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Hello all. A friend of mine had participated in a programming competition for his school. He did pretty well, but he couldn't get one question. The question was, given the numerator and denominator of a rational number, determine if the decimal expansion terminates. This is to say, if I gave you 1/3, you would say it doesn't because the expansion is "0.3333..." Likewise, if I gave you 1/10, you would say it does terminate because the expansion is "0.1"

My friend had tried to solve this problem with string operations, but I found a better way. According to the Wikipedia article for repeating decimals, rational numbers that terminate are in the form a/b -> b = 2^c*5^d where c and d are natural numbers. Given this identity, I developed the following (obfu) one-liner:

print"N",(map{"\rY"if(unpack"b52",pack"d",$=/5**$_)<1}0..log($==pop)), +$/

Given $ARGV[0] = a; $ARGV[1] = b the program will say "Y" if the decimal terminates and "N" if it doesn't.

The spoiler below reveals how the program works:


In reply to Determining if a rational number terminates by blackle

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