Codeforces: B. Limit

The problem is from codeforces: http://codeforces.com/problemset/problem/197/B

It has been a while since last time I submitted Python solutions to codeforces. This time, I pick a math problem that can remind me of the ‘limit’ which was taught in high school.

The inputs are two known polynomials P and Q and their degrees are known. The output should be the limit of P / Q. It seems difficult at first, but when you think for a second, you will realise how easy the solution is. The most important task is to check the coefficients P(0) and Q(0) of the highest degree. If degree of P is larger than Q, the answer is either ‘Infinity’ or ‘-Infinity’ depending on the signs. If degree of P is smaller than Q, the answer is ‘0/1’, otherwise, you will need to compute the GCD (Greatest Common Divisor) of P(0) and Q(0), and the answer will be P(0) / G divided by Q(0) / G.

#!/usr/bin/env python

from sys import stdin

fun = lambda: map(int, stdin.readline().split(" "))

n, m = fun()
a = fun()
b = fun()

def gcd(a, b):
    while b:
        a, b = b, a % b
    return a

if n > m:
    if a[0] * b[0] > 0:
        print "Infinity"
    else:
        print "-Infinity"
elif n == m:
    t = gcd(a[0], b[0])
    print "%d/%d" % (a[0] / t, b[0] / t)
else:
    print "0/1"

–EOF (The Ultimate Computing & Technology Blog) —