How to calculate algorithm time complex

Question

I am trying to multiple two big integer with Karatsuba algorithm. I known that O(n) is time complexity and T(n) is worst-case time complexity.

Can some one please explain why:

T(n) = 4T(n/2) + O(n) is O(n^2)

And

T(n) = 3T(n/2) + O(n) is O(n^1.59)

xenteros · Accepted Answer · 2016-11-15 14:47:25Z

1

T(n) = 4T(n/2) + O(n)

According to the Master theorem:

T(n) is O(n^log_2(4)) = O(n^2)

and

T(n) = 3T(n/2) + O(n)

is

T(n) = O(log_2(3)) ~ O(n^1,5849)

so you can round it to 1.590.

answered Nov 15, 2016 at 9:34

xenteros

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2 Comments

Thanks. Its generic form case 1 of Master theorem.

@NhatDinh yes it is