ECE 242 Spring 2003 Data Structures in Java

1
ECE 242 Spring 2003Data Structures in Java

• http//rio.ecs.umass.edu/ece242
• Algorithm Analysis 1
• Prof. Lixin Gao

2
Todays Topics

• Introduction to analysis of algorithms.
• Big O notation

3
Select Algorithms

• A lot of sorting algorithms
• Selection sort
• Insertion sort
• etc.
• Which one to choose?

4
Criteria Used So Far

• Little code
• Little time to write codes
• Little time to debug
• If its due tomorrow, make it work!!!

5
More Criteria

• Fast execution
• More functionality
• Minimize memory space used
• If there are lots of memory, then make the
  program as fast as possible
• If its critical application, make it as robust
  as possible

6
Important Criteria

• Execution time is the most important
• Memory space is also important
• Might not be first priority as memory is getting
  cheaper
• Need trade execution time with space for some
  problems

7
Analytical Approach vs. Empirical Approach

• Two existing strategies
• Strategy A
• Strategy B
• Empirical approach
• implement both, pick the better one
• Analytical approach
• analyze both, implement the better one

8
Example

• Analysis
• 2 days
• Implementation
• 2 months

9
Analytical Approach

• Analyze Strategy A 2 days
• Analyze Strategy B 2 days
• Compare two analytical results 0 days
• Choose faster strategy 0 days
• Implement faster one 2 months
• Total 2 months4 days

10
Empirical Approach

• Implement Strategy A 2 months
• Implement Strategy B 2 months
• Compare two implementations 2 days
• Choose faster strategy 0 days
• Total 4 months2 days

11
Analytical or Empirical Approach?

• Empirical approach can be faster in some cases.
• Both approaches are important
• Learning both skills can make you a better and
  faster programmer
• Focus on empirical approach
• Lots of coding so far
• Let us do some analysis!

12
Execution Time?

• Real time?
• Machine has different speed
• Number of Operations?
• Comparison
• Assignment
• Instruction

13
Example

• Search
• Search position for 30

14
Sequential Search

• How many key operations? 8
• N inputs
• Worst case N key comparisons
• Average case N/2 key comparisons
• Typically, we use worst case.

15
Enhanced Sequential Search
16
N vs. N/2

• Cost(N) N (sequential)
• Cost(N) N/2 1 (enhanced sequential)

Cost(N)
N
N/2 1
N
17
Binary Search
18
Analysis of Binary Search

• N 2x
• log2N x

19
N vs. log2N
Cost(N)
N
log2N
N
20
Big-O Notation

• O stands for the order of
• Also called asymptotic analysis
• O(N) linear to N
• E.g. N and N/2
• O(logN) order of log N
• E.g. log2N and log3N
• O(N) gt O(logN)

21
Big-O notation

• O(1) constant
• E.g. initialize i
• O(N) gt O(logN) gt O(1)
• Ignore less dominating term.
• Ignore constant
• E.g. N/21 is O(N)

22
Search Algorithms

• Linear search O(N)
• Enhanced Linear search O(N)
• Binary search O(logN)