Suppose you are writing an algorithm to merge k sorted arrays of size n into a single sorted array of size kn. You write an algorithm to do so that (1) makes a recursive call to merge the first k/2 arrays, (2) makes another recursive call to merge the remaining k/2 arrays, then (3) merges the results from the calls in (1) and (2). Suppose the cost of merging two sorted arrays of sizes a and b is a+b. Suppose you are sitting at the root of the recursion tree, where the last two arrays of size kn/2 will be merged. What will be the total cost of the algorithm at this level of the tree? Give your answer as an expression in terms of n and k (in simplest form). nk'log(nk) Question 7 Given the recursive algorithm above for merging k sorted arrays, what will be the total cost of the algorithm at the bottom of the recursion tree (the sum of the work performed at the leaves)? You can assume that k is a power of 2. Give your answer as a simplified expression in terms of n and k.

Suppose you are writing an algorithm to merge k sorted arrays of size n into a single sorted array of size kn. You write an algorithm to do so that (1) makes a recursive call to merge the first k/2 arrays, (2) makes another recursive call to merge the remaining k/2 arrays, then (3) merges the results from the calls in (1) and (2). Suppose the cost of merging two sorted arrays of sizes a and b is a+b. Suppose you are sitting at the root of the recursion tree, where the last two arrays of size kn/2 will be merged. What will be the total cost of the algorithm at this level of the tree? Give your answer as an expression in terms of n and k (in simplest form). nk'log(nk) Question 7 Given the recursive algorithm above for merging k sorted arrays, what will be the total cost of the algorithm at the bottom of the recursion tree (the sum of the work performed at the leaves)? You can assume that k is a power of 2. Give your answer as a simplified expression in terms of n and k.

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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