Ace Test Series: Algorithms - Time Complexity

Question

What is the time complexity of T(n) = T(n/3) + T(n/9) +n?

Comments

O(n^2) ???

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@kumar.dilip

Given Answer is O(n)

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@kumar.dilip can u pls tell how did u get this ?

Answer 1

T(n)= O(n)

Answer 2

We can solve it by tree method.

T(n) = T(n/3) + T(n/9) + n

                                                                n     =======> n

                                                        /               \

                                                  n/3                n/9   =======> 4/9n

                                        /                  \        /            \                             

                                 n/9                  n/27    n/27         n/81   ====> $(4/9)^{2}*n$

 

                             .................................................................

                            T(1)   ....................................................T(1)

Total work done will be = n + (4/9)n + $(4/9)^{2}*n $ + .........................k (times)

Here  n = $(4/9)^{k}$

We can write it like  n* [ 1 + 4/9 + 4/9^2 +------------------------]
So, it will be.
= 9/5 *n

= O(n)

Comments

@kumar.dilip 

n*(1-n)*9/5=O(n^2)

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@kumar.dilip 

 n* [ 1 + 4/9 + 4/9^2 +--------------------------k]

after n everything is constant so, can we write O(n) directly by ignoring constant ..