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Lecture Notes

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Algorithms

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Set of lecture notes for the algorithms classes required for all computer science undergraduate and graduate students at the University of Illinois, Urbana-Champaign.

Jeff Erickson

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Algorithms | Data Structures |

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Added	14 Feb 2009
Updated	14 Feb 2009
Year	2000
Authors	Jeff Erickson

Recursion

Solving recurrences

Recursion

Divide and conquer

Fast Fourier transforms

Dynamic programming

Greedy algorithms

Randomization

Nuts and bolts (randomized quicksort)

Treaps and skip lists

Uniform and universal hashing

Amortized analysis

Aggregation, taxation, potential

Scapegoat trees and splay trees

Maintaining disjoint sets ("union-find")

Fibonacci heaps

Graph algorithms

Representations, traversal

Minimum spanning trees

Single-source shortest paths

All-pairs shortest paths

Maximum flows and minimum cuts

Maximum flow algorithms and applications

Randomized minimum cuts

Number-theoretic algorithms

String matching

Brute force, fingerprinting

Knuth-Morris-Pratt

Geometry

Computational geometry: convex hulls

Line segment intersection

Polygon triangulation

Lower bounds

Decision trees, leaf counting

Adversary arguments ("n-card monte")

Reductions

NP-hardness

Approximation algorithms

Linear programming

J. Definitions and duality

K. The simplex algorithm

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