Algorithms

# Algorithms - CSE 1400 Applied Discrete Mathematics...

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CSE 1400 Applied Discrete Mathematics Algorithms Department of Computer Sciences College of Engineering Florida Tech Spring 2011 1 Algorithms 1 1 . 1 Horner’s Rule 1 1 . 2 Basic Sums 2 Abstract There are many algorithms useful in computing. 1 Algorithms 1 . 1 Horner’s Rule Consider the problem of computing the value of the polynomial p ( x ) = 5 x 3 + 4 x 2 + 7 x + 2 at x = 3. This computation can be organized in several ways, one of which is called Horner . Horner’s rule computes the value p ( 3 ) = 2 + 3 · ( 7 + 3 · ( 4 + 3 · 5 )) ( 1 ) Which is the action of the recursive function + x * (horner x s) on the constant x = 3 and the list ( a : as ) = h 2, 7, 4, 5 i of coefﬁcients whose head is a = 2 and whose tail is as = h 7, 4, 5 i The polynomial coefﬁcients in p ( x ) = 5 x 3 + 4 x 2 + 7 x + 2 can be written in two orders 1 . Little Endian, that is, h 2, 7, 4, 5 i or 2 . Big Endian, that is, h 5, 4, 7, 2 i In the example, Horner’s rule requires 3 multiplies and 3 additions

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Algorithms - CSE 1400 Applied Discrete Mathematics...

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