mathdatech/Python
1
0
Fork 0
mirror of https://github.com/TheAlgorithms/Python.git synced 2025-01-18 08:17:01 +00:00
Code Issues Packages Projects Releases Wiki Activity

Fix style of the first ten solutions for Project Euler (#3242)

Browse Source 
* Fix style of the first ten solutions for Project Euler

- Unify the header docstring, and add reference URLs to wikipedia
  or similar
- Fix docstrings to be properly multilined
- Add newlines where appropriate
- Add doctests where they were missing
- Remove doctests that test for the correct solution
- fix obvious spelling or grammar mistakes in comments and
  exception messages
- Fix line endings to be UNIX. This makes two of the files seem
  to have changed completely
- no functional changes in any of the solutions were done
  (except for the spelling fixes mentioned above)

* Fix docstrings and main function as per Style Guide
This commit is contained in:
Michael D 2020-10-25 04:23:16 +01:00 committed by GitHub
parent 5be77f33f7
commit 98e9d6bdb6
No known key found for this signature in database
GPG Key ID: 4AEE18F83AFDEB23
35 changed files with 717 additions and 469 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

13
project_euler/problem_001/sol1.py
View File

@ -1,13 +1,18 @@
"""
Problem Statement:
Project Euler Problem 1: https://projecteuler.net/problem=1
Multiples of 3 and 5
If we list all the natural numbers below 10 that are multiples of 3 or 5,
we get 3, 5, 6 and 9. The sum of these multiples is 23.
Find the sum of all the multiples of 3 or 5 below N.
Find the sum of all the multiples of 3 or 5 below 1000.
"""
def solution(n: int = 1000) -> int:
"""Returns the sum of all the multiples of 3 or 5 below n.
"""
Returns the sum of all the multiples of 3 or 5 below n.
>>> solution(3)
0
@ -25,4 +30,4 @@ def solution(n: int = 1000) -> int:
if __name__ == "__main__":
print(solution(int(input().strip())))
print(f"{solution() = }")

13
project_euler/problem_001/sol2.py
View File

@ -1,13 +1,18 @@
"""
Problem Statement:
Project Euler Problem 1: https://projecteuler.net/problem=1
Multiples of 3 and 5
If we list all the natural numbers below 10 that are multiples of 3 or 5,
we get 3, 5, 6 and 9. The sum of these multiples is 23.
Find the sum of all the multiples of 3 or 5 below N.
Find the sum of all the multiples of 3 or 5 below 1000.
"""
def solution(n: int = 1000) -> int:
"""Returns the sum of all the multiples of 3 or 5 below n.
"""
Returns the sum of all the multiples of 3 or 5 below n.
>>> solution(3)
0
@ -30,4 +35,4 @@ def solution(n: int = 1000) -> int:
if __name__ == "__main__":
print(solution(int(input().strip())))
print(f"{solution() = }")

10
project_euler/problem_001/sol3.py
View File

@ -1,8 +1,12 @@
"""
Problem Statement:
Project Euler Problem 1: https://projecteuler.net/problem=1
Multiples of 3 and 5
If we list all the natural numbers below 10 that are multiples of 3 or 5,
we get 3, 5, 6 and 9. The sum of these multiples is 23.
Find the sum of all the multiples of 3 or 5 below N.
Find the sum of all the multiples of 3 or 5 below 1000.
"""
@ -57,4 +61,4 @@ def solution(n: int = 1000) -> int:
if __name__ == "__main__":
print(solution(int(input().strip())))
print(f"{solution() = }")

99
project_euler/problem_001/sol4.py
View File

@ -1,47 +1,52 @@
"""
Problem Statement:
If we list all the natural numbers below 10 that are multiples of 3 or 5,
we get 3, 5, 6 and 9. The sum of these multiples is 23.
Find the sum of all the multiples of 3 or 5 below N.
"""
def solution(n: int = 1000) -> int:
"""Returns the sum of all the multiples of 3 or 5 below n.
>>> solution(3)
0
>>> solution(4)
3
>>> solution(10)
23
>>> solution(600)
83700
"""
xmulti = []
zmulti = []
z = 3
x = 5
temp = 1
while True:
result = z * temp
if result < n:
zmulti.append(result)
temp += 1
else:
temp = 1
break
while True:
result = x * temp
if result < n:
xmulti.append(result)
temp += 1
else:
break
collection = list(set(xmulti + zmulti))
return sum(collection)
if __name__ == "__main__":
print(solution(int(input().strip())))
"""
Project Euler Problem 1: https://projecteuler.net/problem=1
Multiples of 3 and 5
If we list all the natural numbers below 10 that are multiples of 3 or 5,
we get 3, 5, 6 and 9. The sum of these multiples is 23.
Find the sum of all the multiples of 3 or 5 below 1000.
"""
def solution(n: int = 1000) -> int:
"""
Returns the sum of all the multiples of 3 or 5 below n.
>>> solution(3)
0
>>> solution(4)
3
>>> solution(10)
23
>>> solution(600)
83700
"""
xmulti = []
zmulti = []
z = 3
x = 5
temp = 1
while True:
result = z * temp
if result < n:
zmulti.append(result)
temp += 1
else:
temp = 1
break
while True:
result = x * temp
if result < n:
xmulti.append(result)
temp += 1
else:
break
collection = list(set(xmulti + zmulti))
return sum(collection)
if __name__ == "__main__":
print(f"{solution() = }")

15
project_euler/problem_001/sol5.py
View File

@ -1,14 +1,19 @@
"""
Problem Statement:
Project Euler Problem 1: https://projecteuler.net/problem=1
Multiples of 3 and 5
If we list all the natural numbers below 10 that are multiples of 3 or 5,
we get 3, 5, 6 and 9. The sum of these multiples is 23.
Find the sum of all the multiples of 3 or 5 below N.
Find the sum of all the multiples of 3 or 5 below 1000.
"""
def solution(n: int = 1000) -> int:
"""Returns the sum of all the multiples of 3 or 5 below n.
A straightforward pythonic solution using list comprehension.
"""
Returns the sum of all the multiples of 3 or 5 below n.
A straightforward pythonic solution using list comprehension.
>>> solution(3)
0
@ -24,4 +29,4 @@ def solution(n: int = 1000) -> int:
if __name__ == "__main__":
print(solution(int(input().strip())))
print(f"{solution() = }")

13
project_euler/problem_001/sol6.py
View File

@ -1,13 +1,18 @@
"""
Problem Statement:
Project Euler Problem 1: https://projecteuler.net/problem=1
Multiples of 3 and 5
If we list all the natural numbers below 10 that are multiples of 3 or 5,
we get 3, 5, 6 and 9. The sum of these multiples is 23.
Find the sum of all the multiples of 3 or 5 below N.
Find the sum of all the multiples of 3 or 5 below 1000.
"""
def solution(n: int = 1000) -> int:
"""Returns the sum of all the multiples of 3 or 5 below n.
"""
Returns the sum of all the multiples of 3 or 5 below n.
>>> solution(3)
0
@ -31,4 +36,4 @@ def solution(n: int = 1000) -> int:
if __name__ == "__main__":
print(solution(int(input().strip())))
print(f"{solution() = }")

13
project_euler/problem_001/sol7.py
View File

@ -1,13 +1,18 @@
"""
Problem Statement:
Project Euler Problem 1: https://projecteuler.net/problem=1
Multiples of 3 and 5
If we list all the natural numbers below 10 that are multiples of 3 or 5,
we get 3, 5, 6 and 9. The sum of these multiples is 23.
Find the sum of all the multiples of 3 or 5 below N.
Find the sum of all the multiples of 3 or 5 below 1000.
"""
def solution(n: int = 1000) -> int:
"""Returns the sum of all the multiples of 3 or 5 below n.
"""
Returns the sum of all the multiples of 3 or 5 below n.
>>> solution(3)
0
@ -29,4 +34,4 @@ def solution(n: int = 1000) -> int:
if __name__ == "__main__":
print(solution(int(input().strip())))
print(f"{solution() = }")

25
project_euler/problem_002/sol1.py
View File

@ -1,19 +1,25 @@
"""
Problem:
Each new term in the Fibonacci sequence is generated by adding the previous two
terms. By starting with 1 and 2, the first 10 terms will be:
Project Euler Problem 2: https://projecteuler.net/problem=2
1,2,3,5,8,13,21,34,55,89,..
Even Fibonacci Numbers
Each new term in the Fibonacci sequence is generated by adding the previous
two terms. By starting with 1 and 2, the first 10 terms will be:
1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
By considering the terms in the Fibonacci sequence whose values do not exceed
n, find the sum of the even-valued terms. e.g. for n=10, we have {2,8}, sum is
10.
four million, find the sum of the even-valued terms.
References:
- https://en.wikipedia.org/wiki/Fibonacci_number
"""
def solution(n: int = 4000000) -> int:
"""Returns the sum of all fibonacci sequence even elements that are lower
or equals to n.
"""
Returns the sum of all even fibonacci sequence elements that are lower
or equal to n.
>>> solution(10)
10
@ -26,6 +32,7 @@ def solution(n: int = 4000000) -> int:
>>> solution(34)
44
"""
i = 1
j = 2
total = 0
@ -38,4 +45,4 @@ def solution(n: int = 4000000) -> int:
if __name__ == "__main__":
print(solution(int(input().strip())))
print(f"{solution() = }")

85
project_euler/problem_002/sol2.py
View File

@ -1,39 +1,46 @@
"""
Problem:
Each new term in the Fibonacci sequence is generated by adding the previous two
terms. By starting with 1 and 2, the first 10 terms will be:
1,2,3,5,8,13,21,34,55,89,..
By considering the terms in the Fibonacci sequence whose values do not exceed
n, find the sum of the even-valued terms. e.g. for n=10, we have {2,8}, sum is
10.
"""
def solution(n: int = 4000000) -> int:
"""Returns the sum of all fibonacci sequence even elements that are lower
or equals to n.
>>> solution(10)
10
>>> solution(15)
10
>>> solution(2)
2
>>> solution(1)
0
>>> solution(34)
44
"""
even_fibs = []
a, b = 0, 1
while b <= n:
if b % 2 == 0:
even_fibs.append(b)
a, b = b, a + b
return sum(even_fibs)
if __name__ == "__main__":
print(solution(int(input().strip())))
"""
Project Euler Problem 2: https://projecteuler.net/problem=2
Even Fibonacci Numbers
Each new term in the Fibonacci sequence is generated by adding the previous
two terms. By starting with 1 and 2, the first 10 terms will be:
1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
By considering the terms in the Fibonacci sequence whose values do not exceed
four million, find the sum of the even-valued terms.
References:
- https://en.wikipedia.org/wiki/Fibonacci_number
"""
def solution(n: int = 4000000) -> int:
"""
Returns the sum of all even fibonacci sequence elements that are lower
or equal to n.
>>> solution(10)
10
>>> solution(15)
10
>>> solution(2)
2
>>> solution(1)
0
>>> solution(34)
44
"""
even_fibs = []
a, b = 0, 1
while b <= n:
if b % 2 == 0:
even_fibs.append(b)
a, b = b, a + b
return sum(even_fibs)
if __name__ == "__main__":
print(f"{solution() = }")

21
project_euler/problem_002/sol3.py
View File

@ -1,19 +1,25 @@
"""
Problem:
Project Euler Problem 2: https://projecteuler.net/problem=2
Even Fibonacci Numbers
Each new term in the Fibonacci sequence is generated by adding the previous
two terms. By starting with 1 and 2, the first 10 terms will be:
1,2,3,5,8,13,21,34,55,89,..
1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
By considering the terms in the Fibonacci sequence whose values do not exceed
n, find the sum of the even-valued terms. e.g. for n=10, we have {2,8}, sum is
10.
four million, find the sum of the even-valued terms.
References:
- https://en.wikipedia.org/wiki/Fibonacci_number
"""
def solution(n: int = 4000000) -> int:
"""Returns the sum of all fibonacci sequence even elements that are lower
or equals to n.
"""
Returns the sum of all even fibonacci sequence elements that are lower
or equal to n.
>>> solution(10)
10
@ -26,6 +32,7 @@ def solution(n: int = 4000000) -> int:
>>> solution(34)
44
"""
if n <= 1:
return 0
a = 0
@ -38,4 +45,4 @@ def solution(n: int = 4000000) -> int:
if __name__ == "__main__":
print(solution(int(input().strip())))
print(f"{solution() = }")

37
project_euler/problem_002/sol4.py
View File

@ -1,21 +1,27 @@
"""
Problem:
Each new term in the Fibonacci sequence is generated by adding the previous two
terms. By starting with 1 and 2, the first 10 terms will be:
Project Euler Problem 2: https://projecteuler.net/problem=2
1,2,3,5,8,13,21,34,55,89,..
Even Fibonacci Numbers
Each new term in the Fibonacci sequence is generated by adding the previous
two terms. By starting with 1 and 2, the first 10 terms will be:
1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
By considering the terms in the Fibonacci sequence whose values do not exceed
n, find the sum of the even-valued terms. e.g. for n=10, we have {2,8}, sum is
10.
four million, find the sum of the even-valued terms.
References:
- https://en.wikipedia.org/wiki/Fibonacci_number
"""
import math
from decimal import Decimal, getcontext
def solution(n: int = 4000000) -> int:
"""Returns the sum of all fibonacci sequence even elements that are lower
or equals to n.
"""
Returns the sum of all even fibonacci sequence elements that are lower
or equal to n.
>>> solution(10)
10
@ -32,26 +38,27 @@ def solution(n: int = 4000000) -> int:
>>> solution(0)
Traceback (most recent call last):
...
ValueError: Parameter n must be greater or equal to one.
ValueError: Parameter n must be greater than or equal to one.
>>> solution(-17)
Traceback (most recent call last):
...
ValueError: Parameter n must be greater or equal to one.
ValueError: Parameter n must be greater than or equal to one.
>>> solution([])
Traceback (most recent call last):
...
TypeError: Parameter n must be int or passive of cast to int.
TypeError: Parameter n must be int or castable to int.
>>> solution("asd")
Traceback (most recent call last):
...
TypeError: Parameter n must be int or passive of cast to int.
TypeError: Parameter n must be int or castable to int.
"""
try:
n = int(n)
except (TypeError, ValueError):
raise TypeError("Parameter n must be int or passive of cast to int.")
raise TypeError("Parameter n must be int or castable to int.")
if n <= 0:
raise ValueError("Parameter n must be greater or equal to one.")
raise ValueError("Parameter n must be greater than or equal to one.")
getcontext().prec = 100
phi = (Decimal(5) ** Decimal(0.5) + 1) / Decimal(2)
@ -62,4 +69,4 @@ def solution(n: int = 4000000) -> int:
if __name__ == "__main__":
print(solution(int(input().strip())))
print(f"{solution() = }")

24
project_euler/problem_002/sol5.py
View File

@ -1,19 +1,25 @@
"""
Problem:
Each new term in the Fibonacci sequence is generated by adding the previous two
terms. By starting with 1 and 2, the first 10 terms will be:
Project Euler Problem 2: https://projecteuler.net/problem=2
1,2,3,5,8,13,21,34,55,89,..
Even Fibonacci Numbers
Each new term in the Fibonacci sequence is generated by adding the previous
two terms. By starting with 1 and 2, the first 10 terms will be:
1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
By considering the terms in the Fibonacci sequence whose values do not exceed
n, find the sum of the even-valued terms. e.g. for n=10, we have {2,8}, sum is
10.
four million, find the sum of the even-valued terms.
References:
- https://en.wikipedia.org/wiki/Fibonacci_number
"""
def solution(n: int = 4000000) -> int:
"""Returns the sum of all fibonacci sequence even elements that are lower
or equals to n.
"""
Returns the sum of all even fibonacci sequence elements that are lower
or equal to n.
>>> solution(10)
10
@ -43,4 +49,4 @@ def solution(n: int = 4000000) -> int:
if __name__ == "__main__":
print(solution(int(input().strip())))
print(f"{solution() = }")

44
project_euler/problem_003/sol1.py
View File

@ -1,16 +1,22 @@
"""
Problem:
The prime factors of 13195 are 5,7,13 and 29. What is the largest prime factor
of a given number N?
Project Euler Problem 3: https://projecteuler.net/problem=3
e.g. for 10, largest prime factor = 5. For 17, largest prime factor = 17.
Largest prime factor
The prime factors of 13195 are 5, 7, 13 and 29.
What is the largest prime factor of the number 600851475143?
References:
- https://en.wikipedia.org/wiki/Prime_number#Unique_factorization
"""
import math
def isprime(num: int) -> bool:
"""Returns boolean representing primality of given number num.
"""
Returns boolean representing primality of given number num.
>>> isprime(2)
True
>>> isprime(3)
@ -22,14 +28,15 @@ def isprime(num: int) -> bool:
>>> isprime(0)
Traceback (most recent call last):
...
ValueError: Parameter num must be greater or equal to two.
ValueError: Parameter num must be greater than or equal to two.
>>> isprime(1)
Traceback (most recent call last):
...
ValueError: Parameter num must be greater or equal to two.
ValueError: Parameter num must be greater than or equal to two.
"""
if num <= 1:
raise ValueError("Parameter num must be greater or equal to two.")
raise ValueError("Parameter num must be greater than or equal to two.")
if num == 2:
return True
elif num % 2 == 0:
@ -41,7 +48,9 @@ def isprime(num: int) -> bool:
def solution(n: int = 600851475143) -> int:
"""Returns the largest prime factor of a given number n.
"""
Returns the largest prime factor of a given number n.
>>> solution(13195)
29
>>> solution(10)
@ -53,26 +62,27 @@ def solution(n: int = 600851475143) -> int:
>>> solution(0)
Traceback (most recent call last):
...
ValueError: Parameter n must be greater or equal to one.
ValueError: Parameter n must be greater than or equal to one.
>>> solution(-17)
Traceback (most recent call last):
...
ValueError: Parameter n must be greater or equal to one.
ValueError: Parameter n must be greater than or equal to one.
>>> solution([])
Traceback (most recent call last):
...
TypeError: Parameter n must be int or passive of cast to int.
TypeError: Parameter n must be int or castable to int.
>>> solution("asd")
Traceback (most recent call last):
...
TypeError: Parameter n must be int or passive of cast to int.
TypeError: Parameter n must be int or castable to int.
"""
try:
n = int(n)
except (TypeError, ValueError):
raise TypeError("Parameter n must be int or passive of cast to int.")
raise TypeError("Parameter n must be int or castable to int.")
if n <= 0:
raise ValueError("Parameter n must be greater or equal to one.")
raise ValueError("Parameter n must be greater than or equal to one.")
max_number = 0
if isprime(n):
return n
@ -91,4 +101,4 @@ def solution(n: int = 600851475143) -> int:
if __name__ == "__main__":
print(solution(int(input().strip())))
print(f"{solution() = }")

32
project_euler/problem_003/sol2.py
View File

@ -1,14 +1,21 @@
"""
Problem:
The prime factors of 13195 are 5,7,13 and 29. What is the largest prime factor
of a given number N?
Project Euler Problem 3: https://projecteuler.net/problem=3
e.g. for 10, largest prime factor = 5. For 17, largest prime factor = 17.
Largest prime factor
The prime factors of 13195 are 5, 7, 13 and 29.
What is the largest prime factor of the number 600851475143?
References:
- https://en.wikipedia.org/wiki/Prime_number#Unique_factorization
"""
def solution(n: int = 600851475143) -> int:
"""Returns the largest prime factor of a given number n.
"""
Returns the largest prime factor of a given number n.
>>> solution(13195)
29
>>> solution(10)
@ -20,26 +27,27 @@ def solution(n: int = 600851475143) -> int:
>>> solution(0)
Traceback (most recent call last):
...
ValueError: Parameter n must be greater or equal to one.
ValueError: Parameter n must be greater than or equal to one.
>>> solution(-17)
Traceback (most recent call last):
...
ValueError: Parameter n must be greater or equal to one.
ValueError: Parameter n must be greater than or equal to one.
>>> solution([])
Traceback (most recent call last):
...
TypeError: Parameter n must be int or passive of cast to int.
TypeError: Parameter n must be int or castable to int.
>>> solution("asd")
Traceback (most recent call last):
...
TypeError: Parameter n must be int or passive of cast to int.
TypeError: Parameter n must be int or castable to int.
"""
try:
n = int(n)
except (TypeError, ValueError):
raise TypeError("Parameter n must be int or passive of cast to int.")
raise TypeError("Parameter n must be int or castable to int.")
if n <= 0:
raise ValueError("Parameter n must be greater or equal to one.")
raise ValueError("Parameter n must be greater than or equal to one.")
prime = 1
i = 2
while i * i <= n:
@ -53,4 +61,4 @@ def solution(n: int = 600851475143) -> int:
if __name__ == "__main__":
print(solution(int(input().strip())))
print(f"{solution() = }")

32
project_euler/problem_003/sol3.py
View File

@ -1,14 +1,21 @@
"""
Problem:
The prime factors of 13195 are 5,7,13 and 29. What is the largest prime factor
of a given number N?
Project Euler Problem 3: https://projecteuler.net/problem=3
e.g. for 10, largest prime factor = 5. For 17, largest prime factor = 17.
Largest prime factor
The prime factors of 13195 are 5, 7, 13 and 29.
What is the largest prime factor of the number 600851475143?
References:
- https://en.wikipedia.org/wiki/Prime_number#Unique_factorization
"""
def solution(n: int = 600851475143) -> int:
"""Returns the largest prime factor of a given number n.
"""
Returns the largest prime factor of a given number n.
>>> solution(13195)
29
>>> solution(10)
@ -20,26 +27,27 @@ def solution(n: int = 600851475143) -> int:
>>> solution(0)
Traceback (most recent call last):
...
ValueError: Parameter n must be greater or equal to one.
ValueError: Parameter n must be greater than or equal to one.
>>> solution(-17)
Traceback (most recent call last):
...
ValueError: Parameter n must be greater or equal to one.
ValueError: Parameter n must be greater than or equal to one.
>>> solution([])
Traceback (most recent call last):
...
TypeError: Parameter n must be int or passive of cast to int.
TypeError: Parameter n must be int or castable to int.
>>> solution("asd")
Traceback (most recent call last):
...
TypeError: Parameter n must be int or passive of cast to int.
TypeError: Parameter n must be int or castable to int.
"""
try:
n = int(n)
except (TypeError, ValueError):
raise TypeError("Parameter n must be int or passive of cast to int.")
raise TypeError("Parameter n must be int or castable to int.")
if n <= 0:
raise ValueError("Parameter n must be greater or equal to one.")
raise ValueError("Parameter n must be greater than or equal to one.")
i = 2
ans = 0
if n == 2:
@ -55,4 +63,4 @@ def solution(n: int = 600851475143) -> int:
if __name__ == "__main__":
print(solution(int(input().strip())))
print(f"{solution() = }")

26
project_euler/problem_004/sol1.py
View File

@ -1,15 +1,21 @@
"""
Problem:
A palindromic number reads the same both ways. The largest palindrome made from
the product of two 2-digit numbers is 9009 = 91 x 99.
Project Euler Problem 4: https://projecteuler.net/problem=4
Find the largest palindrome made from the product of two 3-digit numbers which
is less than N.
Largest palindrome product
A palindromic number reads the same both ways. The largest palindrome made
from the product of two 2-digit numbers is 9009 = 91 × 99.
Find the largest palindrome made from the product of two 3-digit numbers.
References:
- https://en.wikipedia.org/wiki/Palindromic_number
"""
def solution(n: int = 998001) -> int:
"""Returns the largest palindrome made from the product of two 3-digit
"""
Returns the largest palindrome made from the product of two 3-digit
numbers which is less than n.
>>> solution(20000)
@ -23,10 +29,10 @@ def solution(n: int = 998001) -> int:
...
ValueError: That number is larger than our acceptable range.
"""
# fetches the next number
for number in range(n - 1, 9999, -1):
# converts number into string.
str_number = str(number)
# checks whether 'str_number' is a palindrome.
@ -44,8 +50,4 @@ def solution(n: int = 998001) -> int:
if __name__ == "__main__":
import doctest
doctest.testmod()
print(solution(int(input().strip())))
print(f"{solution() = }")

21
project_euler/problem_004/sol2.py
View File

@ -1,15 +1,21 @@
"""
Problem:
A palindromic number reads the same both ways. The largest palindrome made from
the product of two 2-digit numbers is 9009 = 91 x 99.
Project Euler Problem 4: https://projecteuler.net/problem=4
Find the largest palindrome made from the product of two 3-digit numbers which
is less than N.
Largest palindrome product
A palindromic number reads the same both ways. The largest palindrome made
from the product of two 2-digit numbers is 9009 = 91 × 99.
Find the largest palindrome made from the product of two 3-digit numbers.
References:
- https://en.wikipedia.org/wiki/Palindromic_number
"""
def solution(n: int = 998001) -> int:
"""Returns the largest palindrome made from the product of two 3-digit
"""
Returns the largest palindrome made from the product of two 3-digit
numbers which is less than n.
>>> solution(20000)
@ -19,6 +25,7 @@ def solution(n: int = 998001) -> int:
>>> solution(40000)
39893
"""
answer = 0
for i in range(999, 99, -1): # 3 digit numbers range from 999 down to 100
for j in range(999, 99, -1):
@ -29,4 +36,4 @@ def solution(n: int = 998001) -> int:
if __name__ == "__main__":
print(solution(int(input().strip())))
print(f"{solution() = }")

36
project_euler/problem_005/sol1.py
View File

@ -1,23 +1,28 @@
"""
Problem:
2520 is the smallest number that can be divided by each of the numbers from 1
to 10 without any remainder.
Project Euler Problem 5: https://projecteuler.net/problem=5
What is the smallest positive number that is evenly divisible(divisible with no
remainder) by all of the numbers from 1 to N?
Smallest multiple
2520 is the smallest number that can be divided by each of the numbers
from 1 to 10 without any remainder.
What is the smallest positive number that is _evenly divisible_ by all
of the numbers from 1 to 20?
References:
- https://en.wiktionary.org/wiki/evenly_divisible
"""
def solution(n: int = 20) -> int:
"""Returns the smallest positive number that is evenly divisible(divisible
"""
Returns the smallest positive number that is evenly divisible (divisible
with no remainder) by all of the numbers from 1 to n.
>>> solution(10)
2520
>>> solution(15)
360360
>>> solution(20)
232792560
>>> solution(22)
232792560
>>> solution(3.4)
@ -25,26 +30,27 @@ def solution(n: int = 20) -> int:
>>> solution(0)
Traceback (most recent call last):
...
ValueError: Parameter n must be greater or equal to one.
ValueError: Parameter n must be greater than or equal to one.
>>> solution(-17)
Traceback (most recent call last):
...
ValueError: Parameter n must be greater or equal to one.
ValueError: Parameter n must be greater than or equal to one.
>>> solution([])
Traceback (most recent call last):
...
TypeError: Parameter n must be int or passive of cast to int.
TypeError: Parameter n must be int or castable to int.
>>> solution("asd")
Traceback (most recent call last):
...
TypeError: Parameter n must be int or passive of cast to int.
TypeError: Parameter n must be int or castable to int.
"""
try:
n = int(n)
except (TypeError, ValueError):
raise TypeError("Parameter n must be int or passive of cast to int.")
raise TypeError("Parameter n must be int or castable to int.")
if n <= 0:
raise ValueError("Parameter n must be greater or equal to one.")
raise ValueError("Parameter n must be greater than or equal to one.")
i = 0
while 1:
i += n * (n - 1)
@ -60,4 +66,4 @@ def solution(n: int = 20) -> int:
if __name__ == "__main__":
print(solution(int(input().strip())))
print(f"{solution() = }")

58
project_euler/problem_005/sol2.py
View File

@ -1,38 +1,70 @@
"""
Problem:
2520 is the smallest number that can be divided by each of the numbers from 1
to 10 without any remainder.
Project Euler Problem 5: https://projecteuler.net/problem=5
What is the smallest positive number that is evenly divisible(divisible with no
remainder) by all of the numbers from 1 to N?
Smallest multiple
2520 is the smallest number that can be divided by each of the numbers
from 1 to 10 without any remainder.
What is the smallest positive number that is _evenly divisible_ by all
of the numbers from 1 to 20?
References:
- https://en.wiktionary.org/wiki/evenly_divisible
- https://en.wikipedia.org/wiki/Euclidean_algorithm
- https://en.wikipedia.org/wiki/Least_common_multiple
"""
""" Euclidean GCD Algorithm """
def gcd(x: int, y: int) -> int:
"""
Euclidean GCD algorithm (Greatest Common Divisor)
>>> gcd(0, 0)
0
>>> gcd(23, 42)
1
>>> gcd(15, 33)
3
>>> gcd(12345, 67890)
15
"""
return x if y == 0 else gcd(y, x % y)
""" Using the property lcm*gcd of two numbers = product of them """
def lcm(x: int, y: int) -> int:
"""
Least Common Multiple.
Using the property that lcm(a, b) * gcd(a, b) = a*b
>>> lcm(3, 15)
15
>>> lcm(1, 27)
27
>>> lcm(13, 27)
351
>>> lcm(64, 48)
192
"""
return (x * y) // gcd(x, y)
def solution(n: int = 20) -> int:
"""Returns the smallest positive number that is evenly divisible(divisible
"""
Returns the smallest positive number that is evenly divisible (divisible
with no remainder) by all of the numbers from 1 to n.
>>> solution(10)
2520
>>> solution(15)
360360
>>> solution(20)
232792560
>>> solution(22)
232792560
"""
g = 1
for i in range(1, n + 1):
g = lcm(g, i)
@ -40,4 +72,4 @@ def solution(n: int = 20) -> int:
if __name__ == "__main__":
print(solution(int(input().strip())))
print(f"{solution() = }")

27
project_euler/problem_006/sol1.py
View File

@ -1,22 +1,25 @@
"""
Problem 6: https://projecteuler.net/problem=6
Project Euler Problem 6: https://projecteuler.net/problem=6
Sum square difference
The sum of the squares of the first ten natural numbers is,
1^2 + 2^2 + ... + 10^2 = 385
1^2 + 2^2 + ... + 10^2 = 385
The square of the sum of the first ten natural numbers is,
(1 + 2 + ... + 10)^2 = 552 = 3025
(1 + 2 + ... + 10)^2 = 55^2 = 3025
Hence the difference between the sum of the squares of the first ten natural
numbers and the square of the sum is 3025 − 385 = 2640.
Hence the difference between the sum of the squares of the first ten
natural numbers and the square of the sum is 3025 - 385 = 2640.
Find the difference between the sum of the squares of the first N natural
numbers and the square of the sum.
Find the difference between the sum of the squares of the first one
hundred natural numbers and the square of the sum.
"""
def solution(n: int = 100) -> int:
"""Returns the difference between the sum of the squares of the first n
"""
Returns the difference between the sum of the squares of the first n
natural numbers and the square of the sum.
>>> solution(10)
@ -27,9 +30,8 @@ def solution(n: int = 100) -> int:
41230
>>> solution(50)
1582700
>>> solution()
25164150
"""
sum_of_squares = 0
sum_of_ints = 0
for i in range(1, n + 1):
@ -39,7 +41,4 @@ def solution(n: int = 100) -> int:
if __name__ == "__main__":
import doctest
doctest.testmod()
print(solution(int(input().strip())))
print(f"{solution() = }")

27
project_euler/problem_006/sol2.py
View File

@ -1,22 +1,25 @@
"""
Problem 6: https://projecteuler.net/problem=6
Project Euler Problem 6: https://projecteuler.net/problem=6
Sum square difference
The sum of the squares of the first ten natural numbers is,
1^2 + 2^2 + ... + 10^2 = 385
1^2 + 2^2 + ... + 10^2 = 385
The square of the sum of the first ten natural numbers is,
(1 + 2 + ... + 10)^2 = 552 = 3025
(1 + 2 + ... + 10)^2 = 55^2 = 3025
Hence the difference between the sum of the squares of the first ten natural
numbers and the square of the sum is 3025 − 385 = 2640.
Hence the difference between the sum of the squares of the first ten
natural numbers and the square of the sum is 3025 - 385 = 2640.
Find the difference between the sum of the squares of the first N natural
numbers and the square of the sum.
Find the difference between the sum of the squares of the first one
hundred natural numbers and the square of the sum.
"""
def solution(n: int = 100) -> int:
"""Returns the difference between the sum of the squares of the first n
"""
Returns the difference between the sum of the squares of the first n
natural numbers and the square of the sum.
>>> solution(10)
@ -27,16 +30,12 @@ def solution(n: int = 100) -> int:
41230
>>> solution(50)
1582700
>>> solution()
25164150
"""
sum_cubes = (n * (n + 1) // 2) ** 2
sum_squares = n * (n + 1) * (2 * n + 1) // 6
return sum_cubes - sum_squares
if __name__ == "__main__":
import doctest
doctest.testmod()
print(solution(int(input().strip())))
print(f"{solution() = }")

27
project_euler/problem_006/sol3.py
View File

@ -1,23 +1,26 @@
"""
Problem 6: https://projecteuler.net/problem=6
Project Euler Problem 6: https://projecteuler.net/problem=6
Sum square difference
The sum of the squares of the first ten natural numbers is,
1^2 + 2^2 + ... + 10^2 = 385
1^2 + 2^2 + ... + 10^2 = 385
The square of the sum of the first ten natural numbers is,
(1 + 2 + ... + 10)^2 = 552 = 3025
(1 + 2 + ... + 10)^2 = 55^2 = 3025
Hence the difference between the sum of the squares of the first ten natural
numbers and the square of the sum is 3025 − 385 = 2640.
Hence the difference between the sum of the squares of the first ten
natural numbers and the square of the sum is 3025 - 385 = 2640.
Find the difference between the sum of the squares of the first N natural
numbers and the square of the sum.
Find the difference between the sum of the squares of the first one
hundred natural numbers and the square of the sum.
"""
import math
def solution(n: int = 100) -> int:
"""Returns the difference between the sum of the squares of the first n
"""
Returns the difference between the sum of the squares of the first n
natural numbers and the square of the sum.
>>> solution(10)
@ -28,16 +31,12 @@ def solution(n: int = 100) -> int:
41230
>>> solution(50)
1582700
>>> solution()
25164150
"""
sum_of_squares = sum([i * i for i in range(1, n + 1)])
square_of_sum = int(math.pow(sum(range(1, n + 1)), 2))
return square_of_sum - sum_of_squares
if __name__ == "__main__":
import doctest
doctest.testmod()
print(solution(int(input().strip())))
print(f"{solution() = }")

27
project_euler/problem_006/sol4.py
View File

@ -1,22 +1,25 @@
"""
Problem 6: https://projecteuler.net/problem=6
Project Euler Problem 6: https://projecteuler.net/problem=6
Sum square difference
The sum of the squares of the first ten natural numbers is,
1^2 + 2^2 + ... + 10^2 = 385
1^2 + 2^2 + ... + 10^2 = 385
The square of the sum of the first ten natural numbers is,
(1 + 2 + ... + 10)^2 = 552 = 3025
(1 + 2 + ... + 10)^2 = 55^2 = 3025
Hence the difference between the sum of the squares of the first ten natural
numbers and the square of the sum is 3025 − 385 = 2640.
Hence the difference between the sum of the squares of the first ten
natural numbers and the square of the sum is 3025 - 385 = 2640.
Find the difference between the sum of the squares of the first N natural
numbers and the square of the sum.
Find the difference between the sum of the squares of the first one
hundred natural numbers and the square of the sum.
"""
def solution(n: int = 100) -> int:
"""Returns the difference between the sum of the squares of the first n
"""
Returns the difference between the sum of the squares of the first n
natural numbers and the square of the sum.
>>> solution(10)
@ -27,16 +30,12 @@ def solution(n: int = 100) -> int:
41230
>>> solution(50)
1582700
>>> solution()
25164150
"""
sum_of_squares = n * (n + 1) * (2 * n + 1) / 6
square_of_sum = (n * (n + 1) / 2) ** 2
return int(square_of_sum - sum_of_squares)
if __name__ == "__main__":
import doctest
doctest.testmod()
print(solution(int(input("Enter a number: ").strip())))
print(f"{solution() = }")

35
project_euler/problem_007/sol1.py
View File

@ -1,17 +1,34 @@
"""
Problem 7: https://projecteuler.net/problem=7
Project Euler Problem 7: https://projecteuler.net/problem=7
By listing the first six prime numbers:
10001st prime
2, 3, 5, 7, 11, and 13
By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we
can see that the 6th prime is 13.
We can see that the 6th prime is 13. What is the Nth prime number?
What is the 10001st prime number?
References:
- https://en.wikipedia.org/wiki/Prime_number
"""
from math import sqrt
def is_prime(num: int) -> bool:
"""Determines whether the given number is prime or not"""
"""
Determines whether the given number is prime or not
>>> is_prime(2)
True
>>> is_prime(15)
False
>>> is_prime(29)
True
>>> is_prime(0)
False
"""
if num == 2:
return True
elif num % 2 == 0:
@ -25,7 +42,8 @@ def is_prime(num: int) -> bool:
def solution(nth: int = 10001) -> int:
"""Returns the n-th prime number.
"""
Returns the n-th prime number.
>>> solution(6)
13
@ -39,9 +57,8 @@ def solution(nth: int = 10001) -> int:
229
>>> solution(100)
541
>>> solution()
104743
"""
count = 0
number = 1
while count != nth and number < 3:
@ -56,4 +73,4 @@ def solution(nth: int = 10001) -> int:
if __name__ == "__main__":
print(solution(int(input().strip())))
print(f"{solution() = }")

46
project_euler/problem_007/sol2.py
View File

@ -1,16 +1,30 @@
"""
Problem 7: https://projecteuler.net/problem=7
Project Euler Problem 7: https://projecteuler.net/problem=7
By listing the first six prime numbers:
10001st prime
2, 3, 5, 7, 11, and 13
By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we
can see that the 6th prime is 13.
We can see that the 6th prime is 13. What is the Nth prime number?
What is the 10001st prime number?
References:
- https://en.wikipedia.org/wiki/Prime_number
"""
def isprime(number: int) -> bool:
"""Determines whether the given number is prime or not"""
"""
Determines whether the given number is prime or not
>>> isprime(2)
True
>>> isprime(15)
False
>>> isprime(29)
True
"""
for i in range(2, int(number ** 0.5) + 1):
if number % i == 0:
return False
@ -18,7 +32,8 @@ def isprime(number: int) -> bool:
def solution(nth: int = 10001) -> int:
"""Returns the n-th prime number.
"""
Returns the n-th prime number.
>>> solution(6)
13
@ -32,35 +47,32 @@ def solution(nth: int = 10001) -> int:
229
>>> solution(100)
541
>>> solution()
104743
>>> solution(3.4)
5
>>> solution(0)
Traceback (most recent call last):
...
ValueError: Parameter nth must be greater or equal to one.
ValueError: Parameter nth must be greater than or equal to one.
>>> solution(-17)
Traceback (most recent call last):
...
ValueError: Parameter nth must be greater or equal to one.
ValueError: Parameter nth must be greater than or equal to one.
>>> solution([])
Traceback (most recent call last):
...
TypeError: Parameter nth must be int or passive of cast to int.
TypeError: Parameter nth must be int or castable to int.
>>> solution("asd")
Traceback (most recent call last):
...
TypeError: Parameter nth must be int or passive of cast to int.
TypeError: Parameter nth must be int or castable to int.
"""
try:
nth = int(nth)
except (TypeError, ValueError):
raise TypeError(
"Parameter nth must be int or passive of cast to int."
) from None
raise TypeError("Parameter nth must be int or castable to int.") from None
if nth <= 0:
raise ValueError("Parameter nth must be greater or equal to one.")
raise ValueError("Parameter nth must be greater than or equal to one.")
primes = []
num = 2
while len(primes) < nth:
@ -73,4 +85,4 @@ def solution(nth: int = 10001) -> int:
if __name__ == "__main__":
print(solution(int(input().strip())))
print(f"{solution() = }")

35
project_euler/problem_007/sol3.py
View File

@ -1,24 +1,42 @@
"""
Project 7: https://projecteuler.net/problem=7
Project Euler Problem 7: https://projecteuler.net/problem=7
By listing the first six prime numbers:
10001st prime
2, 3, 5, 7, 11, and 13
By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we
can see that the 6th prime is 13.
We can see that the 6th prime is 13. What is the Nth prime number?
What is the 10001st prime number?
References:
- https://en.wikipedia.org/wiki/Prime_number
"""
import itertools
import math
def prime_check(number: int) -> bool:
"""Determines whether a given number is prime or not"""
"""
Determines whether a given number is prime or not
>>> prime_check(2)
True
>>> prime_check(15)
False
>>> prime_check(29)
True
"""
if number % 2 == 0 and number > 2:
return False
return all(number % i for i in range(3, int(math.sqrt(number)) + 1, 2))
def prime_generator():
"""
Generate a sequence of prime numbers
"""
num = 2
while True:
if prime_check(num):
@ -27,7 +45,8 @@ def prime_generator():
def solution(nth: int = 10001) -> int:
"""Returns the n-th prime number.
"""
Returns the n-th prime number.
>>> solution(6)
13
@ -41,11 +60,9 @@ def solution(nth: int = 10001) -> int:
229
>>> solution(100)
541
>>> solution()
104743
"""
return next(itertools.islice(prime_generator(), nth - 1, nth))
if __name__ == "__main__":
print(solution(int(input().strip())))
print(f"{solution() = }")

59
project_euler/problem_008/sol1.py
View File

@ -1,33 +1,36 @@
"""
Problem 8: https://projecteuler.net/problem=8
Project Euler Problem 8: https://projecteuler.net/problem=8
Largest product in a series
The four adjacent digits in the 1000-digit number that have the greatest
product are 9 × 9 × 8 × 9 = 5832.
73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450
73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450
Find the thirteen adjacent digits in the 1000-digit number that have the
greatest product. What is the value of this product?
"""
import sys
N = """73167176531330624919225119674426574742355349194934\
@ -53,12 +56,18 @@ N = """73167176531330624919225119674426574742355349194934\
def solution(n: str = N) -> int:
"""Find the thirteen adjacent digits in the 1000-digit number n that have
"""
Find the thirteen adjacent digits in the 1000-digit number n that have
the greatest product and returns it.
>>> solution(N)
23514624000
>>> solution("13978431290823798458352374")
609638400
>>> solution("13978431295823798458352374")
2612736000
>>> solution("1397843129582379841238352374")
209018880
"""
largest_product = -sys.maxsize - 1
for i in range(len(n) - 12):
product = 1
@ -70,4 +79,4 @@ def solution(n: str = N) -> int:
if __name__ == "__main__":
print(solution(N))
print(f"{solution() = }")

59
project_euler/problem_008/sol2.py
View File

@ -1,34 +1,35 @@
"""
Problem 8: https://projecteuler.net/problem=8
Project Euler Problem 8: https://projecteuler.net/problem=8
Largest product in a series
The four adjacent digits in the 1000-digit number that have the greatest
product are 9 × 9 × 8 × 9 = 5832.
73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450
73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450
Find the thirteen adjacent digits in the 1000-digit number that have the
greatest product. What is the value of this product?
"""
from functools import reduce
N = (
@ -56,12 +57,18 @@ N = (
def solution(n: str = N) -> int:
"""Find the thirteen adjacent digits in the 1000-digit number n that have
"""
Find the thirteen adjacent digits in the 1000-digit number n that have
the greatest product and returns it.
>>> solution(N)
23514624000
>>> solution("13978431290823798458352374")
609638400
>>> solution("13978431295823798458352374")
2612736000
>>> solution("1397843129582379841238352374")
209018880
"""
return max(
[
reduce(lambda x, y: int(x) * int(y), n[i : i + 13])
@ -71,4 +78,4 @@ def solution(n: str = N) -> int:
if __name__ == "__main__":
print(solution(str(N)))
print(f"{solution() = }")

59
project_euler/problem_008/sol3.py
View File

@ -1,29 +1,31 @@
"""
Problem 8: https://projecteuler.net/problem=8
Project Euler Problem 8: https://projecteuler.net/problem=8
Largest product in a series
The four adjacent digits in the 1000-digit number that have the greatest
product are 9 × 9 × 8 × 9 = 5832.
73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450
73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450
Find the thirteen adjacent digits in the 1000-digit number that have the
greatest product. What is the value of this product?
@ -53,13 +55,15 @@ N = """73167176531330624919225119674426574742355349194934\
def str_eval(s: str) -> int:
"""Returns product of digits in given string n
"""
Returns product of digits in given string n
>>> str_eval("987654321")
362880
>>> str_eval("22222222")
256
"""
product = 1
for digit in s:
product *= int(digit)
@ -67,12 +71,11 @@ def str_eval(s: str) -> int:
def solution(n: str = N) -> int:
"""Find the thirteen adjacent digits in the 1000-digit number n that have
the greatest product and returns it.
>>> solution(N)
23514624000
"""
Find the thirteen adjacent digits in the 1000-digit number n that have
the greatest product and returns it.
"""
largest_product = -sys.maxsize - 1
substr = n[:13]
cur_index = 13
@ -88,4 +91,4 @@ def solution(n: str = N) -> int:
if __name__ == "__main__":
print(solution(N))
print(f"{solution() = }")

36
project_euler/problem_009/sol1.py
View File

@ -1,26 +1,35 @@
"""
Problem 9: https://projecteuler.net/problem=9
Project Euler Problem 9: https://projecteuler.net/problem=9
Special Pythagorean triplet
A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
a^2 + b^2 = c^2
For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2.
There exists exactly one Pythagorean triplet for which a + b + c = 1000.
Find the product abc.
Find the product a*b*c.
References:
- https://en.wikipedia.org/wiki/Pythagorean_triple
"""
def solution() -> int:
"""
Returns the product of a,b,c which are Pythagorean Triplet that satisfies
the following:
1. a < b < c
2. a**2 + b**2 = c**2
3. a + b + c = 1000
Returns the product of a,b,c which are Pythagorean Triplet that satisfies
the following:
1. a < b < c
2. a**2 + b**2 = c**2
3. a + b + c = 1000
# The code below has been commented due to slow execution affecting Travis.
# >>> solution()
# 31875000
"""
for a in range(300):
for b in range(400):
for c in range(500):
@ -32,16 +41,17 @@ def solution() -> int:
def solution_fast() -> int:
"""
Returns the product of a,b,c which are Pythagorean Triplet that satisfies
the following:
1. a < b < c
2. a**2 + b**2 = c**2
3. a + b + c = 1000
Returns the product of a,b,c which are Pythagorean Triplet that satisfies
the following:
1. a < b < c
2. a**2 + b**2 = c**2
3. a + b + c = 1000
# The code below has been commented due to slow execution affecting Travis.
# >>> solution_fast()
# 31875000
"""
for a in range(300):
for b in range(400):
c = 1000 - a - b
@ -66,4 +76,4 @@ def benchmark() -> None:
if __name__ == "__main__":
benchmark()
print(f"{solution() = }")

32
project_euler/problem_009/sol2.py
View File

@ -1,30 +1,40 @@
"""
Problem 9: https://projecteuler.net/problem=9
Project Euler Problem 9: https://projecteuler.net/problem=9
Special Pythagorean triplet
A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
a^2 + b^2 = c^2
For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2.
There exists exactly one Pythagorean triplet for which a + b + c = 1000.
Find the product abc.
Find the product a*b*c.
References:
- https://en.wikipedia.org/wiki/Pythagorean_triple
"""
def solution(n: int = 1000) -> int:
"""
Return the product of a,b,c which are Pythagorean Triplet that satisfies
the following:
1. a < b < c
2. a**2 + b**2 = c**2
3. a + b + c = n
Return the product of a,b,c which are Pythagorean Triplet that satisfies
the following:
1. a < b < c
2. a**2 + b**2 = c**2
3. a + b + c = n
>>> solution(1000)
31875000
>>> solution(36)
1620
>>> solution(126)
66780
"""
product = -1
candidate = 0
for a in range(1, n // 3):
"""Solving the two equations a**2+b**2=c**2 and a+b+c=N eliminating c"""
# Solving the two equations a**2+b**2=c**2 and a+b+c=N eliminating c
b = (n * n - 2 * a * n) // (2 * n - 2 * a)
c = n - a - b
if c * c == (a * a + b * b):
@ -35,4 +45,4 @@ def solution(n: int = 1000) -> int:
if __name__ == "__main__":
print(solution(int(input().strip())))
print(f"{solution() = }")

21
project_euler/problem_009/sol3.py
View File

@ -1,5 +1,7 @@
"""
Problem 9: https://projecteuler.net/problem=9
Project Euler Problem 9: https://projecteuler.net/problem=9
Special Pythagorean triplet
A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
@ -8,22 +10,25 @@ A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2.
There exists exactly one Pythagorean triplet for which a + b + c = 1000.
Find the product abc.
Find the product a*b*c.
References:
- https://en.wikipedia.org/wiki/Pythagorean_triple
"""
def solution() -> int:
"""
Returns the product of a,b,c which are Pythagorean Triplet that satisfies
the following:
1. a**2 + b**2 = c**2
2. a + b + c = 1000
Returns the product of a,b,c which are Pythagorean Triplet that satisfies
the following:
1. a**2 + b**2 = c**2
2. a + b + c = 1000
# The code below has been commented due to slow execution affecting Travis.
# >>> solution()
# 31875000
"""
return [
a * b * (1000 - a - b)
for a in range(1, 999)
@ -33,4 +38,4 @@ def solution() -> int:
if __name__ == "__main__":
print(solution())
print(f"{solution() = }")

23
project_euler/problem_010/sol1.py
View File

@ -1,16 +1,23 @@
"""
https://projecteuler.net/problem=10
Project Euler Problem 10: https://projecteuler.net/problem=10
Summation of primes
Problem Statement:
The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.
Find the sum of all the primes below two million.
References:
- https://en.wikipedia.org/wiki/Prime_number
"""
from math import sqrt
def is_prime(n: int) -> bool:
"""Returns boolean representing primality of given number num.
"""
Returns boolean representing primality of given number num.
>>> is_prime(2)
True
>>> is_prime(3)
@ -20,6 +27,7 @@ def is_prime(n: int) -> bool:
>>> is_prime(2999)
True
"""
for i in range(2, int(sqrt(n)) + 1):
if n % i == 0:
return False
@ -28,11 +36,9 @@ def is_prime(n: int) -> bool:
def solution(n: int = 2000000) -> int:
"""Returns the sum of all the primes below n.
"""
Returns the sum of all the primes below n.
# The code below has been commented due to slow execution affecting Travis.
# >>> solution(2000000)
# 142913828922
>>> solution(1000)
76127
>>> solution(5000)
@ -42,6 +48,7 @@ def solution(n: int = 2000000) -> int:
>>> solution(7)
10
"""
if n > 2:
sum_of_primes = 2
else:
@ -55,4 +62,4 @@ def solution(n: int = 2000000) -> int:
if __name__ == "__main__":
print(solution(int(input().strip())))
print(f"{solution() = }")

26
project_euler/problem_010/sol2.py
View File

@ -1,10 +1,14 @@
"""
https://projecteuler.net/problem=10
Project Euler Problem 10: https://projecteuler.net/problem=10
Summation of primes
Problem Statement:
The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.
Find the sum of all the primes below two million.
References:
- https://en.wikipedia.org/wiki/Prime_number
"""
import math
from itertools import takewhile
@ -12,7 +16,9 @@ from typing import Iterator
def is_prime(number: int) -> bool:
"""Returns boolean representing primality of given number num.
"""
Returns boolean representing primality of given number num.
>>> is_prime(2)
True
>>> is_prime(3)
@ -22,12 +28,17 @@ def is_prime(number: int) -> bool:
>>> is_prime(2999)
True
"""
if number % 2 == 0 and number > 2:
return False
return all(number % i for i in range(3, int(math.sqrt(number)) + 1, 2))
def prime_generator() -> Iterator[int]:
"""
Generate a list sequence of prime numbers
"""
num = 2
while True:
if is_prime(num):
@ -36,11 +47,9 @@ def prime_generator() -> Iterator[int]:
def solution(n: int = 2000000) -> int:
"""Returns the sum of all the primes below n.
"""
Returns the sum of all the primes below n.
# The code below has been commented due to slow execution affecting Travis.
# >>> solution(2000000)
# 142913828922
>>> solution(1000)
76127
>>> solution(5000)
@ -50,8 +59,9 @@ def solution(n: int = 2000000) -> int:
>>> solution(7)
10
"""
return sum(takewhile(lambda x: x < n, prime_generator()))
if __name__ == "__main__":
print(solution(int(input().strip())))
print(f"{solution() = }")

30
project_euler/problem_010/sol3.py
View File

@ -1,43 +1,47 @@
"""
https://projecteuler.net/problem=10
Project Euler Problem 10: https://projecteuler.net/problem=10
Summation of primes
Problem Statement:
The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.
Find the sum of all the primes below two million.
References:
- https://en.wikipedia.org/wiki/Prime_number
- https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
"""
def solution(n: int = 2000000) -> int:
"""Returns the sum of all the primes below n using Sieve of Eratosthenes:
"""
Returns the sum of all the primes below n using Sieve of Eratosthenes:
https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
The sieve of Eratosthenes is one of the most efficient ways to find all primes
smaller than n when n is smaller than 10 million. Only for positive numbers.
>>> solution(2_000_000)
142913828922
>>> solution(1_000)
>>> solution(1000)
76127
>>> solution(5_000)
>>> solution(5000)
1548136
>>> solution(10_000)
>>> solution(10000)
5736396
>>> solution(7)
10
>>> solution(7.1) # doctest: +ELLIPSIS
>>> solution(7.1) # doctest: +ELLIPSIS
Traceback (most recent call last):
...
TypeError: 'float' object cannot be interpreted as an integer
>>> solution(-7) # doctest: +ELLIPSIS
>>> solution(-7) # doctest: +ELLIPSIS
Traceback (most recent call last):
...
IndexError: list assignment index out of range
>>> solution("seven") # doctest: +ELLIPSIS
>>> solution("seven") # doctest: +ELLIPSIS
Traceback (most recent call last):
...
TypeError: can only concatenate str (not "int") to str
"""
primality_list = [0 for i in range(n + 1)]
primality_list[0] = 1
primality_list[1] = 1
@ -54,4 +58,4 @@ def solution(n: int = 2000000) -> int:
if __name__ == "__main__":
print(solution(int(input().strip())))
print(f"{solution() = }")