Data update
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Ingy döt Net
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2427 changed files with 31826 additions and 3468 deletions
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@ -1,18 +1,2 @@
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>>> def extended_gcd(aa, bb):
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lastremainder, remainder = abs(aa), abs(bb)
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x, lastx, y, lasty = 0, 1, 1, 0
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while remainder:
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lastremainder, (quotient, remainder) = remainder, divmod(lastremainder, remainder)
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x, lastx = lastx - quotient*x, x
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y, lasty = lasty - quotient*y, y
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return lastremainder, lastx * (-1 if aa < 0 else 1), lasty * (-1 if bb < 0 else 1)
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>>> def modinv(a, m):
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g, x, y = extended_gcd(a, m)
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if g != 1:
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raise ValueError
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return x % m
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>>> modinv(42, 2017)
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>>> pow(42, -1, 2017)
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1969
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>>>
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@ -1,91 +1,18 @@
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from functools import (reduce)
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from itertools import (chain)
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>>> def extended_gcd(aa, bb):
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lastremainder, remainder = abs(aa), abs(bb)
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x, lastx, y, lasty = 0, 1, 1, 0
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while remainder:
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lastremainder, (quotient, remainder) = remainder, divmod(lastremainder, remainder)
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x, lastx = lastx - quotient*x, x
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y, lasty = lasty - quotient*y, y
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return lastremainder, lastx * (-1 if aa < 0 else 1), lasty * (-1 if bb < 0 else 1)
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>>> def modinv(a, m):
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g, x, y = extended_gcd(a, m)
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if g != 1:
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raise ValueError
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return x % m
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# modInv :: Int -> Int -> Maybe Int
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def modInv(a):
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return lambda m: (
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lambda ig=gcdExt(a)(m): (
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lambda i=ig[0]: (
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Just(i + m if 0 > i else i) if 1 == ig[2] else (
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Nothing()
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)
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)
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)()
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)()
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# gcdExt :: Int -> Int -> (Int, Int, Int)
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def gcdExt(x):
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def go(a, b):
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if 0 == b:
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return (1, 0, a)
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else:
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(q, r) = divmod(a, b)
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(s, t, g) = go(b, r)
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return (t, s - q * t, g)
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return lambda y: go(x, y)
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# TEST ---------------------------------------------------
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# Numbers between 2010 and 2015 which do yield modular inverses for 42:
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# main :: IO ()
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def main():
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print (
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mapMaybe(
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lambda y: bindMay(modInv(42)(y))(
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lambda mInv: Just((y, mInv))
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)
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)(
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enumFromTo(2010)(2025)
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)
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)
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# -> [(2011, 814), (2015, 48), (2017, 1969), (2021, 1203)]
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# GENERIC ABSTRACTIONS ------------------------------------
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# enumFromTo :: Int -> Int -> [Int]
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def enumFromTo(m):
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return lambda n: list(range(m, 1 + n))
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# bindMay (>>=) :: Maybe a -> (a -> Maybe b) -> Maybe b
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def bindMay(m):
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return lambda mf: (
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m if m.get('Nothing') else mf(m.get('Just'))
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)
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# Just :: a -> Maybe a
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def Just(x):
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return {'type': 'Maybe', 'Nothing': False, 'Just': x}
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# mapMaybe :: (a -> Maybe b) -> [a] -> [b]
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def mapMaybe(mf):
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return lambda xs: reduce(
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lambda a, x: maybe(a)(lambda j: a + [j])(mf(x)),
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xs,
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[]
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)
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# maybe :: b -> (a -> b) -> Maybe a -> b
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def maybe(v):
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return lambda f: lambda m: v if m.get('Nothing') else (
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f(m.get('Just'))
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)
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# Nothing :: Maybe a
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def Nothing():
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return {'type': 'Maybe', 'Nothing': True}
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# MAIN ---
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main()
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>>> modinv(42, 2017)
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1969
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>>>
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91
Task/Modular-inverse/Python/modular-inverse-3.py
Normal file
91
Task/Modular-inverse/Python/modular-inverse-3.py
Normal file
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@ -0,0 +1,91 @@
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from functools import (reduce)
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from itertools import (chain)
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# modInv :: Int -> Int -> Maybe Int
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def modInv(a):
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return lambda m: (
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lambda ig=gcdExt(a)(m): (
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lambda i=ig[0]: (
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Just(i + m if 0 > i else i) if 1 == ig[2] else (
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Nothing()
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)
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)
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)()
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)()
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# gcdExt :: Int -> Int -> (Int, Int, Int)
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def gcdExt(x):
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def go(a, b):
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if 0 == b:
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return (1, 0, a)
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else:
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(q, r) = divmod(a, b)
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(s, t, g) = go(b, r)
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return (t, s - q * t, g)
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return lambda y: go(x, y)
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# TEST ---------------------------------------------------
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# Numbers between 2010 and 2015 which do yield modular inverses for 42:
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# main :: IO ()
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def main():
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print (
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mapMaybe(
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lambda y: bindMay(modInv(42)(y))(
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lambda mInv: Just((y, mInv))
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)
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)(
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enumFromTo(2010)(2025)
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)
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)
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# -> [(2011, 814), (2015, 48), (2017, 1969), (2021, 1203)]
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# GENERIC ABSTRACTIONS ------------------------------------
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# enumFromTo :: Int -> Int -> [Int]
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def enumFromTo(m):
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return lambda n: list(range(m, 1 + n))
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# bindMay (>>=) :: Maybe a -> (a -> Maybe b) -> Maybe b
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def bindMay(m):
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return lambda mf: (
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m if m.get('Nothing') else mf(m.get('Just'))
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)
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# Just :: a -> Maybe a
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def Just(x):
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return {'type': 'Maybe', 'Nothing': False, 'Just': x}
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# mapMaybe :: (a -> Maybe b) -> [a] -> [b]
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def mapMaybe(mf):
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return lambda xs: reduce(
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lambda a, x: maybe(a)(lambda j: a + [j])(mf(x)),
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xs,
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[]
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)
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# maybe :: b -> (a -> b) -> Maybe a -> b
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def maybe(v):
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return lambda f: lambda m: v if m.get('Nothing') else (
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f(m.get('Just'))
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)
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# Nothing :: Maybe a
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def Nothing():
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return {'type': 'Maybe', 'Nothing': True}
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# MAIN ---
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main()
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