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Elements of Programming
book

Elements of Programming

by Paul McJones, Alexander Stepanov
June 2009
Intermediate to advanced content levelIntermediate to advanced
288 pages
5h 59m
English
Addison-Wesley Professional
Content preview from Elements of Programming

Chapter 3

Associative Operations

This chapter discusses associative binary operations. Associativity allows regrouping the adjacent operations. This ability to regroup leads to an efficient algorithm for computing powers of the binary operation. Regularity enables a variety of program transformations to optimize the algorithm. We then use the algorithm to compute linear recurrences, such as Fibonacci numbers, in logarithmic time.

3.1 Associativity

A binary operation is an operation with two arguments:

Image

The binary operations of addition and multiplication are central to mathematics. Many more are used, such as min, max, conjunction, disjunction, ...

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Publisher Resources

ISBN: 9780321643926Purchase book