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Algorithms

an Introduction

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History

• This course was first taught in the late 1960s

• The main principals that maintained the area

– Find algorithms that are fast for very largeinputs

– Assume a very simple model of a computer

– There are very fast and useful algorithms out

there for the finding.

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Asymptotic Analysis

• We only care about the running time of our

algorithm as the size of the input goes to

infinity.

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The RAM Computer Model

• The random-access-machine(RAM)

– Single processor

– Unit time addressable memory

– Unit time multiplication and addition of

numbers. ( log n bit numbers)

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Amazing Algorithms

• Number Theory and cryptography–   Primes in P

• Linear programming and Business

• Computational Geometry and Graphic

• Graph Algorithms and

– Biology– Internet

– Manufacturing

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Skills Taught

• Proofs of Correctness

• Analysis of running times

• Decomposition of a larger problem– E.g. using data structures

• Classifying different algorithms

• Abstract algorithm problem

• Search the literature

• Demonstrate negative answers