2.6 ORDER STATISTICS A problem closely related to sorting is that of selecting the kth smallest ele- ment in a sequence of n elements.† One obvious solution is to sort the sequence into nondecreasing order and then locate the kth element. As we have seen, this would require n log n comparisons. By a careful application of the divide-and-conquer strategy, we can find the kth smallest element in O(n) steps. An important special case occurs when k = [n/2], in which case we are finding the median of a sequence in linear time. Algorithm 3.6. Finding the kth smallest element. Input. A sequence S of n elements drawn from a linearly ordered set and an integer k, 1 ≤ k ≤ n. Output. The kth smallest element in S. Method. We use the recursive procedure SELECT in Fig. 3.10. ☐ Let us examine Algorithm 3.6 intuitively to see why it works. The basic idea is to partition the given sequence about some element m into three subsequences S₁, S., S₁ such that S, contains all elements less than m, S, all Strictly speaking, the kth smallest of a sequence a₁. da, is an element b in the sequence such that there are at most k - 1 values for i for which a,

2.6 ORDER STATISTICS A problem closely related to sorting is that of selecting the kth smallest ele- ment in a sequence of n elements.† One obvious solution is to sort the sequence into nondecreasing order and then locate the kth element. As we have seen, this would require n log n comparisons. By a careful application of the divide-and-conquer strategy, we can find the kth smallest element in O(n) steps. An important special case occurs when k = [n/2], in which case we are finding the median of a sequence in linear time. Algorithm 3.6. Finding the kth smallest element. Input. A sequence S of n elements drawn from a linearly ordered set and an integer k, 1 ≤ k ≤ n. Output. The kth smallest element in S. Method. We use the recursive procedure SELECT in Fig. 3.10. ☐ Let us examine Algorithm 3.6 intuitively to see why it works. The basic idea is to partition the given sequence about some element m into three subsequences S₁, S., S₁ such that S, contains all elements less than m, S, all Strictly speaking, the kth smallest of a sequence a₁. da, is an element b in the sequence such that there are at most k - 1 values for i for which a,

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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: In searching an element in an array, linear search can be used, even though simple to implement, but not efficient, with only O(n) time complexity. Assuming the array is already in sorted order, modify the search function below, using a better algorithm, so the average time complexity for the search function is O(log n). include <iostream> using namespace std; int search(int al), int s, int v) { 1/ Modify below codes. for (int i = 0; i <s; i++) { if (a[i] = v) return i; return -1; int main() { int intArray:10] = { 5, 7, 8, 9, 10, 12, 13, 15, 20, 34); // Search for element '12' in 10-elements integer array. cout << search(intArray, 10, 12); // '5' will be printed out. // Search for element '35' in 10-elements integer array. cout << search(intArray, 10, 35); // '-1' will be printed out. // Index '-l' means that the element is not found. return 0;
See the pseudo-code of the Binary Search using recursion below. Fill in the XXXX and YYYY in the code Algorithm BinarySearch (A,v,low,hi) Input: array A indexed from low to hi with items sorted from smallest to largest. We are searching for the item v Output: returns a location index of item v in array A; if v is not found, -1 is returned. if (low > hi) then return (-1); mid = (lo + hi)/2; if (A[mid] = v) then == return(mid); if (A[mid] < v) then return(BinarySearch(A, XXXX ,hi, v)); else return(BinarySearch(a, lo, YYYY, v)); О а. ХX: lo+1, YҮҮ: hi O b. XXXX: mid, YYYY: mid О с. ХXXX: lo, YYYY: hi O d. XXXX: lo+1, YYYY: hi-1 O e. XXXX: mid+1. YYYY: mid-1
3. Binary search. (a) Suppose we want to check if a sorted sequence A contains an element v. For this, we can use Binary Search. Binary Search compares the value at the midpoint of the sequence A with v and eliminates half of the sequence from further consideration. The Binary Search algorithm repeats this procedure, halving the size of the remaining portion of the sequence each time. Write a recurrence for the running time of Binary search and solve this recurrence. (b) Ternary Search is a generalization of Binary Search that can be used to find an element in an array. It divides the array with n elements into three parts and determines, with two comparisons, which part may contain the value we are searching for. For instance, initially, the array is divided into three thirds by taking mid1 = ["¹] and mid2 = [²(n-¹)]. Write a recurrence for the running time of Ternary search and solve this recurrence.
ALGO2(A)// A is an integer array, index starting at 11:for i=1 to n-1 do2: for j=n to i+1 do3: if (A[j] < A[j-1]) then4: exchange A[j] with A[j-1] Which function best describes the worst-case running time behaviour of ALGO2 on an array of size n? Option 1) a*(n^2) + b*n +c, where a,b,c are constantsOption 2) a*n + b , where a and b are constantsOption 3) a * n * log(n) + b, where a,b are constantsOption 4) a*(n^3) + b*(n^2) + c*n + d, where a,b,c,d are constants
01... ""Implementation of the Misra-Gries algorithm.Given a list of items and a value k, it returns the every item in the listthat appears at least n/k times, where n is the length of the array By default, k is set to 2, solving the majority problem. For the majority problem, this algorithm only guarantees that if there isan element that appears more than n/2 times, it will be outputed. If thereis no such element, any arbitrary element is returned by the algorithm.Therefore, we need to iterate through again at the end. But since we have filtredout the suspects, the memory complexity is significantly lower thanit would be to create counter for every element in the list. For example:Input misras_gries([1,4,4,4,5,4,4])Output {'4':5}Input misras_gries([0,0,0,1,1,1,1])Output {'1':4}Input misras_gries([0,0,0,0,1,1,1,2,2],3)Output {'0':4,'1':3}Input misras_gries([0,0,0,1,1,1]Output None"""..
12 - Consider the example of sorting, we implemented Bubble sort but the data started to grow and Bubble sort started getting very slow. In order to tackle this we implemented Quick sort. But now although the Quick sort algorithm was doing better for large datasets, it was very slow for smaller datasets. In order to handle this situation, implement a --------- small datasets, bubble sort will be used and for larger, quick sort will be used. design pattern where for According to the system definition given above, which design pattern did designers use when implementing the system. I) Template Method II) Singleton III) Strategy IV) None of the mentioned a) O II b) O IV c) O II d) O I
Let A and B be two integers valued arrays of sizes n1 & n2 respectively. The elements of the two arrays are sorted in increasing order and may contain duplicate elements.It is required to form a list, C, of distinct elements, in increasing order, that are in A but not in B and in B but not in A. (There shall be no duplicate elements in list C.)The two arrays, A & B, can only be traversed once.Example:A: -2, 2, 4, 4, 4, 7, 9, 9, 9, 12, 15,B: 1, 2, 5, 9, 15, 15, 15, 17, 17, 17C: -2, 1, 4, 5, 7, 12, 17
Differentiate between a tree and a graph. b. Give code for a function delete(p) that deletes the node pointed to by p in a circular linked list and returns a pointer to the node after the deleted node. In an mxn matrix, where the row index varies from 1 to m and column index from 1 to n, aij denotes the number in the h row and the jh column. In the computer's memory, all elements are stored linearly using contiguous addresses. Therefore, to store a two-dimensional matrix, two-dimensional address space must be mapped to one- dimensional address space. In the computer's memory, matrices are stored in either row-major order or column- Column-major order major order form. In row-major order, the consecutive elements of a row reside next to each other. In column- major order, the consecutive elements of a column reside а. Row-major order a a12 a13 a a22 a23 с. a1 a12 a13 a23 a22 [5 1] 4 3 6 8 2 7] next to each other. Consider the matrix A = Base address of the matrix is 3FA2H. Each element…
Fun with Sorting :Given the following array of numbers:8 2 3 9 10 1 4 6 7 5Show what the array looks like after each iteration of the following sorting algorithms:1) Bubble2) Selection3) Insertion4) MergesortOnly show the array contents with each algorithm. You do not need to show function callinstances if recursion is used or write any code. Just show the array at key iterations of thealgorithm. You can use your own words to describe them as well for more detail (but do notwrite any code).
18, 19, 20
Transcribed Image Text Q} Code the given problem using python programming language Sereja has an array consisting of n integers a1 < a2 <... < an. Based on this array, he has to answer m queries represented by pairs integers t and d. The answer for a query is the smallest integer i for which there exist some k ( i < k) such that a; + d > a;+1, a; +1 + d2 a;+2, ..., ar – 1 + d> ak, ak <t and ar+1 > t (if it exists).
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