Suppose that two arrays X₁, X2, ..., Xn and y₁, y2, Yn have at least one element in common. The following algorithm finds i, j such that x; = y;. Compute its best-case and worst-case complexity. (Count the number of # comparisons.) i 0 j+n+1 while j=n+ 1 do rii+1 Yn+1 Xi ← j←1 while xi #yj do j+j+1

Suppose that two arrays X₁, X2, ..., Xn and y₁, y2, Yn have at least one element in common. The following algorithm finds i, j such that x; = y;. Compute its best-case and worst-case complexity. (Count the number of # comparisons.) i 0 j+n+1 while j=n+ 1 do rii+1 Yn+1 Xi ← j←1 while xi #yj do j+j+1

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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Let A and B be two arrays of length n, each containing a random permutation of the numbers from 1 to n. An inversion between the two permutations A and B is a pair of values (x, y) where the index of x is less than the index of y in array A, but the index of x is more than the index of y in array B. Design an algorithm which counts the total number of inversions between A and B that runs in O(n log n) time.
please answer briefly thanks Analyze the worst-case time complexity of the bottom algorithms that I generated in the question 1 Assume the length of the input sequence is n. Do not use Big-O notation. question 1, Analysis of the algorithm in part 1 array = {elements in given sequence} pair_ele1 = array[0] pair_ele2 = array[1] n = length(array) for(i=0;i<n;i++) { for(j=i+1;j<n;j++){ if((array[i]+array[j])>(pair_ele1+pair_ele2)){ pair_ele1 = array[i]; pair_ele2 = array[j]; } } } print("Largest Sum = ",(pair_ele1)+(pair_ele2))
Write an efficient algorithm for the following problem, and describe your reasoning. Determine the Time complexity and if you cannot find any polynomial time algorithm, then give a backtracking algorithm. Problem: Binary Array Core Input: Two integers p and q and a binary array A[1...n], i.e., each entry contains either a 0 or 1. Output: Print Yes - if there exists a subarray A[i...k], where 1<= i < k <= n, with exactly p zeros in A[1...i-1] (there may be 1s) and exactly q ones in A[k+1...n] (there may be 0s). Print No - otherwise. Outputs with examples Input: A = [0,1,1,0,1], p = 2, q =1, Output: No. Input: A = [0, 1,1,0, 0,1,0,1], p = 1, q =1, Output: Yes because we can have A[1...i-1] = [0] and A[k+1 ... n] = [0,1,0,1]
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…
Given an unsorted array A of integers of any size, n ≥ 3, and an integer value x, write an algorithm as a pseudo code (not a program!) that would find out if there exist EXACTLY3 occurrences in the array with value x. What is the time complexity of your algorithm, in terms of Big-O? What is the space complexity of your algorithm, in terms of Big-O? What if , the given array A is sorted. Will time complexity change from the case that A was unsorted? • If yes; give a new algorithm that achieves this better complexity (indicate the time complexity as of that algorithm). • If no, explain why such new constraints/conditions cannot lead to a better time complexity.
Describe an efecient in-place algorithm called Partition-Even-Odd(A) that partitions an array A in even and odd numbers. The algorithm must terminate with A containing all its even elements preceding all its odd elements. For example, for input A = [7, 17, 74, 21, 7, 9, 26, 10], the result might be A = [74, 10, 26, 17, 7, 21, 9, 7]. Partition-Even-Odd must be an in-place algorithm. What does this mean about your algorithm? (a) Write the pseudo-code for Partition-Even-Odd. (b) Characterize the complexity of Partition-Even-Odd. Brie y justify your answer. (c) Formalize the correctness of the partition problem as stated above, and prove that Partition-Even- Odd is correct using a loop-invariant.
Given an integer array [A], efficiently find a descending sorted triplet such that: A[i]> A[i]> A[k] and 0 <=i<j <k <n, where n is the array size. For example, Input: A[] = {9, 1, 6, 7, 3, 4, 5) Output: Any one of the following triplets: (9, 7,5) (9, 7, 4) (9, 7, 3) (9, 6, 5) (9, 6, 4) (9, 6, 3) a) Design a brute-force algorithm to solve this problem complexity of your solution b) Design a more efficient algorithm to do the same task with less complexity and analyse the complexity of your solution. c) Develop a python code to implement your efficient algorithm. depend on the correctness of the code, indentation, comments, test-case] d) Prepare a brief report (250 words) comparing the two algorithms
Given two arrays A and B of equal size N, the task is to find if given arrays are equal or not. Two arrays are said to be equal if both of them contain same set of elements, arrangements (or permutation) of elements may be different though.Note : If there are repetitions, then counts of repeated elements must also be same for two array to be equal. Example 1: Input: N = 5 A[] = {1,2,5,4,0} B[] = {2,4,5,0,1} Output: 1.
1. Consider the algorithm for the sorting problem that sorts an array by counting,for each of its elements, the number of smaller elements and then uses thisinformation to put the element in its appropriate position in the sorted array:ALGORITHMComparisonCountingSort(A[0..n − 1])//Sorts an array by comparison counting//Input: Array A[0..n//Output: Array S[0..n− 1] of orderable values− 1] of A’s elements sorted// in nondecreasing orderfor i ← 0 to nCount− 1 do[i]←0for i ← 0 to n − 2 dofor j ← i +1 to n − 1 doif A[i] < A[j ]Count[j ]← Count[j ] + 1else Count[i]← Count[i] + 1for i ←0 to n−1 doS[Count[i]]←A[i]return Sa. Apply this algorithm to sorting the list 60, 35, 81, 98, 14, 47.b. Is this algorithm stable?c. Is it in-place?
Let X(1..n) and Y(1..n) contain two lists of n integers, each sorted in nondecreasingorder. Give the best (worst-case complexity) algorithm that you can think for finding(a) the largest integer of all 2n combined elements.(b) the second largest integer of all 2n combined elements.(c) the median (or the nth smallest integer) of all 2n combined elements.For instance, X = (4, 7, 8, 9, 12) and Y = (1, 2, 5, 9, 10), then median = 7, the nthsmallest, in the combined list (1, 2, 4, 5, 7, 8, 9, 9, 10, 12). [Hint: use the conceptsimilar to binary search]
Write an efficient algorithm (to the best of your knowledge) for the following problem, briefly describe why it is a correct algorithm, and analyze the time complexity. If you cannot find any polynomial-time algorithm, then give a backtracking algorithm. Problem: Repeated Number Input: An array A[1...3n] of positive integers. Output: If any number in the array appears at least n times, then print such a number. Otherwise, print 'none'. Example: Input: A = [1,3,3,3,1,1]. Here 3n = 6 and n =2. Output: 3. Note that here 1 would also be a valid output. You just need to print one if there are many options. Example: Input: A = [4,3,5,7,9,1]. Here 3n = 6 and n =2. Output: 'none'
Question1 (b)Consider the followingalgorithmwhere Small is an array of ninteger values: AlgorithmQ1 //Input: An array Smallcontaining ninteger values b = ∞ for h = 1 to n-1 for k = h + 1 to n if (Small[h] –Small[k]) < b b = Small[h] –Small[k] return b i.Explain what does this algorithm compute. ii.Findthe asymptotic bound/complexity ofthis algorithm. iii.Producean improved algorithm to Question1 (b) above with a better asymptotic complexity/running time. iv.Findthe asymptotic bound/complexity of the improvedalgorithmin Question 1(b)iii. above.