Introduction to Java Programming and Data Structures, Comprehensive Version (11th Edition)
Introduction to Java Programming and Data Structures, Comprehensive Version (11th Edition)
11th Edition
ISBN: 9780134670942
Author: Y. Daniel Liang
Publisher: PEARSON
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Chapter 22.4, Problem 22.4.6CP
Program Plan Intro

Refer the question 22.4.6 in the textbook which needs to compute the complexity of following term using brute force approach and Horner’s approach:

f(x)=anxn+an-1xn-1+an-2xn-2+...+a1x1+a0

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The speed of computers has increased greatly over the history of computing. The traveling salesman problem attempts to find a pathway for a salesman to visit all of the cities on his route using the shortest distance. The brute force method for solving this problem looks at all possible permutations of the cities. There are n! such permutations (where n! = n * (n-1) * (n-2) *…*1). Thus, 5! = 120. Current computers are running with clock speeds in the GigaHz range (10,000,000 times faster than the earliest computers) and they still are not able to solve the traveling salesmen problem using this brute force method for moderate values of n (like 50). If technology keeps moving ahead at the current rate, will this problem soon become feasible (yes or no)? Back up your answer with some sample numbers concerning factorials and speed of computers.
The following method of computing a is due to Archimedes: 1. Let A = 1 and N = 6 2. Repeat 10 times, say: Replace N by 2 Replace A by [2 – V(4 – A?)]/2 Let L = NA/2 Let U = L/I- A² /2 Let P = (U + L)/2 (estimate of n) Let E = (U - L)/2 (estimate of error) Print N, P, E 3. Stop. Write a program to implement the algorithm.
In Python, write a recursive implementation of Fibonacci without memoization. Include a timer to measure how long it takes. The sequence is defined by this recurrence: Fo = 0 F = 1 Fn = Fn-1+ Fn-2 The input should ask the user for the nth value in the sequence they want. Improvement: have your solution print all the values it computes along the way to the nth value in the sequence Bonus Question Improve the implementation above by using a memo dictionary (lecture notes slide 13)

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Introduction to Java Programming and Data Structures, Comprehensive Version (11th Edition)

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