Python/maths/segmented_sieve.py

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"""Segmented Sieve."""
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import math
def sieve(n: int) -> list[int]:
"""Segmented Sieve."""
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in_prime = []
start = 2
end = int(math.sqrt(n)) # Size of every segment
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temp = [True] * (end + 1)
prime = []
while start <= end:
if temp[start] is True:
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in_prime.append(start)
for i in range(start * start, end + 1, start):
temp[i] = False
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start += 1
prime += in_prime
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low = end + 1
high = min(2 * end, n)
while low <= n:
temp = [True] * (high - low + 1)
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for each in in_prime:
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t = math.floor(low / each) * each
if t < low:
t += each
for j in range(t, high + 1, each):
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temp[j - low] = False
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for j in range(len(temp)):
if temp[j] is True:
prime.append(j + low)
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low = high + 1
high = min(high + end, n)
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return prime
print(sieve(10**6))