def permute(digits, index):
if len(digits) == 0: return []
base = euler.factorial(len(digits) - 1)
here = digits.pop(index / base)
rest = permute(digits, index % base)
answer = [here]
answer.extend(rest)
return answer
def permute(digits, index):
if len(digits)==0: return []
base = euler.factorial( len(digits) -1)
here = digits.pop(index/base)
rest = permute(digits, index % base)
answer = [here]
answer.extend(rest)
return answer
def permutation(orig_nums, n):
nums = list(orig_nums)
perm = []
while len(nums):
divider = factorial(len(nums) - 1)
pos = n / divider
n = n % divider
perm.append(nums[pos])
print divider, pos, n
nums = nums[0:pos] + nums[pos + 1 :]
return perm
import euler
print sum(
map(
int,
list(
str(
euler.factorial(100)
)
)
)
)
def nCk(n, k):
return factorial(n) // (factorial(k) * factorial(n-k))
#!/usr/bin/python # coding: UTF-8 """ @author: CaiKnife Factorial digit sum Problem 20 n! means n (n 1) ... 3 2 1 For example, 10! = 10 9 ... 3 2 1 = 3628800, and the sum of the digits in the number 10! is 3 + 6 + 2 + 8 + 8 + 0 + 0 = 27. Find the sum of the digits in the number 100! """ from euler import factorial print sum([int(x) for x in str(factorial(100))])
def is_curious(n):
return sum([factorial(x) for x in get_digits(n)]) == n
def testFactorial(self):
for i in range(1,20):
a = euler.naive_factorial(i)
b = euler.factorial(i)
print a,b
self.assert_( a == b)
#!/usr/bin/env python # Copyright (c) 2008 by Steingrim Dovland <*****@*****.**> from euler import factorial # n! means n * (n - 1) * ... * 3 * 2 * 1 # # Find the sum of the digits in the number 100! print sum(map(int, str(factorial(100))))
import sys
sys.path.append("..")
from euler import factorial_memory as factorial
result = 0
memory = {0: 1, 1: 1}
for i in range(3, 1000000):
digits = [int(x) for x in str(i)]
factorials = [factorial(x, memory) for x in digits]
if sum(factorials) == i:
result += i
print(result)
"""
Runtime without memory: 6.095s
Runtime with memory: 2.910s
Reducing search space from 1,000,000 to 100,000 reduces time to: 0.292s
"""
import euler
f = [euler.factorial(i) for i in range(10)]
def factorialChainNext(n):
seq = euler.intToSeq(n)
seq = [f[i] for i in seq]
return sum(seq)
def factorialChain(n):
lst = []
while n not in lst:
lst.append(n)
n = factorialChainNext(n)
assert (len(lst) <= 60)
lst.append(n)
return lst
def factorialChainLength(n):
return len(factorialChain(n)) - 1
def main():
cnt = 0
for i in range(3000):
fc = factorialChain(i)
fcl = len(fc) - 1
if fcl == 60:
import euler
f = [ euler.factorial(i) for i in range(10) ]
def factorialChainNext(n):
seq = euler.intToSeq(n)
seq = [ f[i] for i in seq ]
return sum(seq)
def factorialChain(n):
lst = []
while n not in lst:
lst.append(n)
n = factorialChainNext(n)
assert(len(lst)<=60)
lst.append(n)
return lst
def factorialChainLength(n):
return len(factorialChain(n))-1
def main():
cnt = 0
for i in range(3000):
fc = factorialChain(i)
fcl = len(fc)-1
if fcl==60:
cnt +=1
print i,fcl,cnt
if i % 10000 == 0:
print '#',i
import euler from numba import jit @jit def main(memoize): i = 0 for i in range(3000000): s = 0 for j in list(str(i)): s += memoize[int(j)] if s==i: print s memoize = dict(zip([i for i in range(0,10)],[euler.factorial(int(i))for i in range(0,10)])) main(memoize)
def ncr(n, r):
nfac, rfac, nrfac = factorial(n), factorial(r), factorial(n - r)
return nfac / (rfac * nrfac)
def expfact(x):
return tuple([ factorial(int(c)) for c in str(x) ])
import sys
sys.path.append("..")
from euler import factorial
f = factorial(100)
digits = [int(i) for i in str(f)]
result = sum(digits)
print(result)
"""
@author: CaiKnife
Combinatoric selections
Problem 53
There are exactly ten ways of selecting three from five, 12345:
123, 124, 125, 134, 135, 145, 234, 235, 245, and 345
In combinatorics, we use the notation, 5C3 = 10.
In general,
nCr =
n!
r!(nr)!
,where r n, n! = n(n1)...321, and 0! = 1.
It is not until n = 23, that a value exceeds one-million: 23C10 = 1144066.
How many, not necessarily distinct, values of nCr, for 1 n 100, are greater than one-million?
"""
from euler import factorial
count = 0
for n in xrange(23, 101):
for r in range(1, n):
if factorial(n) / factorial(r) / factorial(n - r) > 1000000:
count += 1
print count
from euler import digits, factorial print sum(digits(factorial(100)))
#!/usr/bin/python import euler # I did a quick search to find some information about this and found # http://en.wikipedia.org/wiki/Catalan_number, which is close to what I wanted # it describes the number of paths without crossing the diagonal. I then # searched for the sequence: 1, 2, 6 on # http://www.research.att.com/~njas/sequences # and found the "Central binomial coefficients" C(2n,n) = (2n)!/(n!)^2 # # One description jumped out at me: # The number of direct routes from my home to Granny's when Granny # lives n blocks south and n blocks east of my home in Grid City. To # obtain a direct route, from the 2n blocks, choose n blocks on which one # travels south. # Which is what I'm looking for. # n = 20 paths = euler.factorial(2 * n) / (euler.factorial(n) ** 2) print "monotonic paths on",n,"x",n,"grid",paths
#!/usr/bin/python import euler nfact = str(euler.factorial(100)) sum = 0 for c in nfact: sum += int(c) print "100! digit sum =",sum
def digit_factorial_sum(n):
ds = digits(n)
return sum([ factorial(d) for d in ds ])
import euler factorial = euler.factorial(100) print sum(map(int, str(factorial)))
def digit_factorial_sum(n):
ds = digits(n)
return sum([factorial(d) for d in ds])