please answer with proper explanation and step by step solution. 4. Consider an algorithm that works as follows: Starting with an input of size n, itdivides the input into two or more groups, solves each group separately, and thencombines the answers from each group to form its output.Suppose the algorithm creates k groups of sizes n₁,...,nk. Then it takes thealgorithm O(n, log ni) time to solve the ith group whose size is nį and O(n + k)time to divide the input into k groups and combine the partial results to generatethe output.a.Determine an upper bound on the running time of the whole algorithmin terms of n. Note that k and the n's are not fixed values but depend insteadon the input.b.Now redo the question when it takes the algorithm O(n) time to solvethe ith group of size n; and O(n²+ k) time to divide the input into k andgroupsassemble the partial results to form the output.

Please refer to the following step for the complete solution to the problem above.

n, 4. Consider an algorithm that works as follows: Starting with an input of size it divides the input into two or more groups, solves each group separately, and then combines the answers from each group to form its output. Suppose the algorithm creates k groups of sizes n₁,...,nk. Then it takes the algorithm O(n, log n;) time to solve the ith group whose size is ni and O(n + k) time to divide the input into k groups and combine the partial results to generate the output. a. Determine an upper bound on the running time of the whole algorithm in terms of n. Note that k and the ni's are not fixed values but depend instead on the input. b. Now redo the question when it takes the algorithm O(n) time to solve the ith group of size n; and O(n²2 + k) time to divide the input into k groups assemble the partial results to form the output. and

n, 4. Consider an algorithm that works as follows: Starting with an input of size it divides the input into two or more groups, solves each group separately, and then combines the answers from each group to form its output. Suppose the algorithm creates k groups of sizes n₁,...,nk. Then it takes the algorithm O(n, log n;) time to solve the ith group whose size is ni and O(n + k) time to divide the input into k groups and combine the partial results to generate the output. a. Determine an upper bound on the running time of the whole algorithm in terms of n. Note that k and the ni's are not fixed values but depend instead on the input. b. Now redo the question when it takes the algorithm O(n) time to solve the ith group of size n; and O(n²2 + k) time to divide the input into k groups assemble the partial results to form the output. and

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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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

please answer with proper explanation and step by step solution.

4. Consider an algorithm that works as follows: Starting with an input of size n, it
divides the input into two or more groups, solves each group separately, and then
combines the answers from each group to form its output.
Suppose the algorithm creates k groups of sizes n₁,...,nk. Then it takes the
algorithm O(n, log ni) time to solve the ith group whose size is nį and O(n + k)
time to divide the input into k groups and combine the partial results to generate
the output.
a.
Determine an upper bound on the running time of the whole algorithm
in terms of n. Note that k and the n's are not fixed values but depend instead
on the input.
b.
Now redo the question when it takes the algorithm O(n) time to solve
the ith group of size n; and O(n²+ k) time to divide the input into k and
groups
assemble the partial results to form the output.

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