Please help me with Question 2. Please provide a step-by-step explanation of the solution as I am really struggling with this. Introduction to RecurrencesA recurrence is defined as being an equation or inequality that describes a function interms of its value on smaller inputs. For this exercise, we will write an equation for thefunction T(n) to achieve the given sequence. State any initial conditions for the numbersprovided. The initial condition of T(0) = 3.T(n) = 2T(n − 1)To solve this equation, we need to solve for T(n − 1). That can be solved by evaluatingT(n − 1) = 2T ((n − 1) − 1). We can plug this into our original equation for T(n):= 2(2T(n-1-1))We will do the same thing again for the third iteration:= 2(2(2T(n-1-1. -1)))Since we can see an emerging pattern, we can try this where the value k represents thecurrent iteration (e.g. k = 3 for the third call of T(n) in this case):= 2k T(n - k)We will continue to do this until n - k in the function T(n - k) reaches 0. This willhappen when k = n given that n - n = 0. Thus, our final equation can be written as:= 2" T(0)Since we have been given a base case to solve, which is T(0) = 3, we can now solve thisfor any value of n:= 2n (3)Practice Problems1. Solve the equation T(n) = 2n - T(n − 1). The base condition is T(0) = 1.2. Solve the equation T(n) = T(n − 1) + n. The base condition is T(0) = 0.

Answered: 2. Solve the equation T(n) = T(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

See similar textbooks

Related questions

Question

Please help me with Question 2. Please provide a step-by-step explanation of the solution as I am really struggling with this.

Introduction to Recurrences
A recurrence is defined as being an equation or inequality that describes a function in
terms of its value on smaller inputs. For this exercise, we will write an equation for the
function T(n) to achieve the given sequence. State any initial conditions for the numbers
provided. The initial condition of T(0) = 3.
T(n) = 2T(n − 1)
To solve this equation, we need to solve for T(n − 1). That can be solved by evaluating
T(n − 1) = 2T ((n − 1) − 1). We can plug this into our original equation for T(n):
= 2(2T(n-1-1))
We will do the same thing again for the third iteration:
= 2(2(2T(n-1-1. -1)))
Since we can see an emerging pattern, we can try this where the value k represents the
current iteration (e.g. k = 3 for the third call of T(n) in this case):
= 2k T(n - k)
We will continue to do this until n - k in the function T(n - k) reaches 0. This will
happen when k = n given that n - n = 0. Thus, our final equation can be written as:
= 2" T(0)
Since we have been given a base case to solve, which is T(0) = 3, we can now solve this
for any value of n:
= 2n (3)
Practice Problems
1. Solve the equation T(n) = 2n - T(n − 1). The base condition is T(0) = 1.
2. Solve the equation T(n) = T(n − 1) + n. The base condition is T(0) = 0.

Expert Solution

Explaination

here for the recurrence we have the equation . In the equation we have the version of the same equation in the form of (n-1).

now as given in the example

We have the equation as 2T(n-1) Here we can see that for the T(n) we need to find the T(n-1). Hence to solve this what we do is just to replace the n with n-1 and we get

---> 2T(n-1 -1 )

Then we just put it in the original equation T(n) = 2[ 2T(n-1-1) ].

Hence similarly what we can do is keep doing this things in the second equation of yours . We have the equation as

T(n) = T(n-1) + n

We need to find the T(n-1) here also . Hence we get T(n-1) = T(n-1-1) + (n-1)

Hence similary we can keep moving ahead with this logic check the solution in the second step

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.

Similar questions