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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Q:During each iteration of Quick Sort algorithm, the first element of array is selected as a pivot. The algorithm for Quick Sort is given below. Modify it in such a way that last element of array should be selected as a pivot at each iteration. Also explain the advantages.
18, 19, 20
How do i design the following Pseudocode with explanations? Let A[1...N] be a maxheap. Design an algorithm to change the array A into a minheap as the output. Briefly explain the main idea of your algorithm and then present the pseudocode of it. Additional space consumptions for carrying out the algorithm, e.g., additional arrays or linked lists, should be minimized. You may assume that the standard function swap() is given.
Language: Python 3 • Autocomplete Ready O 1 v import ast lst = input(O lst = ast.literal_eval(lst) def binarysearch(lst,x,low,high): if low - high x: 10 11 Algorithm BinarylnsertionSort 12 Input/output: takes an integer array a = {a[0], ..., a[n – 1]} of size n 13 begin BinarylnsertionSort return binarysearch (lst, x, mid, high) 14 for i =1 to n val = a[i] p = BinarySearch(a, val, 0, i – 1) for j = i-1 to p alj + 1]= a[j] j= j-1 end for 15 else: 16 return mid 17 18 def BinaryInsertionSort(lst): 19 print (BinaryInsertionSort(lst)) 20 a[p] = val j=i+1 end for end BinarylnsertionSort Here, val = a[i] is the current value to be inserted at each step i into the already sorted part a[0], ..., ați – 1] of the array a. The binary search along that part returns the position p where the val will be inserted. After finding p, the data values in the subsequent positions j = i- 1, ..., p are sequentially moved one position up to i, ..., p+1 so that the value val can be inserted into the proper…
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During each iteration of Quick Sort algorithm, the first element of array is selected as a pivot. The algorithm for Quick Sort is given below. Modify it in such a way that last element of array should be selected as a pivot at each iteration. Also explain the advantages.
Please do it in python Topic: Searching and Sorting
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