# Japan Bangladesh Economic Relationship Essay

Time complexity is usually calculated in terms of the number of times certain operations are carried out by an algorithm, e. G. , the number of additions or subtractions, the number of multiplications, the number of comparisons made (if statements). Typically, we count the number of times a certain operation, e. G, a comparison, and give a Big-O estimate. There are three possible cases of interest: Best-case: by sheer, dumb luck, what is the easiest problem we might have to solve? Worst-case: by sheer, bad luck, what is the worst problem we might have to solve?

Average-case: what is the mean complexity over all possible sets of inputs. CASES/209 ? Lecture 4: Best, Worst, and Average Case Complexity 3/1 1 Of these, “best-case” is the easiest and “average-case” is the hardest. “Worst-case” is the most important (why? ) and turns out to be asymptotically similar to average-case. Japan Bangladesh Economic Relationship By Kaisers k=l k-1 -1. Exercise Prove that IQ-I = k (k – 1)+1 Lecture 4: Best, Worst, and Average Case Complexity CASES/209 ? Example: Binary Search Recall the Binary Search algorithm?

The Binary Search Algorithm Find the index of the element x in the ordered list {al < a2 <

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Show that the total number of comparisons squired by it for a list of length n is O(no ) 10/11 Exercise (Based on Corner at al, Exert 2. 2-2) The selection sort algorithm works as follows: Find the smallest element in the list , an }, and swap it with the element al . Find the smallest element in the list, {ay , ay , … , an } and swap it with the element ay . Stop when you have sorted item an-I . 1 23 Write a pseudopodia description of this algorithm. What loop invariant does this algorithm maintain? Give best- and worst-case estimates for the number of comparisons required. 11/11