Recurrence Relation Proof By Induction
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- Опубліковано 23 жов 2017
- A proof by induction for recurrence relation.
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Thanks Brandon and I definitely remember not understanding my teachers when it came to these topics.
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Thanks Cecilia!
LOVE IT
Thank you so much for the explanation!
You are welcome Christine. I am glad you liked the video !
Thank you, this video was helpful. I have couple of similar problems but they made no sense, specially the show part.
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Where does the 2 go thats on the far left side of the induction step? Its 2T and i see what happens to the T but then on one line the extra 2 distributes to the -1 but not to the 2^n?
Hello, great video
How do you assume 2(2^n)= 2^(n+1)
minute 6.50
No assumption was made here. You can simply use the laws of exponents.
(2^1) * (2^n) = 2^(n+1).
If you still don't understand how, you can substitute the value n for a number, to give you an example let n=2 to get:
(2^1) * (2^2) = 2^(2+1)
==> (2) * (4) = 2^(3)
==> 8 = 8
I hope that helps and thanks for watching!
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randerson112358
Thank you for the video.... just not following how you went from 2(2^(n) - 1)+1 to 2^(n+1)-2+1. Specifically the 2^(n+1). That just seemed to appear out of nowhere...... 6:44
how did you find 2^n - 1 at 1:36
it was stated in the question
king
Hello, Thanks for your awesome video. Can you also help me to solve this problem?
We have recurrence T(n) for the Merge sort.
T(1) = 0;
T(n) = 2T(n/2) + n;
We now solve the recurrence by induction on n. Please prove that “if T(n) satisfies
the recurrence, then T(n) = n log n”
Base case: n = 1
• Inductive hypothesis: T(n) = n log n
• Goal: Show that T(2n) = 2n log(2n)
Why, induction shown in Introduction to Algorithm by CLRS is so hard to understand compared to this one... Does this qualify as Rigourous Proof ?
Hi, How to solve
T(n) = 2T(n/2) + n
Please help me.
use master method
Please do more of these. Seriously secret math is a salty b***h for those who aren’t used to thinking abstractly. Also suggestion, maybe use a tripod to make life easier?
Thanks again.
how did you get T(n) = 2T(n-1)+1 ?
Trying to figure this out as well
My right ear felt lonely
next time allow time to view the entire solution before putting video cards at the end, its blocking the solution