2. (a) Use the master theorem to find the exact solution of the following recurrence equation. Make sure you find the constants. Assume n is a power of 2. +n, n ≥ 2 4T 3, n = 1 T(n) = 2(b) Use repeated substitution to find the exact solution of the following recurrence. T(n) = { 1, n+T(n-1), n ≥2 n = 1
2. (a) Use the master theorem to find the exact solution of the following recurrence equation. Make sure you find the constants. Assume n is a power of 2. +n, n ≥ 2 4T 3, n = 1 T(n) = 2(b) Use repeated substitution to find the exact solution of the following recurrence. T(n) = { 1, n+T(n-1), n ≥2 n = 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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can you solve 2020 image one I also provided refrences how MY prof solved so based on that pleease solve this image 2020 one step by step formet please use from refrnecs
Transcribed Image Text:2. Use master theorem to find the exact solution of the following recurrence equation.
Find the constants. Assume n is an integer power of 2, n = 2k.
Master Theorm:
a=2, b=2, A=2
h=
lag a = 1
b
T(n)
ũ Tin Anh Bả
T(m)
= An + Bn²
To find constants A, B:
A+B=1
2A+4B=6
2B = 4
A+B=1
- {2T (2) +
So,
⇒ h‡ß
B
T(1)=1
A + B
T (2) = 2T (1) + 2²³ = 2 + 4 = 6
80,
+n², n ≥2
n=1
B=2
A=-1
(T(n) = 2n²_n
= 2A + 4B
Transcribed Image Text:2. (a) Use the master theorem to find the exact solution of the following recurrence
equation. Make sure you find the constants. Assume n is a power of 2.
+n, n ≥ 2
n = 1
4T
= {₁T (G) +
3,
T(n) =
2(b) Use repeated substitution to find the exact solution of the following recurrence.
n+T(n-1),
n ≥ 2
n = 1
T(n)
={n+
1,
=
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