Daniele Fucini
7c055b749e
Added solutions for problem 71, 72, 73, 74 and 75 in C and python and made a few corrections in the code for other problems.
51 lines
1.5 KiB
Python
51 lines
1.5 KiB
Python
#!/usr/bin/python3
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# The fraction 49/98 is a curious fraction, as an inexperienced mathematician in attempting to simplify it may incorrectly believe that 49/98 = 4/8,
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# which is correct, is obtained by cancelling the 9s.
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#
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# We shall consider fractions like, 30/50 = 3/5, to be trivial examples.
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#
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# There are exactly four non-trivial examples of this type of fraction, less than one in value, and containing two digits in the numerator
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# and denominator.
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#
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# If the product of these four fractions is given in its lowest common terms, find the value of the denominator.
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from math import gcd
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from timeit import default_timer
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def main():
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start = default_timer()
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prod_n = 1
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prod_d = 1
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for i in range(11, 100):
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for j in range(11, 100):
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# If the example is non-trivial, check if cancelling the digit that's equal
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# in numerator and denominator gives the same fraction.
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if i % 10 != 0 and j % 10 != 0 and\
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i != j and i % 10 == j // 10:
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n = i // 10
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d = j % 10
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f1 = i / j
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f2 = n / d
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if f1 == f2:
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prod_n = prod_n * i
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prod_d = prod_d * j
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# Find the greater common divisor of the fraction found.
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div = gcd(prod_n, prod_d)
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end = default_timer()
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print('Project Euler, Problem 33')
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print('Answer: {}'.format(prod_d // div))
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print('Elapsed time: {:.9f} seconds'.format(end - start))
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if __name__ == '__main__':
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main()
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