Algorithms

Algorithms - CSE 1400 Applied Discrete Mathematics...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 2

Algorithms - CSE 1400 Applied Discrete Mathematics...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online