I have been trying to implement Karatsuba Algorithm in java without using BigInteger. My code is applicable only when both the integers are same & have same number of digits. I do not get the correct answer however I get answer which is quite near to the right one. For instance I get 149 when 12*12. I can not figure out what is wrong with my code since I believe I have done everything right (by the book). Here's my code.
public static void main(String[] args) {
long ans=karatsuba(12,12);
System.out.println(ans);
}
private static long karatsuba(long i, long j) {
if (i<10 || j<10){
return i*j;
}
int n=getCount(i);
long a=(long) (i/Math.pow(10, n/2));
long b=(long) (i%Math.pow(10, n/2));
long c=(long) (j/Math.pow(10, n/2));
long d=(long) (j%Math.pow(10, n/2));
long first=karatsuba(a,c);
long second=karatsuba(b,d);
long third=karatsuba(a+b,c+d);
return ((long) ((first*Math.pow(10, n))+((third-first-second)*Math.pow(10,n/2))+third));
}
private static int getCount(long i) {
String totalN=Long.toString(i);
return totalN.length();
}
EDIT:
Thanks to Ziyao Wei, the problem was replacing "third" by "second". However I have another issue now which is:
If karatsuba(1234,5678) is called I get the correct answer however when I call karatsuba(5678,1234) I do not get the right answer. Could anyone possibly know the reason for that? My updated code is:
public static void main(String[] args) {
//wrong answer
long ans=karatsuba(5678,1234);
System.out.println(ans);
//correct answer
long ans1=karatsuba(1234,5678);
System.out.println(ans1);
}
private static long karatsuba(long i, long j) {
if (i<10 || j<10){
return i*j;
}
int n=getCount(i);
long a=(long) (i/Math.pow(10, n/2));
long b=(long) (i%Math.pow(10, n/2));
long c=(long) (j/Math.pow(10, n/2));
long d=(long) (j%Math.pow(10, n/2));
long first=karatsuba(a,c);
long second=karatsuba(b,d);
long third=karatsuba(a+b,c+d);
return ((long) ((first*Math.pow(10, n))+((third-first-second)*Math.pow(10, n/2))+second));
}
UPDATE:
I have managed to round up value for "n/2" hence it solves the problem however if numbers more than four digits are used bugs occur. Here is my updated code:
public static void main(String[] args) {
System.out.println(Math.round(5.00/2));
//correct answer
long ans=karatsuba(5678,1234);
System.out.println(ans);
//correct answer
long ans1=karatsuba(1234,5678);
System.out.println(ans1);
//wrong answer
long ans2=karatsuba(102456,102465);
System.out.println(ans2);
}
private static long karatsuba(long i, long j) {
if (i<10 || j<10){
return i*j;
}
double n=Math.round(getCount(i));
long a=(long) (i/Math.pow(10, Math.round(n/2)));
long b=(long) (i%Math.pow(10, Math.round(n/2)));
long c=(long) (j/Math.pow(10, Math.round(n/2)));
long d=(long) (j%Math.pow(10, Math.round(n/2)));
long first=karatsuba(a,c);
long second=karatsuba(b,d);
long third=karatsuba(a+b,c+d);
return ((long) ((first*Math.pow(10, Math.round(n)))+((third-second-first)*Math.pow(10, Math.round(n/2)))+second));
}
private static double getCount(long i) {
String totalN=Long.toString(i);
return totalN.length();
}
If somebody comes up with the solution for larger numbers (more than four digits) without using BigInteger then please do let me know. Thanks.
ntomax(getCount(i), getCount(j)). – Impute