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Lecture11

# Lecture11 - Algorithms in Systems Engineering IE170 Lecture...

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Unformatted text preview: Algorithms in Systems Engineering IE170 Lecture 11 Dr. Ted Ralphs IE170 Lecture 11 1 References for Today’s Lecture • Required reading – CLRS Chapter 11 • References – D.E. Knuth, The Art of Computer Programming, Volume 3: Sorting and Searching (Third Edition), 1998. – R. Sedgewick, Algorithms in C++ (Third Edition), 1998. IE170 Lecture 11 2 Hash Tables • We now consider data structure for storing a dictionary that support only the operations • Most data structures for storing dictionaries depend on using comparison and exchange to order the items. • This limits the efficiency of certain operations (recall the lower bound on the efficiency of comparison-based sorting). • A hash table is a generalization of an array that takes advantage of our ability to access an arbitrary array element in constant time. • Using hashing, we determine where to store an item in the table (and how to find it later) without using comparison. • This allows us to perform all the basic operations extremely efficiently. IE170 Lecture 11 3 Addressing using Hashing • Recall the array-based implementation of a dictionary from Lecture 9. • In this implementation, we allocated one memory location for each possible key. • How can we extend this method to the case where the set U of possible keys is extremely large? • Answer : Use hashing . • A hash function is a function h : U → ,...,M- 1 that takes a key and converts it into an array index (called the hash value )....
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Lecture11 - Algorithms in Systems Engineering IE170 Lecture...

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