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 62P
Perform an experimental analysis to test the hypothesis that Java’s Array.sort method runs in O(n log n) time on average.
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Given an array of unsorted integers, you are requested to investigate whether there exist a pair of numbers in this array that has a sum equal to a given key or not. For example, if the arr = [8, 7, 2, 5, 3] and the key = 12, the answer will be "Yes" as the array has a pair (7 and 5) where their sum = 12 = key, otherwise "No" is returned. To solve this problem, the following idea can be used:
i. Consider every pair in the given array and check if their sum = key.
ii. Sort the array first, keeping two pointers to on the minimum and maximum of the array and then move from both directions toward the center of the array while checking whether the sum = key or not.
Answer the following questions:
a) Transform each of the above ideas (i) & (ii) into algorithm (pseudocode) and compute their complexities
b) Critic these two ideas: [Which is better? Why?]
c) Design a better solution with less complexity. [note: your idea should be…
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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