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

2. Review - A smart music app

3. 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 = > best case scenario
target = > worst case scenario
target = > 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 = > worst case scenario
target = > worst case scenario 18

4. 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)

5. 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

6. 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 = > best case scenario
target = 1 9
Data

7. 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?

8. 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?

9. What does Big O Notation tell us?
# of comparisons
Computing Scientists are interested in knowing how an algorithm performs as n gets large!

10. 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) + …
= n (n + 1) 2
= n2 + n
Computing scientists mainly care about the highest order term. Therefore we consider selection sort to be quadratic -> O(n2)

11. 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?