$C_1 = 0$, $C_n = 4C_{\lfloor n/2 \rfloor} + n$

Prove that $Cn$ less than or equal to $4(n - 1)^2$

What I did:

Base step: n = 1

$C1$ <= $4(1 - 1)^2$

0 <= 0 therefore true

how do you do the induction step?


$c_1=0\leq 4(1-1)^2=0$.

Suppose that this stands for every $c_i$ ,$i\leq n$,i will show that it stands for $c_{n+1}$.

$c_{n+1}=4c_{[\frac {n+1}{2}]}+n+1\leq 16([\frac {n+1}{2}]-1)^2+n+1\leq 4(n-1)^2+n+1=4n^2-8n+4+n+1=4n^2-7n+5<4n^2=4((n+1)-1)^2$


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.