贪心算法奇怪的行为

Question

I've implemented the Greedy algorithm to solve Egyptian fractions, however I'm getting some unexpected results. Here's my code

from math import ceil
from fractions import Fraction

def go(frac):
    ret = []
    while frac > 0:
        if frac.numerator == 1:
            ret.append(frac)
            break
        x = Fraction(1, ceil(frac.denominator / frac.numerator))
        frac -= x
        ret.append(x)
    return ret

input1 = int(raw_input('numerator: '))
input2 = int(raw_input('denominator: '))

print go(Fraction(input1, input2))

I constantly am getting the error "TypeError: both arguments should be Rational instances"

I've been logging and it crashes upon the first iteration of the while loop.

EDIT: the error in detail is:

File "egypt.py", line 19, in <module>
print go(Fraction(input1, input2))
File "egypt.py", line 10, in go
x = Fraction(1,ceil(frac.denominator / frac.numerator))
File "/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/fractions.py", line 158, in __new__
raise TypeError("both arguments should be "
TypeError: both arguments should be Rational instances

Why is this? Thank you.

Answer 1

You have 2 problems in your code.

1. you're dividing int with int which always returns an int ; in your case, you're dividing a / b where a < b so it'll always be rounded down to 0.
2. Then, you ceil() that, which returns a float (0.0) which is something Fraction doesn't like;it wants int s.

So try this instead:

Fraction(1, int(ceil(float(frac.denominator) / frac.numerator)))

The rest of the code looks good.

Answer 2

Try changing this:

x = Fraction(1, ceil(frac.denominator / frac.numerator))

to this:

x = Fraction(1,int(ceil(frac.denominator / float(frac.numerator))))