Consider the following algorithm, which may be called on an array that is not necessarily sorted. and returns the array in sorted form. GoofySort (A) : if (len (A) <= 3): SelectionSort (A) else: Let t + ſlen(A)/3] A[1:2t] + GoofySort (A[1:2t]) A[t+1:n] + GoofySort (A[t+1:n]) //sort the back 2/3rds //sort the front 2/3rds A[1:2t] GoofySort (A[1:2t]) //sort the front 2/3rds (a) Write a recurrence which captures the runtime of this algorithm. Your recurrence should be of the form T (n) =?. You can ignore any non-recursive operations (i.e. you only need to focus on operations in the last three lines). You do not need to handle base cases here. You can assumen is divisible by 3 for convenience. (b) Solve your recurrence using the substitution method. Show your work. You may assume a base case of T (1) = 1. State what the big-O runtime is for this algorithm (hint: it should be a polynomial written in the form n). %3D

Consider the following algorithm, which may be called on an array that is not necessarily sorted. and returns the array in sorted form. GoofySort (A) : if (len (A) <= 3): SelectionSort (A) else: Let t + ſlen(A)/3] A[1:2t] + GoofySort (A[1:2t]) A[t+1:n] + GoofySort (A[t+1:n]) //sort the back 2/3rds //sort the front 2/3rds A[1:2t] GoofySort (A[1:2t]) //sort the front 2/3rds (a) Write a recurrence which captures the runtime of this algorithm. Your recurrence should be of the form T (n) =?. You can ignore any non-recursive operations (i.e. you only need to focus on operations in the last three lines). You do not need to handle base cases here. You can assumen is divisible by 3 for convenience. (b) Solve your recurrence using the substitution method. Show your work. You may assume a base case of T (1) = 1. State what the big-O runtime is for this algorithm (hint: it should be a polynomial written in the form n). %3D

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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Question

Consider the following algorithm, which may be called on an array that is not necessarily sorted.
and returns the array in sorted form.
GoofySort (A) :
if (len (A) <= 3): SelectionSort(A)
else:
[len(A)/3]
+ GoofySort (A[1:2t])
GoofySort (A[t+1:n]) //sort the back 2/3rds
+ GoofySort (A[1:2t])
Let t +
A[1:2t]
//sort the front 2/3rds
A[t+1:n]
A[1:2t]
//sort the front 2/3rds
(a) Write a recurrence which captures the runtime of this algorithm. Your recurrence should
be of the form T (n) =?. You can ignore any non-recursive operations (i.e. you only need to
focus on operations in the last three lines). You do not need to handle base cases here. You
can assumen is divisible by 3 for convenience.
(b) Solve your recurrence using the substitution method. Show your work. You may assume a
base case of T (1) = 1. State what the big-0 runtime is for this algorithm (hint: it should be a
polynomial written in the form nº).

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