76 lines
1.8 KiB
Python
76 lines
1.8 KiB
Python
import unittest
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max_digit = 2**31 - 1
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def lil_divmod(A, B):
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'''
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Return the greatest digit in 1..max_digit such that B * digit <= A
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and the remainder A - B * digit.
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'''
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assert A > 0 and B > 0
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assert A >= B
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assert B * (max_digit + 1) > A
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predicate = lambda n: B * n <= A
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digit = find_greatest(1, max_digit, predicate)
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remainder = A - digit * B
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return digit, remainder
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def find_greatest(low, high, f):
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'''
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Return the highest number n: low <= n <= high
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for which f(n) and not f(n+1) is True.
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The greatest n which makes f(n) True.
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'''
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assert low <= high
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# Maybe the high number is already the one?
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if f(high):
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return high
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# No such luck, let's pick a number between low and high
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pivot = (low + high) >> 1
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#print(low, pivot, high)
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# If there isn't any such number in between low and high,
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# that means there's only two numbers it could be: low or high
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# and we already know it isn't high from the test above
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# so it must be low.
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if low == pivot:
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assert f(low) and not f(low + 1)
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return low
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assert low < pivot < high
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return (
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find_greatest(pivot, high - 1, f)
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if f(pivot) else
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find_greatest(low, pivot - 1, f)
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)
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class find_greatest_Test(unittest.TestCase):
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def test_find_greatest(self):
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k = 23300
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a = 1
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b = 2**31-1
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f = lambda n: n <= k
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n = find_greatest(a, b, f)
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self.assertEqual(n, k)
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class BigIntTest(unittest.TestCase):
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def test_to_int(self):
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a = 10*max_digit-3
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b = 123
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a = (max_digit-3) * b
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digit, remainder = lil_divmod(a, b)
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#print(f'divmod({a}, {b}) == ({digit}, {remainder}) # ? ')
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self.assertEqual((digit, remainder), divmod(a, b))
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if __name__ == '__main__':
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unittest.main()
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