
Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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- You are given k > 2 linked lists, each containing n > k natural numbers sorted in increasing order. All n · k numbers in these lists are distinct. Describe an algorithm that finds the k-th smallest element among all n k numbers. Your algorithm should run in O(k log k) time. Analyze the running time of your algorithm and prove its correctness.arrow_forwardAlgorthim of how to find the largest element missing in an unsorted array of n positive integers and the running time of the algorthim is in O(n). Example of this is that the n=6 array C= [5,90,8,6,26,9] The largest element missing in the array is 7arrow_forwardA sequential search of a sorted list can halt when the target is less than a given element in the list. Define a modified version of this algorithm and state the computational complexity, using big-O notation, of its best-, worst-, and average- case performances.arrow_forward
- For each question, an algorithm will be described that operates on N elements, and your answer should include: (a) a big-O expression that describes the total number of operations in the worst case (for ex- ample, O(N³)) (b) a description of how to achieve the same effect as the algorithm described, but achieved with a better big-O time bound (for example, "use mergesort instead of insertion sort") (c) the big-O time bound for your improved approach. Your improved algorithm does not need to be provably the best possible, but it should have a different and better big-O bound. (It may not be as simple as substituting one named algorithm for another; consider what is redundant about the work done by the existing algorithm.) You don't need to use pseudocode to describe your algorithms - the style used in the problem descriptions is also sufficient for your solutions. You can use pseudocode if you like. Do not write real code. If you wish to use an algorithm described in class, you can name…arrow_forwardGiven A[1...n] which is an increasingly sorted array of distinct positive integers, and t which is an integer; provide an O(n) algorithm deciding whether A contains two distinct elements x and y such that x + y = t.arrow_forward
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