如何在Python中将分数转换为连分数？

Got it, I see you're trying to convert a fraction like 181/101 into its continued fraction coefficients (which should be 1 1 3 1 4 4), but you struggled to adapt code using the Fraction module. Let's break this down step by step.

How Continued Fractions Work #

For any fraction a/b, the process to get coefficients is:

• Take the integer part q = a // b (this is your next coefficient)
• Calculate the remainder r = a % b
• If r is 0, we're done. Otherwise, repeat the process with the fraction b/r
• Collect all the q values to get your sequence

Using the Fraction Module #

The Fraction module simplifies handling fractions by automatically managing numerators and denominators, so we don't have to deal with manual simplification. Here's a working implementation:

from fractions import Fraction

def get_continued_fraction_coefficients(fraction):
    coefficients = []
    while True:
        # Extract the integer part of the fraction
        integer_part = fraction.numerator // fraction.denominator
        coefficients.append(integer_part)
        
        # Calculate remainder after removing the integer part
        remainder = fraction.numerator % fraction.denominator
        if remainder == 0:
            break
        
        # Update the fraction to be the reciprocal of the remaining fractional part
        fraction = Fraction(fraction.denominator, remainder)
    
    return coefficients

# Test with your example input
input_fraction = Fraction(181, 101)
result = get_continued_fraction_coefficients(input_fraction)
print(' '.join(map(str, result)))  # Output: 1 1 3 1 4 4

Adapting to Your Inputs #

If you're starting with a string like "181/101" instead of a Fraction object, you can parse it easily:

input_str = "181/101"
num, den = map(int, input_str.split('/'))
input_fraction = Fraction(num, den)

Key Notes #

• The Fraction module handles all simplification for you, so even if your input fraction isn't in lowest terms (like 362/202), it'll still produce the correct coefficients.
• For integer inputs (like Fraction(5,1)), the function will return just [5], which is the correct continued fraction representation.

Let me know if you need any tweaks to fit your specific use case!

内容的提问来源于stack exchange，提问作者Marked as Duplicate