Moe, Larry and Curly have just purchased three new computers and use three different algorithms to sort lists: Comparisons / sec Search Algorithm T(n) Мое 50 Linear Search Larry 5 Curly 1 Optimal Chunk Search 2/n Binary Search log2 n where T(n) is the number of comparisons it takes, in the worst case, to sort a list of size n How large must n be to ensure that for every list

Moe, Larry and Curly have just purchased three new computers and use three different algorithms to sort lists: Comparisons / sec Search Algorithm T(n) Мое 50 Linear Search Larry 5 Curly 1 Optimal Chunk Search 2/n Binary Search log2 n where T(n) is the number of comparisons it takes, in the worst case, to sort a list of size n How large must n be to ensure that for every list

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Assume you have the following list of numbers: 12, 14, 23, 34, 37, 37, 45, 53, 55, 59, 66, 71, 74, 79 How many comparisons will be made by a binary search algorithm to find 79 in the above list? a) 2 b) 4 c) 3 d) 5
35. A particular sorting algorithm takes integer list 10, 6, 8 and incorrectly sorts the list to 6, 10, 8. What is true about the algorithm's correctness for sorting an arbitrary list of three integers? A.The algorithm is correct. B.The algorithm is incorrect. C.The algorithm's correctness is unknown. D.The algorithm only works for 10, 6, 8.
1. You, Alice and Bob are working on recursive search algorithms and have been studying avariant of binary search called trinary search. Alice has created the following pseudocodefor this algorithm:TSearch(A[a...b], t)If a > b return -1Let p1 = a + Floor((b - a)/3)If A[p1] = t return p1If A[p1] > t return TSearch(A[a...p1-1],t)Let p2 = a + Ceiling(2(b - a)/3)If A[p2] = t return p2If A[p2] > t return TSearch(A[p1+1...p2-1],t)Return TSearch(A[p2+1...b],t)EndTSearcha) State a recurrence relation that expresses the number of operations carried out bythis recursive algorithm when called on an input array of size n.b) Bob has heard that trinary search is no more efficient than binary search whenconsidering asymptotic growth. Help prove him correct by using induction to showthat your recurrence relation is in Θ(log2 n) as well.i. Split the tight bound into and upper (big-O) and lower (big-Ω).ii. For each bound select a function from Θ(log2 n) to use in your proof, likea log2 n or a…
1. Given an unsorted list of N numbers, how many list elements will be checked to find a value K using linear search in the worst case? A. O(1) B. O(N) C. O(log N) D. O(N log N) E. O(N * N) 2. Given a sorted list of N numbers, how many list elements will be checked to find a value K using binary search in the worst case? A. O(1) B. O(N) C. O(log N) D. O(N log N) E. O(N * N) 3. For the linear/sequential/serial search, which is the time complexity in its best case? A. O(1) Constant running time B. O(N) Linear running time C. O(log N) Logarithmic running time 4. For the linear/sequential/serial search, which is the time complexity in its worst case? A. O(1) Constant running time B. O(N) Linear running time C. O(log N) Logarithmic running time 5. Which of the following statements is correct? A. Binary search has a logarithmic running time B. Binary search has a constant running time for the best case…
a. Write a version of the sequential search algorithm that can be used to search a sorted list. (1, 2) b. Consider the following list: 2, 20, 38, 41, 49, 56, 62, 70, 88, 95, 100, 135, 145 Using a sequential search on ordered lists, that you designed in (a), how many comparisons are required to determine whether the following items are in the list? (Recall that comparisons mean item comparisons, not index comparisons.) (1, 2) 2 57 88 70 135 Write a program to test the function you designed. Note: Have the function,seqOrdSearch, return -1 if the item is not found in the list. (return the index of the item if found).
The bubble sort algorithm discussed in class is used to sort the following sequence of integers: 2 16 38 9 4 14 How many passes must the algorithm perform to guarantee the entire sequence is sorted? What is the list obtained after the first pass? What is the list obtained after the third pass? What is the list obtained after the final pass?
(b) Now assume that one is given another list Bn = {bi}ni=1 of n distinct positive integers whosemedian mB is already known. Develop an algorithm that returns the sum of the twoelements with value closest to mB, such that one of them is greater than mB and the otheris lower than mB. Although sorting Bn would yield a quick solution, we will see later onthat this is a exhorbitantly slow process and one can solve the problem without sortingBn in singnificantly faster time. Hence, in your solution, Do Not Sort Bn and propose asolution that goes without Sorting. (c) State a loop invariant for the algorithm you proposed in part (b) above.(d) Prove the loop invariant you proposed in part (c) above.
Given an unsorted array of integers, find the length oflongest increasing subsequence.Example:Input: [10,9,2,5,3,7,101,18]Output: 4Explanation: The longest increasing subsequence is [2,3,7,101], therefore thelength is 4.Time complexity:First algorithm is O(n^2).Second algorithm is O(nlogx) where x is the max element in the listThird algorithm is O(nlogn)Space complexity:First algorithm is O(n)Second algorithm is O(x) where x is the max element in the listThird algorithm is O(n)""" def longest_increasing_subsequence(sequence): """ Dynamic Programming Algorithm for counting the length of longest increasing subsequence type sequence: list[int] rtype: int """ length = len(sequence) counts = [1 for _ in range(length)] for i in range(1, length): for j in range(0, i): if sequence[i] > sequence[j]: counts[i] = max(counts[i], counts[j] + 1) print(counts) return max(counts) def…
3. Show how the binary search algorithm searches for 25 in the sorted listbelow: 4 6 17 25 32 39 41 43 45 49 let i = be the first number j = be the last number m = be the middle number I need to see how this is done and how the numbers narrow down to 25. Please break this down in described steps. I'm really confused.
Select all the statements that are false, bubble sort is defined below:* Quicksort is the fastest sorting algorithm If you are lucky, you can get O(n) time complexity in Mergesort On the worst case, Bubble sort will give you O(n logn) time complexity Average time complexity of insertion sort is much better than bubble sort Selection sort has the worst space complexity among all the sorting algorithm
5. Let F(n) denote the Fibonacci numbers. Prove the following property for all n ≥ 1 (Hint: Induction)F(1) + F(2) + · · · + F(n) = F(n + 2) − 1 7. The binary search algorithm is used with the following sorted list, with parameter x having the value“Chicago”. Name the elements against which x is compared.Boston, Charlotte, Indianapolis, New Orleans, Philadelphia, San Antonio, Yakima 8. The binary search algorithm is used with the following sorted list, with parameter x having the value“flour”. Name the elements against which x is compared.butter, chocolate, eggs, flour, shortening, sugar
We talked about the trade-off between using sequential search on an unsorted list as opposed to sorting the list and then using binary search. If the list size is n = 9,000, about how many worst-case searches must be done before the second alternative is better in terms of number of comparisons? (Hint: Let p represent the number of searches done.) Use selection search to sort the binary search list.