Now suppose that you are given two unsorted arrays A and B, con-taining m and n elements respectively. You are also given a blackbox O(n) selection algorithm SEL that can be called on A and Bseparately and, in addition, a small number (say, ten) of extra mem-ory words that can be used to store some extra data. Using SELas a subroutine, design an O(n + m) algorithm for finding the kthsmallest element in the combined set of O(m + n) elements.You may not merge the two arrays in another array and call an algo-rithm (either SEL or something you wrote) on this third array. Thisis because there is no extra memory available to build this third array. (b) Now suppose that you are given two unsorted arrays A and B, con-taining m and n elements respectively. You are also given a blackbox O(n) selection algorithm SEL that can be called on A and Bseparately and, in addition, a small number (say, ten) of extra mem-ory words that can be used to store some extra data. Using SELas a subroutine, design an O(n + m) algorithm for finding the kthsmallest element in the combined set of O(m + n) elements.You may not merge the two arrays in another array and call an algo-rithm (either SEL or something you wrote) on this third array. Thisis because there is no extra memory available to build this third array.

The SEL algorithm is called for each array, A and B. Iterate till the sum of index is less than k.…

selection algorithm SEL that can be called on A and B separately and, in addition, a small number (say, ten) of extra mem- ory words that can be used to store some extra data. Using SEL as a subroutine, design an O(n + m) algorithm for finding the kth smallest element in the combined set of O(m + n) elements. You may not merge the two arrays in another array and call an algo- rithm (either SEL or something you wrote) on this third array. This is because there is no extra memory available to build this third array.

selection algorithm SEL that can be called on A and B separately and, in addition, a small number (say, ten) of extra mem- ory words that can be used to store some extra data. Using SEL as a subroutine, design an O(n + m) algorithm for finding the kth smallest element in the combined set of O(m + n) elements. You may not merge the two arrays in another array and call an algo- rithm (either SEL or something you wrote) on this third array. This is because there is no extra memory available to build this third array.

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter8: Arrays And Strings

Section: Chapter Questions

Problem 24PE

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Concept explainers

Counting sort

The counting sort algorithm sorts an array’s contents by counting the repetition of each element that occurs in the array. A counting sort algorithm is a stable algorithm that works the best when the range of elements in the array is small, say for example from 0 to 9. The count which is the number of repetitions of an element in the array is mapped to an index of an auxiliary array, which is then saved in an auxiliary array. The counting sort algorithm has a stable time complexity of the order of O(size of array + size of auxiliary array). Let’s discuss the algorithm in detail as follows.

Question

Now suppose that you are given two unsorted arrays A and B, con-
taining m and n elements respectively. You are also given a black
box O(n) selection algorithm SEL that can be called on A and B
separately and, in addition, a small number (say, ten) of extra mem-
ory words that can be used to store some extra data. Using SEL
as a subroutine, design an O(n + m) algorithm for finding the kth
smallest element in the combined set of O(m + n) elements.
You may not merge the two arrays in another array and call an algo-
rithm (either SEL or something you wrote) on this third array. This
is because there is no extra memory available to build this third array.

(b) Now suppose that you are given two unsorted arrays A and B, con-
taining m and n elements respectively. You are also given a black
box O(n) selection algorithm SEL that can be called on A and B
separately and, in addition, a small number (say, ten) of extra mem-
ory words that can be used to store some extra data. Using SEL
as a subroutine, design an O(n + m) algorithm for finding the kth
smallest element in the combined set of O(m + n) elements.
You may not merge the two arrays in another array and call an algo-
rithm (either SEL or something you wrote) on this third array. This
is because there is no extra memory available to build this third array.

Process or set of rules that allow for the solving of specific, well-defined computational problems through a specific series of commands. This topic is fundamental in computer science, especially with regard to artificial intelligence, databases, graphics, networking, operating systems, and security.

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