) verity by induction the correctness of the solution of recusiveequation for the ruming time of MERGE-SORT2) Solve the fullowing se cursivo equation by usingJomin andcangetransfor mation,the prove your solufion by induction:TI)=1T()=3T()+h-n, n>l

Name: ) verity by induction the correctness of the solution of recusiveequa
Uploaded: 2024-03-20T06:38:58.000Z
Channel: Bartleby
Description: ) verity by induction the correctness of the solution of recusiveequation for the ruming time of MERGE-SORT2) Solve the fullowing se cursivo equation by usingJomin andcangetransfor mation,the prove your solufion by induction:TI)=1T()=3T()+h-n, n>l

Answered: ) verity by induction the correctness…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Concept explainers

Topic Video

Question

) verity by induction the correctness of the solution of recusive
equation for the ruming time of MERGE-SORT
2) Solve the fullowing se cursivo equation by using
Jomin and
cange
transfor mation,the prove your solufion by induction:
TI)=1
T()=3T()+h-n, n>l

Expert Solution

Step 1

Since you have asked multiple questions, we will solve the first question for you. If you want any specific question to be solved then please specify the question number or post only that question.

The equation for Merge Sort is given by,

$T (n) = \{\begin{cases} 1, f o r n = 1 \\ 2 T (\frac{n}{2}) + 1 f o r n \geq 2 \end{cases}$

$T (n) = n \log n + n$ .............................................................(1)

We have to verify by induction that equation (1) is the solution for the above equation.

Step 2

Induction Process.

Step1: Induction Base.

For $n = 1$ , we have $T (1) = 1$ .

Substitute $n = 1$ in equation (1).

$T (1) = 1 \log (1) + 1 = 0 + 1 = 1$

Hence it is true for $n = 1$ .

Step2: Induction Hypothesis

Assume $T (k) = k \log (k) + k$ is true for all $k \in n$ .

Step by step

Solved in 4 steps

Knowledge Booster

$Sequence$

Learn more about

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

Similar questions