mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-30 16:31:08 +00:00
4d0a8f2355
* optimized recursive_bubble_sort
* Fixed doctest error due whitespace
* reduce loop times for optimization
* fixup! Format Python code with psf/black push
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
70 lines
1.9 KiB
Python
70 lines
1.9 KiB
Python
"""
|
||
Euler discovered the remarkable quadratic formula:
|
||
n2 + n + 41
|
||
It turns out that the formula will produce 40 primes for the consecutive values
|
||
n = 0 to 39. However, when n = 40, 402 + 40 + 41 = 40(40 + 1) + 41 is divisible
|
||
by 41, and certainly when n = 41, 412 + 41 + 41 is clearly divisible by 41.
|
||
The incredible formula n2 − 79n + 1601 was discovered, which produces 80 primes
|
||
for the consecutive values n = 0 to 79. The product of the coefficients, −79 and
|
||
1601, is −126479.
|
||
Considering quadratics of the form:
|
||
n² + an + b, where |a| < 1000 and |b| < 1000
|
||
where |n| is the modulus/absolute value of ne.g. |11| = 11 and |−4| = 4
|
||
Find the product of the coefficients, a and b, for the quadratic expression that
|
||
produces the maximum number of primes for consecutive values of n, starting with
|
||
n = 0.
|
||
"""
|
||
|
||
import math
|
||
|
||
|
||
def is_prime(k: int) -> bool:
|
||
"""
|
||
Determine if a number is prime
|
||
>>> is_prime(10)
|
||
False
|
||
>>> is_prime(11)
|
||
True
|
||
"""
|
||
if k < 2 or k % 2 == 0:
|
||
return False
|
||
elif k == 2:
|
||
return True
|
||
else:
|
||
for x in range(3, int(math.sqrt(k) + 1), 2):
|
||
if k % x == 0:
|
||
return False
|
||
return True
|
||
|
||
|
||
def solution(a_limit: int, b_limit: int) -> int:
|
||
"""
|
||
>>> solution(1000, 1000)
|
||
-59231
|
||
>>> solution(200, 1000)
|
||
-59231
|
||
>>> solution(200, 200)
|
||
-4925
|
||
>>> solution(-1000, 1000)
|
||
0
|
||
>>> solution(-1000, -1000)
|
||
0
|
||
"""
|
||
longest = [0, 0, 0] # length, a, b
|
||
for a in range((a_limit * -1) + 1, a_limit):
|
||
for b in range(2, b_limit):
|
||
if is_prime(b):
|
||
count = 0
|
||
n = 0
|
||
while is_prime((n ** 2) + (a * n) + b):
|
||
count += 1
|
||
n += 1
|
||
if count > longest[0]:
|
||
longest = [count, a, b]
|
||
ans = longest[1] * longest[2]
|
||
return ans
|
||
|
||
|
||
if __name__ == "__main__":
|
||
print(solution(1000, 1000))
|