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))