Karatsuba Algorithm without BigInteger in Java, unexpected behaviour while recursion

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So I want to run Karatsuba Algorithm without using class BigInteger in Java, so upon following the pseudo-code and this question, I came with the following code

public static long recKaratsuba(long i1, long i2){

        if(i1<10 || i2<10) {
            return i1*i2 ;

        long len = Math.round(Long.toString(Math.max(i1,i2)).length());
        long N  = Math.round(len/2) ;

        long b = (long) (i1% Math.pow(10, N)) ;
        long a = (long) (i1/ Math.pow(10,N));
        long d = (long) (i2% Math.pow(10,N)) ;
        long c = (long) (i2/ Math.pow(10,N));

        //System.out.println("a,b,c,d :" + a + b + c + d);

        long ac = recKaratsuba(a, c) ;
        long bd = recKaratsuba(b, d) ;
        long pos = recKaratsuba(a+b,c+d) ;

        return ((long)(bd + ac*Math.pow(10,len) + (pos -ac -bd)*Math.pow(10,N) )) ;

Now, the problem with this is that it’s producing the wrong answer, 1234*5678 is giving 11686652, which should’ve been 7006652. As a beginner to Java and algorithms, I am unable to pinpoint the exact bug in this code, also I do realize that this program is very inefficient and doesn’t work for more than 4 digits (according to the linked question ). But this is intuitively what I came up with originally after learning the pseudo-code.

So my question is, what is the problem in my code and how do I execute the following algorithm without using the BigInteger method?


There are a few things i notice:

  • Instead of i1 and i2 maybe use x and y
  • Variables len and N are int, not long
  • No need to round the maximum of the lengths of the string-representations: Lengths are ints, ints are whole numbers and cant be rounded
  • No need to round the division by 2: Dividing a whole number will always result in a whole number (integer division is done)
  • The error is in the return-statement: Math.pow(10, len) should be Math.pow(10, 2 * N) instead, this is important if N is uneven
  • Avoid multiple identical calculations: especially Math.pow(10, N)

The fixed code gives the correct results for all examples that i have tested.

    public static long recKaratsuba2(long x, long y) {
        if (x < 10 || y < 10) {
            return x * y;

        int len = Long.toString(Math.max(x, y)).length();
        double den = Math.pow(10, len / 2);
        long a = (long) (x / den);
        long b = (long) (x % den);
        long c = (long) (y / den);
        long d = (long) (y % den);

        long ac = recKaratsuba2(a, c);
        long bd = recKaratsuba2(b, d);
        long pos = recKaratsuba2(a + b, c + d);

        return (long) (bd + den * (ac * den + (pos - ac - bd)));

Source: stackoverflow