O(n^2) ???

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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)

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)