> the solution is specifically stated to be between 0 and infinity, and you can't surmise that the number is necessarily closer to 0.
Closer to 0 than what? Infinity? By any reasonable definition, every integer is closer to 0 than infinity.
I think the problem as stated is underspecified; I disagree that increasing "exponentially" (the solution your interviewer described would increase exponentially; your version is doubly exponential, I think) is always faster. Both versions have the same worst-case running time, and if you want to talk about expected running time you need to make assumptions about the data distribution. As a counterexample, if you start with an initial guess of 2 and keep squaring, but the true number is 2^1025, then you end up doing much more work than if you had doubled instead of squaring.
I can certainly agree with you that lecturing in an interview is unproductive. Not only is it understandably off-putting, but it doesn't give the interviewer any additional input to the hiring decision and therefore is a waste of everyone's time. (Unless one of the job requirements is coping well with being lectured to, I guess.)
Closer to 0 than what? Infinity? By any reasonable definition, every integer is closer to 0 than infinity.
I think the problem as stated is underspecified; I disagree that increasing "exponentially" (the solution your interviewer described would increase exponentially; your version is doubly exponential, I think) is always faster. Both versions have the same worst-case running time, and if you want to talk about expected running time you need to make assumptions about the data distribution. As a counterexample, if you start with an initial guess of 2 and keep squaring, but the true number is 2^1025, then you end up doing much more work than if you had doubled instead of squaring.
I can certainly agree with you that lecturing in an interview is unproductive. Not only is it understandably off-putting, but it doesn't give the interviewer any additional input to the hiring decision and therefore is a waste of everyone's time. (Unless one of the job requirements is coping well with being lectured to, I guess.)