CSE 331

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Lecture 28

• CSE 331
• Nov 4, 2011

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HW 7 due today
Q1, Q2 and Q3 in separate piles
I will not take any HW after 115pm
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Other HW related stuff
HW 6 will be available for pickup from Monday
Solutions to HW 7 at the end of the lecture
HW 8 has been posted (link on the blog)
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On Algorithms, Practicality and Proofs
Indeed most of you will not write proofs in your
jobs
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A request and a warning
Please ask questions if something is not clear
The pace of the lectures is going to pick up
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High Level view of the course
Problem Statement
Problem Definition
Three general techniques
Done with greedy
Algorithm
Implementation
Data Structures
Analysis
CorrectnessRuntime Analysis
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Sorting
Given n numbers order them from smallest to
largest
Works for any set of elements on which there is a
total order
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Divide and Conquer
Divide up the problem into at least two
sub-problems
Recursively solve the sub-problems
Patch up the solutions to the sub-problems for
the final solution
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Mergesort Algorithm
Divide up the numbers in the middle
Unless n2
Sort each half recursively
Merge the two sorted halves into one sorted output
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HW 7 due today
Q1, Q2 and Q3 in separate piles
I will not take any HW after 115pm
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How fast can sorted arrays be merged?
Group talk time
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Mergesort algorithm
Input a1, a2, , an
Output Numbers in sorted order
If n 1 return the order a1
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An example run
If n 1 return the order a1
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Correctness
Input a1, a2, , an
Output Numbers in sorted order
By induction on n
If n 1 return the order a1
Inductive step follows from correctness of MERGE