Because the numbers are HUGE! If you believe that algorithm X has polynomial complexity, try to write the polynomial which expresses its complexity. If you succeed then X has polynomial complexity, if you fail you may want to console yourself with the thought that X does not have polynomial complexity, which will be more comforting than the thought that you have failed to find the or a polynomial.
But, more seriously, try writing an equation for the complexity of integer factorization in terms of the number of digits in the integer and study its form. Add a comment. Active Oldest Votes.
Improve this answer. Ryan Culpepper Ryan Culpepper 9, 4 4 gold badges 28 28 silver badges 28 28 bronze badges. Isn't the size of the input, the interpretation of the input? And why do we use bits to represent the size of the input rather than the interpretation of the input? Actually it will take twice as long if you add two digits I think that is the definition of exponential runtime: Make n one bit longer, the algorithm takes twice as long.
Thilo Thilo k 94 94 gold badges silver badges bronze badges. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown. The Overflow Blog. Podcast Explaining the semiconductor shortage, and how it might end.
Does ES6 make JavaScript frameworks obsolete? Featured on Meta. Now live: A fully responsive profile. Visit chat. Related To me, intuitively, doubling the input to this problem means e. If we use bits to measure input size, well, of course most algorithms are going to be exponential, since the numeric value increases exponentially with the number of digits by definition!
It seems like artificially "pumping" how difficult the problem appears. So why do we do this? Show 1 more comment. Hendrik Jan Hendrik Jan One is approximately the square root of ten, the other is approximately pi.
There were some cultures that thought pi was equal to the square root of ten because of their proximity. Kaveh Kaveh Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password.
Post as a guest Name. Email Required, but never shown. Featured on Meta. Now live: A fully responsive profile. Version labels for answers. Linked 0. Related Hot Network Questions. Question feed. My interpretation of Sarnak's belief isn't that he sees some good reasons other people don't appreciate. Rather, it just feels plausible to him, and he's perhaps a little annoyed that lots of people firmly believe the opposite for no good reason, so he makes a point of stating a strong opinion.
Sign up to join this community. The best answers are voted up and rise to the top. Asked 10 years ago. Active 10 years ago. Viewed 5k times. Improve this question. Andrej Bauer Add a comment. Active Oldest Votes. Improve this answer.
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