Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 31, Problem 2P
a.
Program Plan Intro
To show that the given method requires
b.
Program Plan Intro
To define
c.
Program Plan Intro
To show Euclid(a,b) requires
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Compute and/or bound the interpolation error for a polynomial of degree 2 (i.e.,
n = 2) where
f(x) = 4 cos(x)
using
n
f(x) - Pn(x)
f(n+1) ((x))
(n+1)!
II(x-x₁)
i=0
Let o = π; x₁ = 0; and x₂ = π.
=
Let C be the binary linear code with basis
B = (0011001, 1000010, 1111111)
with information bits in positions 2, 4, and 6.
State the codeword x that encodes the message m = 110:
Tip You can solve equations and use row reductions here- but since the basis is smal, it might be easiest just to look at its codewords and
use intelligent trial and error.
A correct answer is 0111101, which can be typed in as follows:
0111101
Let Cbe the cnde cansis
Construct a (6, 3) binary linear code with generator matrix
1 0 0 11 0
G=0 10 0 1 1
[o 0 1 1 0 1,
Decode each of the received words
001001, 011000, 000110, 100001
by the following methods:
a. Nearest-neighbor method.
b. Parity-check matrix method.
c. Coset decoding using a standard array.
d. Coset decoding using the syndrome method.
Chapter 31 Solutions
Introduction to Algorithms
Ch. 31.1 - Prob. 1ECh. 31.1 - Prob. 2ECh. 31.1 - Prob. 3ECh. 31.1 - Prob. 4ECh. 31.1 - Prob. 5ECh. 31.1 - Prob. 6ECh. 31.1 - Prob. 7ECh. 31.1 - Prob. 8ECh. 31.1 - Prob. 9ECh. 31.1 - Prob. 10E
Ch. 31.1 - Prob. 11ECh. 31.1 - Prob. 12ECh. 31.1 - Prob. 13ECh. 31.2 - Prob. 1ECh. 31.2 - Prob. 2ECh. 31.2 - Prob. 3ECh. 31.2 - Prob. 4ECh. 31.2 - Prob. 5ECh. 31.2 - Prob. 6ECh. 31.2 - Prob. 7ECh. 31.2 - Prob. 8ECh. 31.2 - Prob. 9ECh. 31.3 - Prob. 1ECh. 31.3 - Prob. 2ECh. 31.3 - Prob. 3ECh. 31.3 - Prob. 4ECh. 31.3 - Prob. 5ECh. 31.4 - Prob. 1ECh. 31.4 - Prob. 2ECh. 31.4 - Prob. 3ECh. 31.4 - Prob. 4ECh. 31.5 - Prob. 1ECh. 31.5 - Prob. 2ECh. 31.5 - Prob. 3ECh. 31.5 - Prob. 4ECh. 31.6 - Prob. 1ECh. 31.6 - Prob. 2ECh. 31.6 - Prob. 3ECh. 31.7 - Prob. 1ECh. 31.7 - Prob. 2ECh. 31.7 - Prob. 3ECh. 31.8 - Prob. 1ECh. 31.8 - Prob. 2ECh. 31.8 - Prob. 3ECh. 31.9 - Prob. 1ECh. 31.9 - Prob. 2ECh. 31.9 - Prob. 3ECh. 31.9 - Prob. 4ECh. 31 - Prob. 1PCh. 31 - Prob. 2PCh. 31 - Prob. 3PCh. 31 - Prob. 4P
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