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Q1);Show, by applying the limit test, that each of the following is true.;a) The functions f(n)= n(n-1)/2 and g(n)= n^2 grow asymptotically at equal rate.;b) The functions f(n)=log n grow asymptotically at slower rate than g(n)=n.;Q2);Show that log (n!) =? (nlog n);Q3);Design an algorithm that uses comparisons to select the largest and the;second largest of n elements. Find the time complexity of your algroithm;(expressed using the big-O notation).;Q4);Given an a binary array or list of n elements, where each element is either;a 0 or 1, we would like to arrange the elements so that all of those that;are equal to 0's appear first followed by all the elements that are equal;to 1's.;a) Write an algroithm or a function that uses comparisons to arrange the;elements as given above. Do not use any extra arrays in your algorithm.;b) Find the time, T(n), needed by your algorithm in the worst-case and;then express it using the big-O notation.;c) Find the time, T(n), needed by your algorithm in the best-case and;then express it using the big-? notation.;d) Find the time, T(n), needed by your algorithm in the average-case;and express it using the big-? notation.

 

Paper#73515 | Written in 18-Jul-2015

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