26 September, Day 9
Collect Wassn3
Return / review Sassn1 (presentation) grades
Return / review Wassn2 (if not done last time)
Chapter 15 – time and space complexity
quick overview
Big-O notation is used to analyze algorithms for efficiency – example …
Big-O notation; O is “order”
Example use: we say an algorithm is O(n) “Order n”
Purpose of Big-O notation: convenience in comparing algorithms on
time and space complexity (usage)
What does this mean? Ex: which sorting algorithm is “better?” {bubble,
shell, quick, insertion, etc} Can answer based upon Order.
Quicksort, which is O(n log n) on average, running on a small PC can
beat bubble sort, which is O(n²), running on a supercomputer if there
are many values to sort. To sort 1,000,000 numbers, quicksort takes
20,000,000 steps on average, while bubble sort takes
1,000,000,000,000 (1 trillion) steps!
Chapter problem: find duplicates in a list
Two possible algorithms: 1. Scan, 2. Stor
Which is “better?”
SCAN algorithm
a simple-minded doubly nested loop; SCAN will exit (stop) when it finds
the first match.
Space complexity means memory or storage for data. In this case, it
depends upon the size of array n
Space complexity is O(n+2). n for the number of array elements in A.
Where did the +2 come from? need memory for variables i and j.
Time complexity means ‘time of execution.’ Count number of executed
statements; what’s the worst case? {Answer O 3n2 … a quadratic}
Time complexity …starts out with an example, say n is 4.
outer loop i <- 1, 3
inner loop j <- i+1 to n
1st time outer loop i = 1 [tallest lines for outer loop]
inner loop j = 2 (i + 1)
inner loop j = 3
CSC 490 Course Notes and Outline, © Dr. Gary Locklair, Fall 2006
