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 22.3, Problem 22.3.5CP

Example 7 in Section 22.3 assumes n = 2k. Revise the algorithm for an arbitrary n and prove that the complexity is still O(logn).

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Find the union of differences of two sets of numbers (A – B) U (B – A). Your algorithm's time complexity should be 0(n log n) or better. If your algorthm's time complexity is worse than O(n log n), you will receive half of the points at most. Prove your algorithm's time complexity. Algorithm FindUnion0f Diff(A[0 ... n – 1], B[0..m – 1]) // Input: Arrays A[1..n] and B[1..n] whose elements are unique ( A and B are sets). // Array A and array B are appeneded and assigned to array C.The index i is used for array C, //Output: Array R What is the time complexity of the algorithm for the worst case?
2. Computer scientists tend to get lazy and omit the base when writing a logarithm. Your job in this question is to justify this from an asymptotic perspective. Prove that for any a > 1 and b > 1, log(n) ≤ (log(n)). This shows that the base of the logarithm does not affect the asymptotic complexity.
Write for the following problem a recursive algorithm whose worst-case timecomplexity is not worse than Θ(n ln n). Given a list of n distinct positiveintegers, partition the list into two sublists, each of size n/2, such that thedifference between the sums of the integers in the two sublists is maximized.You may assume that n is a multiple of 2.

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

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