Q1. The number of runs an for a recursive algorithm satisfies the recurrence relation (for any even positive integer n) an = 2an/2+n, for n ≥ 2, with a₁ = 0. Find the big-O notation for the running time of this algorithm. Q2. How many 6-digit numbers can be formed using {1,2,..., 9} with no repetitions such that 1 and 2 do not occur in consecutive positions? Q3. What is the value of k after the following algorithm has been executed? Justify your answer. What counting principle did you apply? k = 1; for ₁1 to 1 for 12 = 1 to 2 for i3 1 to 3 : for 1991 to 99 k = k + 1;
Q1. The number of runs an for a recursive algorithm satisfies the recurrence relation (for any even positive integer n) an = 2an/2+n, for n ≥ 2, with a₁ = 0. Find the big-O notation for the running time of this algorithm. Q2. How many 6-digit numbers can be formed using {1,2,..., 9} with no repetitions such that 1 and 2 do not occur in consecutive positions? Q3. What is the value of k after the following algorithm has been executed? Justify your answer. What counting principle did you apply? k = 1; for ₁1 to 1 for 12 = 1 to 2 for i3 1 to 3 : for 1991 to 99 k = k + 1;
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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Transcribed Image Text:Q1. The number of runs an for a recursive algorithm satisfies the recurrence relation (for any
even positive integer n)
an 2an/2+n, for n ≥ 2, with a₁ = 0.
Find the big-O notation for the running time of this algorithm.
Q2. How many 6-digit numbers can be formed using {1, 2, ..., 9} with no repetitions such that
1 and 2 do not occur in consecutive positions?
-
Q3. What is the value of k after the following algorithm has been executed? Justify your answer.
What counting principle did you apply?
k = 1;
for it = 1 to 1
for 12
for i3
:
1 to 2
= 1 to 3
for 199 = 1 to 99
k = k + 1;
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