2. Write a recurrence relation describing the worst case running time of each of the followingalgorithms and determine the asymptotic complexity of the function defined by therecurrence relation. Justify your solution. You may not use the Master Theorem asjustification of your answer. Simplify and express your answer as (nk) or (nk log₂ n)whenever possible. If the algorithm is exponential just give exponential lower bounds.a) function func(A,n)if n ≤ 5 then return A(1)elsefor i=1 to nfor j = i to n-1A(j) A(j) + A(i) + 3/* endfor *//* endfor */wwwwwwwwwwy ← func(A, n-6)return (y) b) function func(A,n)if n <= 2 then return A(1)y func(A, floor(n/3))for i = n-5 to ny + y + A(i) + 3/* endfor */return (y)

a) Let T(n) be the worst case running time of the function func(A, n). We can see that when n <…

Answered: a) function func(A,n) if n ≤ 5 then…

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a) function func(A,n) if n ≤ 5 then return A(1) else for i=1 to n for j = i to n-1 Ail(i) + A/i) + 2

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

2. Write a recurrence relation describing the worst case running time of each of the following
algorithms and determine the asymptotic complexity of the function defined by the
recurrence relation. Justify your solution. You may not use the Master Theorem as
justification of your answer. Simplify and express your answer as (nk) or (nk log₂ n)
whenever possible. If the algorithm is exponential just give exponential lower bounds.
a) function func(A,n)
if n ≤ 5 then return A(1)
else
for i=1 to n
for j = i to n-1
A(j) A(j) + A(i) + 3
/* endfor */
/* endfor */
wwwwwwwwww
y ← func(A, n-6)
return (y)

b) function func(A,n)
if n <= 2 then return A(1)
y func(A, floor(n/3))
for i = n-5 to n
y + y + A(i) + 3
/* endfor */
return (y)

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