42 lines
830 B
Python
42 lines
830 B
Python
import math
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from .tools import cache
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def factorial(n: int) -> int:
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"""
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n! = 1 * 2 * 3 * 4 * ... * n
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1, 1, 2, 6, 24, 120, 720, ...
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"""
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return math.factorial(n)
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def fibonacci(n: int) -> int:
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"""
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F(n) = F(n-1) + F(n-2) with F(0) = 0 and F(1) = 1
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0, 1, 1, 2, 3, 5, 8, 13, 21, ...
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"""
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if n < 2:
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return n
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l, r = 1, 1
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for _ in range(n - 2):
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l, r = l + r, l
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return l
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def triangular(n: int) -> int:
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"""
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a(n) = binomial(n+1,2) = n*(n+1)/2 = 0 + 1 + 2 + ... + n
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0, 1, 3, 6, 10, 15, ...
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"""
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return n * (n + 1) // 2
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def pentagonal(n: int) -> int:
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"""
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A pentagonal number is a figurate number that extends the concept of triangular and square numbers to the pentagon
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0, 1, 5, 12, 22, 35, ...
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"""
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return ((3 * n * n) - n) // 2
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