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Consider the following algorithm to determine if a given positive interger n is prime. For each integer i between 2 and n , check if
Consider the following algorithm to determine if a given positive interger n is prime.
For each integer i between and
n check if i is a factor of n ie if dividing n by i leaves a remainder
of If the answer is yes for any i return that n is composite. Otherwise, return that n is prime.
What is the size of the input to this problem? Is it because there is only one number in the input?
Is it n because the input is n It is not the first option, because the input may be an immensely large
number which we cannot represent with a constant size. It is not the second option, since the value
of the input is n which is not the same as the size of the input. The correct way to think about the
input size in this case is the number of bits needed to represent n
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