def partition_test():
from ProjectEuler import partition_slow, partition
end = 60
def test1():
print "partition_slow"
for i in range(0, end):
print partition_slow(i)
def test2():
print "partition"
for i in range(0, end):
print partition(i)
time_func(test1)
time_func(test2)
def string_reverse_test():
from projecteuler import str_reverse
L = list()
for i in range(100000):
L.append(str(i))
string = "".join(L)
def test1():
str_reverse(string)
time_func(test1)
def test2():
string[::-1]
time_func(test2)
def str_reverse3(string):
tmp = list(string)
tmp.reverse()
return "".join(tmp)
def test3():
str_reverse3(string)
time_func(test3)
# Project Euler problem 77
# cf. http://blog.dreamshire.com/2009/06/08/project-euler-problem-77-solution/
from pyprimes import primes_below
from projecteuler import time_func
def main():
primes = list(primes_below(80))
target = 11 # how many ?
while True:
ways = [1] + [0] * target
for i in primes:
for j in range(i, target + 1):
ways[j] += ways[j - i]
if ways[target] > 5000:
break
target += 1
print target
if __name__ == "__main__":
time_func(main)
# Project Euler problem 69
# cf. http://d.hatena.ne.jp/tanakaBox/20080516/1210893388
from pyprimes import primes_below
from projecteuler import time_func, totient
def main1():
primes = list(primes_below(18))
products = 1
for prime in primes:
if products < 1000000:
products *= prime
else:
break
print products
def main2():
max_value = 0
max_n = 0
for n in xrange(1, 1000001):
value = n / float(totient(n))
if max_value < value:
max_value = value
max_n = n
print max_n
if __name__ == '__main__':
time_func(main1)
upperbound = 5000
prime_nums = [x for x in primes_below(upperbound) if x > lowerbound]
semiprimes = set()
for prime1 in prime_nums:
for prime2 in prime_nums:
semiprime = prime1 * prime2
if semiprime < end:
semiprimes.add(semiprime)
return semiprimes
def main2():
semiprimes = create_semiprimes()
numbers = set() # totient(n) is a permutation of n
min_value = 100
min_n = 0
for semiprime in semiprimes:
if is_perm(semiprime, totient(semiprime)):
numbers.add(semiprime)
for num in numbers:
tmp = num / float(totient(num))
if tmp < min_value:
min_value = tmp
min_n = num
print min_n
if __name__ == '__main__':
time_func(main2)
if counter == n:
break
def gen_digits(n):
while n:
yield n % 10
n /= 10
def square_root(n, l, m=0):
if l == 0:
return m
d = head(dropwhile(lambda d: d * (d + 20 * m) <= n, count(1))) - 1
n -= d * (d + 20 * m)
m = m * 10 + d
return square_root(n * 100, l - 1, m)
def main2():
N = 100
M = 100
print sum(
map(lambda n: sum(gen_digits(square_root(n, M))),
filter(lambda n: square_root(n, 1)**2 != n, range(1, N + 1))))
if __name__ == '__main__':
time_func(main2)
# project-euler-71-proper-fractions-ascending-order/
a = 3
b = 7
r = 0
s = 1
start = 10 ** 6
for q in xrange(start, 2, -1):
p = (a * q - 1 ) / b
if p * s > r * q:
s = q
r = p
print Fraction(r, s)
def main3():
"""Original"""
target = 10 ** 6
a, b = 2, 5
c, d = 3, 7
while True:
if b < target:
#print a, b
a, b = a + c, b + d
else:
a, b = a - c, b - d
break
#print Fraction(a, b)
print a
if __name__ == '__main__':
time_func(main3)