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30 lines
911 B
Python
30 lines
911 B
Python
#!/usr/bin/env python
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'''
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Created on 10 feb. 2012
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@author: Julien Lengrand-Lambert
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DESCRIPTION: Solves problem 57 of Project Euler
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It is possible to show that the square root of two can be expressed
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as an infinite continued fraction.
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sqrt 2 = 1 + 1/(2 + 1/(2 + 1/(2 + ... ))) = 1.414213...
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By expanding this for the first four iterations, we get:
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1 + 1/2 = 3/2 = 1.5
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1 + 1/(2 + 1/2) = 7/5 = 1.4
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1 + 1/(2 + 1/(2 + 1/2)) = 17/12 = 1.41666...
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1 + 1/(2 + 1/(2 + 1/(2 + 1/2))) = 41/29 = 1.41379...
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The next three expansions are 99/70, 239/169, and 577/408,
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but the eighth expansion, 1393/985, is the first example where the number
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of digits in the numerator exceeds the number of digits in the denominator.
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In the first one-thousand expansions, how many fractions contain a numerator
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with more digits than denominator?
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'''
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if __name__ == '__main__':
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print "plouf"
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#print "Answer : %d " % (last_ten()) |