Dgdrxrt

Why are there uneven bright areas in this photo of black hole?

What is the most efficient way to store a numeric range?

What is this business jet?

Why was M87 targeted for the Event Horizon Telescope instead of Sagittarius A*?

Why can't devices on different VLANs, but on the same subnet, communicate?

Did the UK government pay "millions and millions of dollars" to try to snag Julian Assange?

"as much details as you can remember"

Is it ok to offer lower paid work as a trial period before negotiating for a full-time job?

Will it cause any balance problems to have PCs level up and gain the benefits of a long rest mid-fight?

What is preventing me from simply constructing a hash that's lower than the current target?

Dropping list elements from nested list after evaluation

How do you keep chess fun when your opponent constantly beats you?

How can I have a shield and a way of attacking with a ranged weapon at the same time?

How much of the clove should I use when using big garlic heads?

Alternative to の

Did Scotland spend $250,000 for the slogan "Welcome to Scotland"?

Keeping a retro style to sci-fi spaceships?

How can I add encounters in the Lost Mine of Phandelver campaign without giving PCs too much XP?

Cooking pasta in a water boiler

How to charge AirPods to keep battery healthy?

Loose spokes after only a few rides

Button changing its text & action. Good or terrible?

Is it ethical to upload a automatically generated paper to a non peer-reviewed site as part of a larger research?

Why didn't the Event Horizon Telescope team mention Sagittarius A*?

solving a recurrence equation $T(n) = T(cn) + T((1-c)n) + 1$

1

1

$begingroup$

first, this question has been asked here before, however I have some issues with it that haven't been answered yet :

give asymptotic bounds of $ T(n) $ where

$ T(n) = T(cn)+ T((1-c)n) +1 , 0<c<1 $

this is the original post link
I didn't quite understand why the answer given over there was with a linear solution $S(n) = nS(1)$

and another thing, I've been told by someone that an even tighter bound is $theta(log(n))$ is possible.

so two things, is this true, and why is the linear solution is of the form given before.

thanks ahead.

recurrence-relations asymptotics

share|cite|improve this question

edited Apr 1 at 14:48

user

6,48311031

asked Mar 30 at 17:27

lidor718lidor718

175

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  The title has $+1$ on the rhs, the body has $+n$. The Akra–Bazzi method is applicable to both cases, giving $p = 1$.
  $endgroup$
  – Maxim
  Apr 1 at 13:24
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  It’s suppose to be +1
  $endgroup$
  – lidor718
  Apr 1 at 13:45
  

  
  
  
  

add a comment | 

1

1

$begingroup$

first, this question has been asked here before, however I have some issues with it that haven't been answered yet :

give asymptotic bounds of $ T(n) $ where

$ T(n) = T(cn)+ T((1-c)n) +1 , 0<c<1 $

this is the original post link
I didn't quite understand why the answer given over there was with a linear solution $S(n) = nS(1)$

and another thing, I've been told by someone that an even tighter bound is $theta(log(n))$ is possible.

so two things, is this true, and why is the linear solution is of the form given before.

thanks ahead.

recurrence-relations asymptotics

share|cite|improve this question

edited Apr 1 at 14:48

user

6,48311031

asked Mar 30 at 17:27

lidor718lidor718

175

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  The title has $+1$ on the rhs, the body has $+n$. The Akra–Bazzi method is applicable to both cases, giving $p = 1$.
  $endgroup$
  – Maxim
  Apr 1 at 13:24
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  It’s suppose to be +1
  $endgroup$
  – lidor718
  Apr 1 at 13:45
  

  
  
  
  

add a comment | 

$begingroup$

first, this question has been asked here before, however I have some issues with it that haven't been answered yet :

give asymptotic bounds of $ T(n) $ where

$ T(n) = T(cn)+ T((1-c)n) +1 , 0<c<1 $

this is the original post link
I didn't quite understand why the answer given over there was with a linear solution $S(n) = nS(1)$

and another thing, I've been told by someone that an even tighter bound is $theta(log(n))$ is possible.

so two things, is this true, and why is the linear solution is of the form given before.

thanks ahead.

recurrence-relations asymptotics

share|cite|improve this question

edited Apr 1 at 14:48

user

6,48311031

asked Mar 30 at 17:27

lidor718lidor718

175

$endgroup$

share|cite|improve this question

edited Apr 1 at 14:48

user

6,48311031

asked Mar 30 at 17:27

lidor718lidor718

175

share|cite|improve this question

edited Apr 1 at 14:48

user

6,48311031

asked Mar 30 at 17:27

lidor718lidor718

175

edited Apr 1 at 14:48

user

6,48311031

edited Apr 1 at 14:48

user

6,48311031

asked Mar 30 at 17:27

lidor718lidor718

175

asked Mar 30 at 17:27

lidor718lidor718

175