Computer Systems: A Programmer's Perspective (3rd Edition)
3rd Edition
ISBN: 9780134092669
Author: Bryant, Randal E. Bryant, David R. O'Hallaron, David R., Randal E.; O'Hallaron, Bryant/O'hallaron
Publisher: PEARSON
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Chapter 5.7, Problem 5.6PP
Practice Problem 5.6 (solution page 575)
Let us continue exploring ways to evaluate polynomials, as described in Practice Problem 5 5. We can reduce the number of multiplications in evaluating a polynomial by applying Horner’s method, named after British mathematician William G. Horner (1786-1837). The idea is to repeatedly factor out the powers of x to get the following evaluation:
a0+x(a1+x(a2+···x(an-1+xan)···)) (5.3)
Using Horner's method, we can implement polynomial evaluation using the following code:
- A. For degree n, how many additions and how many multiplications does this code perform?
- B. On our reference machine, with the arithmetic operations having the latencies shown in Figure 5.12, we measure the CPE for this function to be 8.00. Explain how this CPE arises based on the data dependencies formed between iterations due to the operations implementing line 7 of the function.
- C. Explain how the function shown in Practice Problem 5.5 can run faster, even though it requires more operations.
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Q1)
Write a computer program that uses Newton's method to find the root of a given
function, and apply this program to find the root of the following functions, using co
as given. Stop the iteration when the error as estimated by n+1 - Enl is less than
10-6. Compare to your results for bisection.
(a) f(x) = 1-2xe-/2, xo = 0;
(b) f(x)=5-x-¹, x = ¹;
(c) f(x)= x³ - 2x - 5, xo = 2;
(d) f(x)=e-2, xo = 1;
(e) f(x)=x-e, xo = 1;
(f) f(x)=x-x-1, xo = 1;
(g) f(x)=x²-sinx, xo =/;
(h) f(x)= x³-2,0 = 1;
(i) f(x) = x + tan x, zo = 3;
(j) f(x)=2x-¹ In x, xo = 3.
ENGINEERING • COMPUTER-ENGINEERING
2 - calculate the first four iterations for the
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a) Bissection Method. Use as interval for the
root the values [2,3].
Problem 1 (Ransom Note Problem) in python
A kidnapper kidnaps you and writes a ransom note. He does not write it by hand to avoid having his hand writing being recognized, so he uses a magazine to create a ransom note. We need to find out, given the ransom string and magazine string, is it possible to create a given ransom note. The kidnapper can use individual characters of words.
Here is how your program should work to simulate the ransom problem:
your program should prompt the user to enter a long String to represent the magazine and another short String to represent the required ransom note.
your program needs to check if the magazine string contains all required characters in equal or greater number present in the ransom note.
your program should print true if it is possible to create the given ransom note from the given magazine, and print false otherwise.
Break up your code into a set of well-defined functions. Each function should include a comment block that briefly describes…
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