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Project Euler 65 Solution #3035

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Merged
dhruvmanila merged 11 commits into from
Oct 24, 2020
Merged

Project Euler 65 Solution #3035

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fa750c9
Add solution for Project Euler 65, Fixes: #2695
peteryao7 Oct 8, 2020
ad934bf
Add URL to problem 65 and don't pass in parameter to solution()
peteryao7 Oct 8, 2020
6fbc596
Remove solution() tests
peteryao7 Oct 8, 2020
542ca5a
Add tests for solution(), add fstring and positional arg for solution
peteryao7 Oct 15, 2020
6ebfdb7
Merge branch 'master' into peteryao7_project-euler-67
peteryao7 Oct 16, 2020
e5d1933
Merge changes
peteryao7 Oct 16, 2020
5918f97
Rename directory and problem number to 065
peteryao7 Oct 16, 2020
a53bb63
Merge branch 'peteryao7_project-euler-67' of https://github.com/peter…
peteryao7 Oct 16, 2020
8cac24d
Remove directory
peteryao7 Oct 16, 2020
d81a171
Move up explanation to module code block
peteryao7 Oct 16, 2020
27d0614
Move solution() below helper function, rename variables
peteryao7 Oct 16, 2020
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Move up explanation to module code block
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@peteryao7
peteryao7 committed Oct 16, 2020
commit d81a171fcb58997e8e6e47085390a3b5bbd1d50b
35 changes: 20 additions & 15 deletions project_euler/problem_065/sol1.py
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Expand Up @@ -33,26 +33,31 @@

Find the sum of the digits in the numerator of the 100th convergent
of the continued fraction for e.
"""

-----

def solution(max: int = 100) -> int:
"""
The solution mostly comes down to finding an equation that will generate
the numerator of the continued fraction. For the i-th numerator, the
pattern is:
The solution mostly comes down to finding an equation that will generate
the numerator of the continued fraction. For the i-th numerator, the
pattern is:

n_i = m_i * n_(i-1) + n_(i-2)

n_i = m_i * n_(i-1) + n_(i-2)
for m_i = the i-th index of the continued fraction representation of e,
n_0 = 1, and n_1 = 2 as the first 2 numbers of the representation.

for m_i = the i-th index of the continued fraction representation of e,
n_0 = 1, and n_1 = 2 as the first 2 numbers of the representation.
For example:
n_9 = 6 * 193 + 106 = 1264
1 + 2 + 6 + 4 = 13

n_10 = 1 * 193 + 1264 = 1457
1 + 4 + 5 + 7 = 17
"""

For example:
n_9 = 6 * 193 + 106 = 1264
1 + 2 + 6 + 4 = 13

n_10 = 1 * 193 + 1264 = 1457
1 + 4 + 5 + 7 = 17
def solution(max: int = 100) -> int:
"""
Returns the sum of the digits in the numerator of the max-th convergent of
the continued fraction for e.

>>> solution(9)
13
Expand All @@ -75,7 +80,7 @@ def solution(max: int = 100) -> int:

def sum_digits(num: int) -> int:
"""
Adds all the single digits of an int together.
Returns the sum of every digit in num.

>>> sum_digits(1)
1
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