Data Structures and Algorithms in Java

6th Edition

ISBN: 9781118771334

Author: Michael T. Goodrich

Publisher: WILEY

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Textbook Question

Chapter 4, Problem 2R

The number of operations executed by *A* and *B* is 8*n* log *n* and 2*n*^{2}, respectively. Determine *n*_{0} such that *A* is better than *B* for *n* ≥ *n*_{0}.

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Students have asked these similar questions

The number of operations executed by algorithms A is 5n^2 and by algorithm B is 30n^3. Determine n0 such that B is better than A for all n > n0.

Please solve sections, Find the asymptotic (large-Θ) limits for the running times of the algorithms whose running time is given iteratively.
1. T (n) = 4T (n/4) + 5n2. T (n) = 4T (n/5) + 5n3. T (n) = 5T (n/4) + 4n4. T (n) = T (n/2) + 2T (n/5) + T (n/10) + 4n

What does the above Algorithm computes?
Is it a memorized algorithm? Justify your answer.
Execute the given algorithm when n=4 and k=2.

# Chapter 4 Solutions

Data Structures and Algorithms in Java

Ch. 4 - Prob. 1RCh. 4 - The number of operations executed by algorithms A...Ch. 4 - The number of operations executed by algorithms A...Ch. 4 - Prob. 4RCh. 4 - Prob. 5RCh. 4 - Prob. 6RCh. 4 - Prob. 7RCh. 4 - Prob. 8RCh. 4 - Prob. 9RCh. 4 - Prob. 10R

Ch. 4 - Prob. 11RCh. 4 - Prob. 12RCh. 4 - Prob. 13RCh. 4 - Prob. 14RCh. 4 - Prob. 15RCh. 4 - Prob. 16RCh. 4 - Prob. 17RCh. 4 - Prob. 18RCh. 4 - Prob. 19RCh. 4 - Prob. 20RCh. 4 - Prob. 21RCh. 4 - Prob. 22RCh. 4 - Show that 2n+1 is O(2n).Ch. 4 - Prob. 24RCh. 4 - Prob. 25RCh. 4 - Prob. 26RCh. 4 - Prob. 27RCh. 4 - Prob. 28RCh. 4 - Prob. 29RCh. 4 - Prob. 30RCh. 4 - Prob. 31RCh. 4 - Prob. 32RCh. 4 - Prob. 33RCh. 4 - Prob. 34RCh. 4 - Prob. 35CCh. 4 - Prob. 36CCh. 4 - Prob. 37CCh. 4 - Prob. 38CCh. 4 - Prob. 39CCh. 4 - Prob. 40CCh. 4 - Prob. 41CCh. 4 - Prob. 42CCh. 4 - Prob. 43CCh. 4 - Draw a visual justification of Proposition 4.3...Ch. 4 - Prob. 45CCh. 4 - Prob. 46CCh. 4 - Communication security is extremely important in...Ch. 4 - Al says he can prove that all sheep in a flock are...Ch. 4 - Consider the following justification that the...Ch. 4 - Consider the Fibonacci function, F(n) (see...Ch. 4 - Prob. 51CCh. 4 - Prob. 52CCh. 4 - Prob. 53CCh. 4 - Prob. 54CCh. 4 - An evil king has n bottles of wine, and a spy has...Ch. 4 - Prob. 56CCh. 4 - Prob. 57CCh. 4 - Prob. 58CCh. 4 - Prob. 59CCh. 4 - Prob. 60PCh. 4 - Prob. 61PCh. 4 - Perform an experimental analysis to test the...Ch. 4 - Prob. 63P

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Similar questions

When the order of growth of the running time of an algorithm is N log N, the doubling test will lead to the hypothesis that the running time is ~ a N for a constant a. Isn’tthat a problem?

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When the order of increase of an algorithm's running time is N log N, the doubling test leads to the hypothesis that the running time is a N for a constant a. Isn't that an issue?

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Two algorithms A, B sort the same problem. When you go through each algorithm and break them down into their primitive operations, each can be represented as below
A = n4 + 100n2 + 10n + 50
B = 10n3 + 2n2 + nlogn + 200
For very large values of n which of these algorithms explain why B
will run in the shortest time to solve the problem

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Give an O(n2)-time algorithm to find the longest monotonically increasing subsequence of a sequence of n numbers.

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Prove that the running time of an algorithm is ‚theta(g(n)) if and only if its worst-case
running time is O(g(n)) and its best-case running time is Omega(g(n)).

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Given two sorted arrays a[] and b[], of lengths n1 and n2 and an integer 0≤k<n1+n2, design an algorithm to find a key of rank k. The order of growth of the worst case running time of your algorithm should be log n, where n =n1+n2
using java.

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Let n be a positive integer, and consider the following algorithm segment.
for i := 1 to n
for j := 1 to i
[Statements in body of inner loop.
None contain branching statements
that lead outside the loop.]
next j
next i
How many times will the inner loop be iterated when the algorithm is implemented and run?

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Consider the following recursive algorithm, where // denotes integer division: 3//2 = 1, 5//2 = 2, etc.
H(n):
if n <= 1:
return
H(n//2)
for i from 0 to n
print(min(3, i))
Let function T(n) denote the running time of this algorithm. Derive T(n) and prove its worst case time complexity

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For relatively small values of n, algorithms with larger orders can be more efficient than algorithms with smaller orders. Use a graphing calculator or computer to answer this question.
For what values of n is an algorithm that requires n operations more efficient than an algorithm that requires
[50 log2(n)]
operations? (Assume n is an integer such that n > 1.)
n?

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Give a Θ(lg n) algorithm that computes the remainder when xn is divided byp. For simplicity, you may assume that n is a power of 2. That is, n = 2k forsome positive integer k.

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Consider the following recursive algorithm, where // denotes integer division: 3//2 = 1, 5//2 = 2, etc.
F(n):if n <= 1: returnF(n//2)for i from 0 to n for j from 0 to n//2 print(i+j)
Let function T(n) denote the running time of this algorithm. Derive T(n) and prove its worst case timecomplexity

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