CMPT 120 Lecture 33 – Unit 5 – Internet and Big Data Complexity Analysis of Searching and Sorting algorithms and Big O Notation

Review - A smart music app https://repl.it/repls/ShortEducatedSearchengine

Review – Linear Search Complexity How many comparison operations are performed in linear search? Test Case: # of Comparisons n (size of data) data = [1, 3, 4, 7, 9, 11, 12, 14, 21] target = 1 -> best case scenario target = 21 -> worst case scenario target = 34 -> worst case scenario 1 9 data = [1, 3, 4, 7, 9, 11, 12, 14, 21, 56, 67, 77, 82, 85, 91, 99, 100, 101] target = 101 -> worst case scenario target = 226 -> worst case scenario 18

Linear Search and Big O Notation So, as n increases linearly, so does the # of comparisons We say that the complexity of the linear search algorithm is Big O of n (or Order n) -> O(n)

Log2 n Pattern D Size of data in 1st iteration: n Binary Search Algorithm At each iteration: We compare the middle element with target and if target not found We partition the list in half, ignoring one half and searching the other Size of data in 1st iteration: n Size of data in 2nd iteration : n/2 D Size of data in 3rd iteration : n/4 Size of data in Tth iteration : 1

Review – Binary Search Complexity How many comparison operations are performed in binary search? Test Case: # of Comparisons n (size of data) data = [1, 3, 4, 7, 9, 11, 12, 14, 21] target = 9 -> best case scenario target = 1 9 Data

Linear Search and Big O Notation So, as n increases linearly, so does the # of comparisons, but not linearly, instead it increases in a logarithmic fashion We say that the complexity of the binary search algorithm is O(log2 n) But what does that mean?

What does Big O Notation tell us? What if I have 5 algorithms (or functions) that do the same thing, for example, extract red jelly beans from a bag of multicolour jelly beans Algorithm A -> O(1) Algorithm B -> O(n) Algorithm C -> O(log2 n) Algorithm D -> O(n log2 n) Algorithm E -> O(n!) Which one is the fastest?

What does Big O Notation tell us? # of comparisons Computing Scientists are interested in knowing how an algorithm performs as n gets large! https://en.wikipedia.org/wiki/Big_O_notation

Complexity of Selection Sort Selection Sort looks for the smallest element multiple times, by going through n elements, then n-1 elements, then n-2 elements, … The total number of comparisons is therefore = n + (n-1) + (n-2) + … + 3 + 2 + 1 = n (n + 1) 2 = n2 + n 2 2 Computing scientists mainly care about the highest order term. Therefore we consider selection sort to be quadratic -> O(n2)

Next Lecture We have already seen how computers deal with letters and characters … remember ASCII? We’ll have our Practice Exercise 8 So, bring your laptop!  Monday, we shall start our last unit Unit 6. Under The Hood We shall look at how the computer represents numbers Computers use 0 and 1 to represent everything Do you know why?