Problem 1: Give an asymptotic estimate for the number b(n) of “B”s printed by Algorithm PRINT_BS below. Your solution must consist of the following steps: (a) First express b(n) using the summation notation. (b) Next, give a closed-form expression¹ for b(n). (c) Finally, give the asymptotic value of b(n) using the e-notation. Show your work and include justification for each step. Algorithm PRINT BS (n: integer) for j← 1 to n +3 do for k← 1 to 5j do print("B") for j← 1 to n do for k← 1 to (j+ 1)² do print("B")
Problem 1: Give an asymptotic estimate for the number b(n) of “B”s printed by Algorithm PRINT_BS below. Your solution must consist of the following steps: (a) First express b(n) using the summation notation. (b) Next, give a closed-form expression¹ for b(n). (c) Finally, give the asymptotic value of b(n) using the e-notation. Show your work and include justification for each step. Algorithm PRINT BS (n: integer) for j← 1 to n +3 do for k← 1 to 5j do print("B") for j← 1 to n do for k← 1 to (j+ 1)² do print("B")
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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give an asymptotic estimate for the number b(n) of "B's" printed by
Transcribed Image Text:Problem 1: Give an asymptotic estimate for the number b(n) of "B"s printed by Algorithm PRINT_BS
below. Your solution must consist of the following steps:
(a) First express b(n) using the summation notation Σ.
(b) Next, give a closed-form expression¹ for b(n).
(c) Finally, give the asymptotic value of b(n) using the O-notation.
Show your work and include justification for each step.
Algorithm PRINT_BS (n: integer)
for j← 1 to n + 3 do
for k1 to 5j do print("B")
for j1 to n do
for k← 1 to (j+ 1)² do print(“B”)
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