Database System Concepts
Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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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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Transcribed Image Text: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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