Determine a Value for the constant $C$ and use it to estimate the number of bit operations needed to multiply two 64-bit integers using the Fast Multiplication Algorithm
Attempt/Analysis-:
Let me write the recursive equation for Fast Multiplication (Karatsuba_algorithm)
$f \left(2n\right)$=$3*f \left(n\right)+C*n$
As The bit operations involves 3 operation -:
$1 .\text{Shift operation} $
$2 .\text{Add operation} $
$3 .\text{Subtract operation} $
$\Rightarrow \text{I know that shifting $n$ places would require n bit operation.} $
$\Rightarrow \text{I know that Addition of 2$n$ bit number would require atmost $3n$ bit operation.} $
$\Rightarrow \text{I know that Subtraction of 2$n$ bit number would require atmost $3n$ bit operation.} $
I am unable to move forward ....please help me out...answer is $50$n