Recursion Tree Method

Recursion tree method for solving recurrences running time example

An algorithm analysis example:
What is the running time of the following code ?

Easy Algorithm Analysis Tutorial:

►Please Subscribe !

►Videos:

►Visit my Website:

►Summation Formulas:

►RESOURCES:

Helpful Books:
Algorithm Analysis Books:

Discrete Mathematics Workbooks:

[charithbiyanwila]

2 hours of lecture just in 15mins. Fantastic!!

[lucascolepichette]

You are a beautiful human. My professor explained this in... not an ideal way, and I spent HOURS trying to understand it.I felt very confident as what to do by the 4:52 timestamp.

[julianyumanji]

ayyy its a brotha doing cs lets go. I love when I see another one of us in cs go ahead man do that shit

[roxiogamer]

Suddenly Master Theory doesn't look that bad lol. Great video, really helped!

[joeloyolabordagaray]

I just needed to drop a comment, you are gold man! Thanks for the videos!

[sunnystarfish]

the way it took me forever to understand this concept until i found this video :, ) thank you

[amirghorban]

Thank you very much this lecture is magic for me Nice explanation best short tutoriol

[Alexgamer-pphm]

Thank you so much for the video! it helped me understand the concept a lot better. Also, you have a very easy to listen to voice :)

[celestynkinny]

Hello,
I know this video is very old, and I want to thank-you for teaching me the concept.

But, I have a question... Why are you using the summation formula instead of representing the summation as a series of (1/2^i)?

Because n^2 can be taken outside as it is a common occurrence throughout the series, then the series can be represented as a constant variable because the series was finite. After applying the Big-O notation rules the constant we had taken will be removed leaving us n^2 and O(n^2).

If we were to solve this series we end up with a function where when i = 0 we have f(i) = 1 and when i > 1 we have f(i) = 1 + (1 + 1/2)*1/2^(log(base 2 of n)-1), and the answer is O(n^2) after solving further.

[MW-fmqq]

Thank you very very much! This is the best of the best lecture! You make hard concept so easy to understand! Thank you!

[johngilmore]

You are literally the best you tuber I have found who teaches these subjects! Keep making videos and helping us learn! Is there any chance you could make a video on guess and check substitution? Not just Iterative substitution?

[daisy-fbjc]

I wish you could be my professor!!! You have done a much greater job than she does. My brain have never been so clear since this semester started...

[amphivalo]

Hey!
In your solution you never used that T(1)=4 ...
After drawing the tree you took the sum from 0 to h.
I think it should be from 0 to h-1 and we also add 2^h * T(1) which is the cost of the last level.
Therefore the answer is 2n^2 + 2n.
Please tell me if you agree or disagree.

[louise]

Great. Nice voice too, it's very relaxing.

[kseniiaamelina]

How did you remove the exponent log(n) from the summation?

[rayjennings]

Could you explain how you get T(1) = 4 ? I thought it would be T(1) = 1. Also, do you split each node into 2 branches because of the 2T? If you had 3T would it be 3 branches from each node?

[mikado]

Thank you so much! Very helpful and understandable

[oscarmejia]

Please break down the math simplification step by step

[NassosKranidiotis]

Thanks for the video. It was very helpful.

[meechol]

Thanks a lot, this video was very helpful.