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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Question
Chapter 30, Problem 6P
a.
Program Plan Intro
To provide a simple heuristic argument for expecting k to be approximately , in case one search for the smallest k such that
b.
Program Plan Intro
To show that discrete Fourier Transform and inverse Fourier transform are inverse operation.
c.
Program Plan Intro
To show how to make the FFT and its inverse work modulo p in time
d.
Program Plan Intro
To compute the DFT modulo p = 17 of the
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Implement the modular exponentiation (a.k.a. fast exponentiation)
function mod_exp (b, n, m) to compute bn (mod m) more efficiently. (Hint: to
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a) Test your function for b = 3, n = 231 – 2, m = 231 – 1.
b) Report the result and the time (in seconds) it takes to find the result.
Q3. [30 pts] Modify your is_prime function to use the mod_exp (b, n, m) instead of
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Given an integer say 45, to find the sum of 45 with 8 in binary form (see
the figure below), we can use the TM designed in slides 79-90 of the notes
"Turing Machines and Equivalent Models I" twice to find the result. A more
effective way is to design a TM to do the addition with 8 directly.
1000
101101 A
+
=
?
Such a TM can be designed by extending the TM designed in slides 79-90
of the notes "Turing Machines and Equivalent Models I". The TM has 14
instructions and 6 states: 0, 1, 2, 3, 4, and halt. Six instructions of such a
TM have been given in the first and the second tables below. Fill out the
remaining blanks in the first and the second tables and also blanks in the
third table to show the remaining instructions of the TM (you have to use
your own text boxes here)
Implement the following error detection and error correction algorithms using C programming for Hamming code.
For Hamming codes, flip a bit in the data and implement the algorithm to correct the same on the receiver side.
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