Let M(m,n) denote the number of comparisons required to merge two sorted lists of sizes m and n. a) Derive an "information theoretic" lower bound on M(m,n). b) Find an interesting relation between M(m,n) and the analogous function S defined for sorting. Use this relation to derive a lower bound for M(m,n) in terms of S. (Hint: Start with an upper bound on S(m+n).

Let M(m,n) denote the number of comparisons required to merge two sorted lists of sizes m and n. a) Derive an "information theoretic" lower bound on M(m,n). b) Find an interesting relation between M(m,n) and the analogous function S defined for sorting. Use this relation to derive a lower bound for M(m,n) in terms of S. (Hint: Start with an upper bound on S(m+n).

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

Consider a list of data components L[0:5] = 23, 14, 98, 45, 67, and 53. Let's look for the K = 53 key. Naturally, the search moves down the list, comparing key K with each element until it discovers it as the final element in the list. When looking for the key K = 110, the search moves forward but eventually drops off the list, making it a failed search. Write the algorithmic steps for both sorted and unordered linear searches, along with the times involved.
Let's assume that there are n keys that have been inserted in this fashion, and let's also assume that the keys (after sorting) are not entirely consecutive (i.e., each key is not 1 greater than the key preceding it). Answer the following questions about the resulting binary search tree. What is an asymptotic notation that best describes the height of the resulting binary search tree? In a sentence or two, explain why. What is an asymptotic notation that best describes the time required to insert another key into that binary search tree after it's been built, assuming the key was chosen completely at random and not subject to the arrangement described above? In a sentence or two, explain why.
Display the resulting graphs of the following set operations, and state if any of the results are isomorphically identical to any of the other results. (1.1) 4 - 1 (1.2) 2 ∩ 4 (1.3) (2 U 3) - 1
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)
Suppose (X[mX]+Y [mY ]) > 0. What can you infer about each of the four subproblems (namely, (X1, Y1), (X1, Y2), (X2, Y1), and (X2, Y2))? Clearly identify the ones that do not have to solved anymore, and those that still have to be solved. Briefly justify.
Correct answer will be upvoted else Multiple Downvoted. Computer science. You are given an arrangement an of length n comprising of integers from 1 to n. The grouping may contain duplicates (for example a few components can be equal). Track down the number of tuples of m=3 components with the end goal that the maximum number in the tuple varies from the base by close to k=2. Formally, you want to view as the number of triples of lists i<j<z with the end goal that max(ai,aj,az)−min(ai,aj,az)≤2. For example, on the off chance that n=4 and a=[1,2,4,3], there are two such triples (i=1,j=2,z=4 and i=2,j=3,z=4). In the event that n=4 and a=[1,1,1,1], all four potential triples are suitable. Input The principal line contains a solitary integer t (1≤t≤2⋅105) — the number of experiments. Then, at that point, t experiments follow. The principal line of each experiment contains an integer n (1≤n≤2⋅105) — the length of the succession a. The following line contains n…
When I am adding nodes into a data structure, how can I ensure that the insertion, deletion, and searching operations have a temporal complexity that is less than O(n), regardless of the number of nodes?
Provide an example of a recursive function in which the amount of work on each activation is constant. Provide the recurrence equation and the initial condition that counts the number of operations executed. Specify which operations you are counting and why they are the critical ones to count to assess its execution time. Draw the recursion tree for that function and determine the Big-Θ by determining a formula that counts the number of nodes in the tree as a function of n.
Computer Science whrite down the recurrence relationship(Functions) of the following Algorithms for their Worst, Best and Average cases and slove them by using subtitution Method: 1.Quick sort 2.Selection sort 3.Heap Sort 4. Insertion sort 5.Bubble sort 6. Radix Sort 7.Merge Sort 8.Conting Sort
A useful operation in databases is the naturalj oin.If we view a database as a list of ordered pairs of objects, then the natural join of databases A and B is the list of all ordered triples (x,y,z) such that the pair (x,y) is in A and the pair (y,z) is in B. Describe and analyze an efficient algorithm for computing the natural join of a list A of n pairs and a list B of m pairs. Data Structures & Algorithms C-7.55
Answer the given question with a proper explanation and step-by-step solution. C++ 11.12 LAB: Fibonacci sequence (recursion) The Fibonacci sequence begins with 0 and then 1 follows. All subsequent values are the sum of the previous two, for example: 0, 1, 1, 2, 3, 5, 8, 13. Complete the Fibonacci() function, which takes in an index, n, and returns the nth value in the sequence. Any negative index values should return -1. Ex: If the input is: 7 the output is: Fibonacci(7) is 13 Note: Use recursion and DO NOT use any loops. main.cpp #include <iostream>using namespace std; int Fibonacci(int n) {/* Type your code here. */ } int main() {int startNum;cin >> startNum;cout << "Fibonacci(" << startNum << ") is " << Fibonacci(startNum) << endl;return 0;}
*Data Structures and Algorithm Professor Holmes came up with the idea of a sorting algorithm that he calls Trinary Sort which he claims is asymptotically faster than merge sort, despite being similar in logic. Unlike merge sort, trinary sort splits the input list into three roughly equal parts at each step of the recursion as long as the list is splittable (i.e., has at least 3 elements in this case). The merge operation, similar to what it does in mergeSort, takes three already sorted subarrays, and merges them. (a) In merge sort, merge operation makes exactly n−1 comparisons in total to merge two lists of size n/2 in the worst case, which takes O(n) time. How many comparisons will the merge operation of Trinary sort make in the worst case to merge three sublists of size (n/3) (give an exact number)? Why? What would be the asymptotic bound? (b) What is the total running time of the Trinary Search algorithm? Show it using the tree expansion method.