How to apply karatsuba algorithm if a number is odd digits number ?

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Recently i am learning a algorithm karatsuba which is the fasted multiplication algorithm..It was fine when x = 1234 , y = 4658 ,because the number is even digits number. So i can easily separate two portion of x and y

x= 1234 , so a = 12 , b = 34
y= 4658 , so c = 46 , d = 58

. But if x = 123 then how can i separate two portion ?

Posted 18-Oct-15 10:02am

Devils-ey3

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Andreas Gieriet · Accepted Answer · 2015-10-18T10:16:00

Solution 1

a = 1, b = 23
Or am I missing something?
See https://en.wikipedia.org/wiki/Karatsuba_algorithm[^] and follow the example. In your case, the factor is 100, not 1000 as in the example.
Regards
Andi

Posted 18-Oct-15 10:16am

Andreas Gieriet

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Devils-ey3 18-Oct-15 17:51pm

But one confusion. Let consider x = 6 bit number, y = 4 bit number.
The formula is x.y = 10^n * AC + 10^(n/2) (AD+BC) + BD
where A = first 3 bits of x and b = last 3 bits of x,
C = first 2 bit of y and D = last 2 bit of y.
So what will be the value of n ?

Andreas Gieriet 19-Oct-15 16:01pm

To my understanding, both numbers have to be split with respect to the same base B. The algorithm does not work if you split the numbers differently. E.g. if your base is 2 and you split to 3 bits, your x is 3 + 3 bits, y is 1 + 3 bits.
Regards
Andi