def cycle(polygons, index=0):
global sequence
if index == 0:
for elem in polygons[index]:
sequence = [elem] + [None] * 5
cycle(polygons, index + 1)
return False
else:
if index < 5:
for elem in polygons[index]:
if elem // 100 == sequence[index - 1] % 100:
sequence[index:] = [elem] + [None] * (5 - index)
cycle(polygons, index + 1)
return False
else:
for elem in polygons[index]:
if elem // 100 == sequence[index - 1] % 100 and \
elem % 100 == sequence[0] // 100:
sequence[index] = elem
print(sum(sequence))
timer.stop()
quit()
Problem:
Find the sum of digits in the numerator of the 100th convergent of the
continued fraction for e.
Performance time: ~0.0012s
"""
from fractions import Fraction
from timer import timer
from utils import sum_of_digits
timer.start()
a = [int(n / 3 * 2) if n % 3 == 0 else 1 for n in range(1, 101)]
a[0] = 2
def convergent_e(limit=-1, index=0):
if limit == 0:
return a[0]
elif index == limit - 1:
return a[index] + Fraction(1, a[index+1])
else:
return a[index] + Fraction(1, convergent_e(limit, index+1))
print(sum_of_digits(Fraction(convergent_e(99)).numerator))
timer.stop()
"""
Problem :
working out the alphabetical value for each name,
multiply this value by its alphabetical position in the list to obtain a
name score.
What is the total of all the name scores in the file?
Performance time: ~0.0089s
"""
from timer import timer
timer.start()
with open("./data/names.txt") as f:
names = sorted(f.read().upper().replace("\"", "").split(","))
print(
sum((i + 1) * sum(ord(c) - 64 for c in names[i])
for i in range(len(names))))
timer.stop()
