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CSE 332: Data Structures
Asymptotic Analysis
Richard Anderson, Steve Seitz
Winter 2014
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Announcements
•Homework requires you get the textbook
(either E2 or E3)
•Go to Thursdays sections
•Homework #1 out on today (Wednesday)
–Due at the beginning of class
next Wednesday(Jan 17).
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Algorithm Analysis
•Correctness:
–Does the algorithm do what is intended.
•Performance:
–Speed time complexity
–Memory space complexity
•Why analyze?
–To make good design decisions
–Enable you to look at an algorithm (or code)
and identify the bottlenecks, etc.
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Correctness
Correctness of an algorithm is established
by proof. Common approaches:
–(Dis)proof by counterexample
–Proof by contradiction
–Proof by induction
•Especially useful in recursive
algorithms
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Proof by Induction
•Base Case: The algorithm is correct for
a base case or two by inspection.
•Inductive Hypothesis (n=k): Assume
that the algorithm works correctly for
the first k cases.
•Inductive Step (n=k+1): Given the
hypothesis above, show that the k+1
case will be calculated correctly.
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Recursive algorithm for sum
•Write a recursive function to find the sum of
the first n integers stored in array v.
sum(int array v, int n) returns int
if n = 0 then
sum = 0
else
sum = nth number + sum of first n-1 numbers
return sum
