def Chudnovsky(n:int=100, prec:int=100) -> Decimal: # https://en.wikipedia.org/wiki/Chudnovsky_algorithm
"""
parameter
int n is for rounds of iteration
as n increses
time uses for computing increses also
"""
getcontext().prec = prec
sum = Decimal(0.0)
for i in range(n):
top = factorial(6*i)*(545140134*i+13591409)
bottom = factorial(3*i)*factorial(i)**3*(-262537412640768000)**i
sum = sum + Decimal(top)/Decimal(bottom)
return Decimal(426880)*Decimal(10005).sqrt() / sum
def cs(coins,args):
#Compare to Schurs
start = 1
step = 1
iterations = int(args[0])
without = lc(coins,[start,step,iterations]).split("\n")[0]
xAxis = list(range(1,1+iterations))
yAxis = []
productOfCoins = 1
for i in range(0,len(coins)):
productOfCoins*=coins[i]
firstTerm = 1/(factorial(len(coins)-1)*productOfCoins)
degree = len(coins)-1
for i in xAxis:
yAxis.append(getChange(i,coins) - i**degree*firstTerm)
reg = calcRegression(xAxis,yAxis,degree-1)[0]
for i in reg:
i = round(i,PRECISION)
equation = str(round(firstTerm,PRECISION))+"x^"+str(degree) + " "
for i in range(0,len(reg)):
equation+=str(round(reg[i],5))+"x^"+str(degree-(1+i))
equation+=" "
return [without,equation]
def Ramanujan(n:int=100, prec:int=100) -> Decimal: # Ramanujan's formulae
"""
parameter int n is for rounds of iteration
as n increses
time uses for computing is longer
"""
getcontext().prec = prec
sum = Decimal(0.0)
first = Decimal((2.0*pow(2.0,(1/2)))/9801.0)
for k in range(n):
second = Decimal(factorial(4*k))
third = Decimal(1103.0 + 26390.0*k)
forth = Decimal(pow(factorial(k), 4.0))
fifth = Decimal(pow(396.0,(4.0*k)))
sum = sum + (second*third)/(forth*fifth)
sum = sum * first
return Decimal(1/sum) # can approximate around 15 decimal digit
def main():
# We know how to calculate the number of permutations using factorial.
# Instead of forming every permutation, we just skip them in chunks using
# factorial calculations.
digits = ["0", "1", "2", "3", "4", "5", "6", "7", "8", "9"]
permutation = []
count = 0
while digits:
for i in range(len(digits)):
permutations = factorial(len(digits) - 1)
if count + permutations >= 1000000:
permutation.append(digits[i])
digits = digits[:i] + digits[i + 1:]
break
count += permutations
print("".join(permutation))
def problem_20(): return digits_sum(factorial(100))
def fact_digits(x):
return sum(factorial(i) for i in digits(x))
def p_lineage( population ):
return c_lineage( population ) / float( util.factorial( len( population ) - 1 ) )
def problem020(n): return sum(int(c) for c in str(util.factorial(n)))
import util factorials = [util.factorial(i) for i in xrange(0, 10)] def problem034(): return sum(i for i in xrange(3, factorials[9]*7) if i == sum_of_digit_factorial(i)) def sum_of_digit_factorial(n): return sum(factorials[int(c)] for c in str(n)) def solution(): return problem034() def test(): assert sum_of_digit_factorial(145) == 145 test() print solution()
def problem015(m, n): return factorial(m + n) / (factorial(m) * factorial(n))
#!/usr/bin/env python
from util import factorial
nCr = lambda n, r: factorial(n) / (factorial(r) * factorial(n - r))
def main():
total = 0
for n in range(23, 101):
for r in range(1, n + 1):
if nCr(n, r) > 1000000:
total += 1
print total
if __name__ == "__main__":
main()
def solve():
return sum(int(c) for c in str(factorial(100)))
def iscurious(i):
return i == sum(factorial(j) for j in splitdigits(i))
def main():
print sum(i for i in range(3,50000) if sum(factorial(d) for d in digits(i)) == i)
def main():
print(sum(int(x) for x in str(factorial(100))))
""" Project Euler 34: Find the sum of all numbers which are equal to the sum of the factorial of their digits """ import util sum_all_valid_number = 0 for i in range(11,409114): digit = list(str(i)) sum_factorial = 0 for j in range(0,len(digit)): sum_factorial += util.factorial(int(digit[j])) if sum_factorial == i: print i sum_all_valid_number += i print sum_all_valid_number
""" Project Euler 20: Find the sum of the digits in 100! """ import util def sumDigit(n): if n <10: return n else: return n%10 + sumDigit(n//10) n = 100 print sumDigit(util.factorial(n))
def main():
print sum(int(i) for i in str(factorial(100)))
