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 given time complexity is: m T(m-1) + ca     > 1 cb                      = 0 expanding using substitution: m T(m-1) + ca m[(m-1) T(m-2) + ca]+ ca m(m-1) T(m-2) + mca + ca  m(m-1) [(m-2) T(m-3) + ca] + mca + ca  m(m-1)(m-2) T(m-3) + m(m-1)ca + mca + ca  what is the time complexity?   form an expression for adding all the ca
Consider the problem of counting, in a given text, the number of substrings that start with an A and end with a B. For example, there are four such substrings in CABAAXBYA.a. Design a brute-force algorithm for this problem and determine its efficiency class.b. Design a more efficient algorithm for this problem with complexity O (n)
I'm trying to understand how both of these algorithms, separated by a) and b), have a time complexity of O(n), could you explain how this is?  a)int i = 0;while (i < n) { ... i++;}for(int j = 3; j < n * n; j += n) { ...}int k = 1;while (k < n) { ... k *= 2;} b)for(int i = 1; i < n; i += 3) { for(int j = 3; j < 10; j++) { for(int k = 5; k < n; k += n) { ... } }}

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

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