Computer Science Algorithm Analysis
Why can't we just code the algorithm and run it to see how it works?
-Different computers have different architectures -Language translation differs -Programmers have different skill levels -Loads on multiuser systems may vary -Math is good
How many comparison does Binary Search make?
2 comparison at most (if the item matches the current location; if not, whether its less than or greater than the midpoint)
In a list of 15 Elements, what is the average case for binary search?
About log(2) N
What are the Best, Worst, & Average Cases on Linear Search?
Best: 1 item examined Worst: N items examined Average: About N/2 items examined
What is the point of Linear & Binary Analysis?
Binary search works well if we have ordered data in a direct access data structure
How big is the instance characteristics?
Greater than or at least 1
What is the size of the problem (n) called?
Instance Characteristics of the problem.
How many elements of an ordered list do we need to examine before a search stops?
It Depends
Definition of Algorithm Analysis
Mathematical study of the performance of program statements, in terms of the size of the problem being solved.
Does a BST perform as binary search does?
Only on a perfectly even tree, It is just as good to search as a binary search on an ordered array.
What does the list have to be before a Binary Search in the list?
The list HAS to be ordered. Won't work on in-ordered list
Are approximations for functions allowed?
They are ok!
Binary Function Examples
log_2(N)
Linear Function Examples
n (n/2) 3n + 5
In a list of 15 Elements, how many are worst case or almost worst case for binary search?
12/15
How many comparison does Linear Search make?
1 comparison per item examined. (if the item matches the current location)