Question

Algorithm 1 Sort a list al,..., an for i=1 to n-1 do for j=1 to n-i do if aj > aj+1 then interchange a; and a;+1 end if end for end for (b) Algorithm 1 describes a sorting algorithm called bubble sort for a list al,...,an of at least two numbers. Prove that the algorithm is complete, correct and terminates. (2) Complexity of Algorithms (Learning Target C2) (a) What is the time complexity of your algorithm for finding the sum of elements of a list in terms of number of additions? Justify your answer. (b) What is the worst-case complexity of the bubble sort (Algorithm 1) in terms of the number of comparisons made? Justify your answer. (C) Show that n log(n) is O(n?). (d) Arrange the functions (1.5)", n100, (log n), nlog n, 10", n!, and n98 + n°7 in a list so that each function is big-O of the next function.

Solve ques no. 2 a, b, c, d .

Answer 1

for 1st each (b) worst case complerity is O(n) because the outer loop element in the list while the inner loop j iterates in time (j=1 to nal), n-1 times second (i=2 to nod) when it jel to no when i=2 = 1 do n-2 i iterates times for the so on No of comparisons = (n-1) + (n-2) + ... + (2) + (1) - O 0(ne) [ Aman) " sum = n(ne) the set of natural nas (e) ndog (n) is 0 (12) for NEN N is We know that dognan Multiplying a on both sides nlogn < n2 Therefore nlag (n) = 0(m2)