Question 2: Recurrences (a) Below is the pseudo-code for two algorithms: Practice1(A,s,f) and Practice2(A,s,f), which take as nput a sorted array A, indexed from s to f. The algorithms make a call to Bsearch(A,s,f,k) which we saw in class. Determine the worst-case runtime recurrence for each algorithm: T1(n) and T2(n). Show that T;(n) is O((log n)²) and T2(n) is O(n log n). Practicel (A,s,f) if s < f ql = [(s+ f)/2] if BSearch(A,s,q1,1) = true Practice2(A,s,f) if s < f if BSearch(A,s+1,f,1) = true return true return true else else return Practice2(A, s, f-1) return Practicel(A, ql+1, f) else else return false return false

Question 2: Recurrences (a) Below is the pseudo-code for two algorithms: Practice1(A,s,f) and Practice2(A,s,f), which take as nput a sorted array A, indexed from s to f. The algorithms make a call to Bsearch(A,s,f,k) which we saw in class. Determine the worst-case runtime recurrence for each algorithm: T1(n) and T2(n). Show that T;(n) is O((log n)²) and T2(n) is O(n log n). Practicel (A,s,f) if s < f ql = [(s+ f)/2] if BSearch(A,s,q1,1) = true Practice2(A,s,f) if s < f if BSearch(A,s+1,f,1) = true return true return true else else return Practice2(A, s, f-1) return Practicel(A, ql+1, f) else else return false return false

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

See similar textbooks

Similar questions

The recursive algorithm below takes as input an array A of distinct integers, indexed between s andf, and an integer k. The algorithm returns the index of the integer k in the array A, or ?1 if the integerk is not contained within A. Complete the missing portion of the algorithm in such a way that you makethree recursive calls to subarrays of approximately one third the size of A.• Write and justify a recurrence for the runtime T(n) of the above algorithm.• Use the recursion tree to show that the algorithm runs in time O(n).FindK(A,s,f,k)if s < fif f = s + 1if k = A[s] return sif k = A[f] return felseq1 = b(2s + f)=3cq2 = b(q1 + 1 + f)=2c... to be continued.else... to be continued.
Q2: Recall the problem of finding the median of an array of an unsorted list. How fast can one complete the median? What is the recurrence relation that the algorithm follows? (Do not state the algorithm or solve the recurrence relation)
Problem 3: Array ReversalWe have come through an old algorithm whose name indicates that it reverses the arrayelements; its pseudo-code was defined as follows: note n := A.length denotes the size ofthe array, number of items.Algorithm 2 Reverse-Array(A)s ← ⌊n−12 ⌋, e ← ⌊n2 ⌋while s ≥ 0 ∧ e ≤ (n − 1) doswap (A[s],A[e])s ← s − 1e ← e + 1end whilea) Implement the algorithm in Python, and test itb) Empirically, show the performance curve of the algorithm using time measurementsc) Using the basics of the theoretical analysis, write the complexity of its worst-casetime.d) Prove that the algorithm is actually correct
Consider the following variant of Mergesort. If the array has more thantwo elements, it recursively sorts the first two-third and the last one-third. Then, it mergesthe first two-third with the last one-third. If the array has at most two elements, then ittrivially sorts the array. For completeness, here is the pseudocode for sorting the arrayA[l..r]. Write a recurrence relation for the worst-case running time of Newsort. Solve the recurrencerelation to obtain aΘ-bound on the running time of the algorithm, in terms of the lengthnof the array. You must use the tree method to solve the recurrence. You may also ignorefloors and ceilings in your calculations.
Provide a tight theoretical lower bound for the problems given below. Provide justification for your answer. a) Given a list of sizencontaining Trues and Falses, determine whether True or False is more common (or if there is a tie). b) Given a list ofnnumbers, all assumed to be integers between 1 and 100 , sort them. c) Given ann×narray whose rows are sorted (but whose columns may not be), find the largest overall entry in the array. For example, the array could look like: \[ \left(\begin{array}{ccccccccc} -2 & 4 & 7 & 8 & 10 & 12 & 20 & 21 & 50 \\ -30 & -20 & -10 & 0 & 1 & 2 & 3 & 21 & 23 \\ -10 & -2 & 0 & 2 & 4 & 6 & 30 & 31 & 35 \end{array}\right) \] This is ann×narray, withn=9(there are 3 rows and 9 columns). Each row is sorted, but the columns aren't. Please give proper explanation and typed answer only.
1.a)Given an array which is sorted in descending [large to small] order and got no repeated numbers. You are asked to apply linear search. You are asked to find a number which exists. What should be the worst time complexity and why? b) A. Given the array of numbers 50 10 90 120 -13 3 89, you are asked to apply Binary Search to find a certain number. show the simulation and what would be the best achievable time complexity?
Modify the Partition function so that after running it, any input array A is partitioned into three parts: the left part consisting of all elements < pivot, the middle part consisting of all elements = pivot, and the right part consisting of the rest Write down the pseudo-code for this modified version of the Partition function. (must be an in-place algorithm with Θ(n) time complexity.) Hint: Define three indices: i as the end of the left part, k as the end of the middle part, and j denoting the current index which is used in the for-loop.
1. Consider a problem of computing the prefix average of a sequence of numbers stored in an array P consisting of P integers. We want to compute an array P such that P is the average of P for P . Consider the two algorithms related to the above problem. Answer the questions given below
s algorithm for finding all occurrences of a sequence in anothersequence using the suffix array of the latter sequence can be implemented inPerl in a straightforward way, as shown in the following Perl script. Recallthat the suffix array of a sequence of length n will be a permutation of arraypositions 0, 1, . . . , n − 1, because Perl arrays do not start with position 1 but,rather, with position 0.
That's enough for you! def first_preceded_by_smaller(items, k=1): Find and return the 0irst element of the given list of items that is preceded by at least k smaller elements in the list. These required k smaller elements can be positioned anywhere before the current element, not necessarily consecutively immediately before that element. If no element satisfying this requirement exists in the list, this function should return None. Since the only operation performed for the individual items is their order comparison, and especially no arithmetic occurs at any point during execution, this function should work for lists of any types of elements, as long as those elements are pairwise comparable with each other. items k Expected result [4, 4, 5, 6] 2 5 [42, 99, 16, 55, 7, 32, 17, 18, 73] 3 18 [42, 99, 16, 55, 7, 32, 17, 18, 73] 8 None ['bob', 'carol', 'tina', 'alex', 'jack', 'emmy', 'tammy', 'sam', 'ted']…
Create a bottom-up mergesort that takes advantage of array order by doing the following each time it has to identify two arrays to merge: locate a sorted subarray (by incrementing a pointer until it finds an entry in the array that is smaller than its predecessor), then locate the next, and finally merge them. Examine the algorithm's running time in terms of array size and the number of maximal rising sequences in the array.
Multiplying Factors For a pair of integers (x,y) and an integer k, the multiplying factor is defined as minimum positive integer m such that LCM(x,y) * m is divisible by k. Here LCM(x,y) represents the smallest positive integer divisible by both x and y, their least common multiple. Given an array arr of n integers and an integer k, find the sum of multiplying factors over all pairs of integers (arr[i], arr[j]) and k0 <= i,j < n. Example Suppose n=3, arr =[4,5,6] and k=12. Pair Multiplying Factor Remarks (4, 3 LCM(4,4)**3=4**3 =12 4 ) LCM(5,5)**12=5** 12=60 (5, 12 LCM(6,6)**2=6**2 5) (6, 2 12 6 )