For each of the following questions, briefly explain your answer. (20 points) a. if i prove an algorithm takes 2 ) worst-case time, is it possible that it takes o(n) on some inputs? b. if i prove an algorithm takes 2 ) worst-case time, is it possible that it takes o(n) on all inputs? c. if i prove an algorithm takes θ 2 ) worst-case time, is it possible that it takes o(n) on some inputs? d. if i prove an algorithm takes θ 2 ) worst-case time, is it possible that it takes o(n) on all inputs?