [-8]))
print(math.hypot(1, 1))
print(math.prod(likelihoods, start=prior))
print(math.perm(10, 3))
print(math.comb(10, 3))
print(math.isqrt(s - 1))
print("--------")
def pr_block(self):
a2 = self.pr_infinitesimal_generator()
p0 = a2[0]
if (self.M >= self.N + self.r):
prod_1 = ((self.theta / self.C)**(self.N)) * (math.perm(
self.M, self.N + self.r))
prod_2 = ((self.eps)**(self.N + self.r)) / (math.prod([
self.C / self.theta + i * self.gama
for i in range(1, self.r + 1)
]))
p_block = prod_1 * prod_2 * p0
return p_block
else:
return 0
def pr_infinitesimal_generator(self):
prob = []
if (self.M >= self.N + self.r):
p01_1 = sum([
math.perm(self.M, n) * (((self.eps * self.theta) / self.C)**n)
for n in range(1, self.N + 1)
])
p01_2 = sum([
math.perm(self.M, n) * (self.eps**n) /
(math.prod([(self.C / self.theta + i * self.gama)
for i in range(1, n - self.N + 1)]))
for n in range(self.N + 1, self.N + self.r + 1)
])
p01 = (1 + p01_1 + p01_2)**(-1)
prob.append(p01)
elif (self.M >= self.N and self.M < self.N + self.r):
p02_1 = sum([
math.perm(self.M, n) * (((self.eps * self.theta) / self.C)**n)
for n in range(1, self.N + 1)
])
p02_2 = sum([
math.perm(self.M, n) * (self.eps**n) /
(math.prod([(self.C / self.theta + i * self.gama)
for i in range(1, n - self.N + 1)]))
for n in range(self.N + 1, self.M + 1)
])
p02 = (1 + p02_1 + p02_2)**(-1)
prob.append(p02)
else:
p03_1 = sum([
math.perm(self.M, n) * (((self.eps * self.theta) / self.C)**n)
for n in range(1, self.M)
])
p03 = (1 + p03_1)**(-1)
prob.append(p03)
return prob
def rec(self, n, k):
if n < k:
return 0
if k == 1:
return factorial(n-1) % 1000000007
if n == k:
return 1
res = 0
for i in range(1,n+1):
if n-i < k - 1:
break
# delta = (self.rec(n-i, k-1) * comb(n-1,i-1) * factorial(i-1)) % 1000000007
delta = (self.rec(n-i, k-1) * (perm(n-1,i-1) % 1000000007)) % 1000000007
res = (res + delta) % 1000000007
print(n, k, res)
return res % 1000000007
def sortBruteForce(self):
self.setStatus("Sorted")
self.algorithm = 'BruteForce'
print('Running Brute Force Sort')
bestRoute = []
bestRouteMiles = 90000
packageList = self.packageList
i = 0
perm = math.perm(len(packageList))
print("number of perms " + str(perm))
for x in itertools.permutations(packageList):
if calculateMileage(x) < bestRouteMiles:
bestRouteMiles = calculateMileage(x)
bestRoute = x
i += 1
if i % 1000000 == 0:
print("perm " + str(round((i / perm) * 100, 2)) +
"% complete ")
self.packageList = bestRoute
"""
Number of possibilities to choose k items from n items without repetition with order
------------------------------------------------------------------------------------
Input: n (int) number of all elements
k (int) number of elements to choose
whether k = None, function returns n!
Output: (int) number of possibilities
n! / (n - k)! when k < n
n! when k = None
0 when k > n
"""
# This function is available from Python 3.8
from math import perm
# You have a deck contained 52 cards. You should select 5 of them.
# How many ways can 5 cards be chosen?
n = 52 # size of deck
k = 5 # number of selection
# NOTE: Permutation isn't equals to combination. If you want to calculate
# chance, use combination instead of permutation.
# Result of combination: 2,598,960
result = perm(n, k)
print('You can pick {} cards from {} carded deck in {} different ways.'.format(
k, n, result))
import math print(math.perm(3,2))
print("The factorial of 0 is :", math.factorial(0)) #The factorial of 0 is : 1
print("The factorial of 4 is :",
math.factorial(4)) #The factorial of 4 is : 24
print("The factorial of 7 is :",
math.factorial(7)) #The factorial of 7 is : 5040
print("The factorial of 9 is :",
math.factorial(9)) #The factorial of 9 is : 362880
print("The factorial of 15 is :",
math.factorial(15)) #The factorial of 15 is : 1307674368000
'''
4- math.perm(n, k=None)
Return the number of ways to choose k items from n items without repetition and with order.
Evaluates to n! / (n - k)! when k <= n and evaluates to zero when k > n.
If k is not specified or is None, then k defaults to n and the function returns n!.
'''
print("math.perm(10, 2) :", math.perm(10, 2)) #math.perm(10, 2) : 90
print("math.perm(5, 3) :", math.perm(5, 3)) #math.perm(5, 3) : 60
'''
5- math.comb(n, k)
Return the number of ways to choose k items from n items without repetition and without order.
Evaluates to n! / (k! * (n - k)!) when k <= n and evaluates to zero when k > n.
Also called the binomial coefficient because it is equivalent to the coefficient
of k-th term in polynomial expansion of the expression (1 + x) ** n
'''
print("math.comb(10, 2) :", math.comb(10, 2)) #math.comb(10, 2) : 45
print("math.comb(5, 3) :", math.comb(5, 3)) #math.comb(5, 3) : 10
'''
6- math.copysign(x, y)
Return a float with the magnitude (absolute value) of x but the sign of y.
On platforms that support signed zeros, copysign(1.0, -0.0) returns -1.0.
'''
def perm(n, k=None):
return math.perm(n, k=None)
# Round square root numbers downward to the nearest integer print(math.isqrt(10)) print(math.isqrt(12)) print(math.isqrt(68)) print(math.isqrt(100)) #Returns x * (2**i). This is also called as inverse of Python frexp() print(math.ldexp(4, 3)) #Return the fractional and integer parts of x print(math.modf(100.12)) # Print the number of ways to choose k items from n items #print (math.perm(n, k)) print(math.perm(7, 5)) #Returns the product of an iterable (lists, array, tuples, etc.) print(math.prod((1, 2, 3, 4, 5))) # Find the value n that makes x completely divisible by y print(math.remainder(9, 2)) print(math.remainder(17, 4)) # Return the truncated integer parts of different numbers print(math.trunc(2.77)) print(math.trunc(8.32)) print(math.trunc(-99.29)) #find the exponential of the specified value print(math.exp(65))
def get_linspace(self, n: int) -> np.ndarray:
vectors = list(itertools.permutations(self.domain, r=self.length))
end = math.perm(len(self.domain), self.length) - 1
domain_array = self._convert_to_array(vectors)
index = np.linspace(0, end, n, dtype=int)
return domain_array[index]
import math print(math.factorial(9)) print(math.perm(9))
# Em um grupo de n pessoas, calcule a probabilidade de haver pelo menos duas pessoas que façam aniversário no mesmo dia.
import math
n = int(input("Há quantas pessoas no grupo? "))
prob = (1 - math.perm(365, n) / 365**n)
print(
f"\n Num grupo de {n} pessoas, a probabilidade de haver pelo menos duas pessoas que tenham o mesmo dia de aniversário é de %.2f."
% round(prob, 2))
from sys import argv
import re
from itertools import combinations, permutations
from math import sqrt, perm, ceil
with open(argv[1] if len(argv) > 1 else "input") as f:
lines = f.readlines()
p1 = re.compile("\-+ scanner (\d+)")
p2 = re.compile("(-?\d+),(-?\d+),(-?\d+)")
scannersInput = dict()
positions = dict()
distancesM = dict()
distancesE = dict()
common_n = perm(12, 2) // 2
final_beacons = dict()
curScanner = None
for line in lines:
m = p1.match(line)
if m:
curScanner = int(m.group(1))
scannersInput[curScanner] = set()
else:
m = p2.match(line)
if m:
scannersInput[curScanner].add(tuple(int(x) for x in m.groups()))
final_beacons[0] = scannersInput[0].copy()
inf = inf
nan = nan
pi = 3.141592653589793
tau = 6.283185307179586
FILE
/Library/Frameworks/Python.framework/Versions/3.9/lib/python3.9/lib-dynload/math.cpython-39-darwin.so
>>> 10%7
3
>>> math.remainder(10,7)
3.0
>>> math.comb(3,2)
3
>>> math.perm(3,2)
6
>>> math.sqrt(5.43)
2.3302360395462087
>>>
>>> x= 12.3
>>> y =54.5
>>> x+y
66.8
>>> x-y
-42.2
>>> x**y
2.5108951247437656e+59
>>> #complex Number:
>>> x = 5+7j
>>> x.real
from math import comb
from math import perm
t = int(input())
for i in range(t):
n, m = sorted([int(x) for x in input().split()])
ans = 0
for j in range(n + 1):
ans += comb(n, j) * perm(m, j)
ans %= 10005
print(ans)
def main():
cmp = math.comb(49, 6) # 49 adet içinde 6 seçilecek loto :) kombinasyon
print("Kombinasyon 49c6: {:,}".format(cmp))
prm = math.perm(49,
6) # 49 adet içinde sıralı olarak 6 seçilecek permütasyon
print("Permutasyon 49p6: {:,}".format(prm))
import math print(math.pi) # 3.141592653589793 print(math.e) # 2.718281828459045 print(math.sin(23)) # -0.8462204041751706 print(math.perm(3)) # 6 permutations print(math.perm(4)) # 24 permutations print(math.perm(4, 2)) # 12 permutations print(math.lcm(120, 42)) # 840 least common multiple print(math.gcd(120, 42)) # 6 greatest common divisor
import math math.perm(100, -2)
assert math.gamma(2) == 1.0 # issue 1113 assert math.lgamma(2) == 0.0 # issue 1246 assertRaises(TypeError, math.cos) # issue 1308 assert math.factorial(69) == 171122452428141311372468338881272839092270544893520369393648040923257279754140647424000000000000000 # issue 1312 assert math.comb(5, 2) == 10 assert math.comb(69, 12) == 8815083648488 assert math.perm(69, 12) == 4222439171759589580800 x = math.prod(range(1, 33)) assert x == 263130836933693530167218012160000000 assert math.isqrt(x) == 512962802680363491 y = math.factorial(69) assert math.isqrt(y) == 13081378078327271990661335578798848847474255303826 assert math.dist([1, 2, 3], [4, 5, 6]) == 5.196152422706632 # issue 1314 assert math.gcd(pow(2, 53) - 2, 2) == 2 assert math.gcd(pow(2, 53) - 1, 2) == 1
import math
n = int(input("Digite quantos elementos"))
k = int(input("Digite de quanto em quanto"))
print("A permutacao (", n, ",", k, ") é de ", math.perm(n, k))
