我首先使用 long 编写了 Karasuba 算法的代码。我认为它工作得很好。使用相同的逻辑,我将代码转换为 BigInteger,但由于某些原因,它给出了 StackOverflowError。
我不明白为什么。请帮忙。
EDIT1:长时间的代码也有一个逻辑缺陷。我不确定是什么。
EDIT2: long 的代码现在可以工作了。我错误地将“%”运算符换成了“/”。
EDIT3:现在一切都好。我将 .xor 更改为 .pow,将 == 更改为 .equals,并修复了 return 语句中的一些括号问题。谢谢大家的帮助!
这是正确的代码:
public static BigInteger karatsuba3(BigInteger i, BigInteger j){
if (i.compareTo(Ten) == -1 || j.compareTo(Ten) == -1)
return i.multiply(j);
String length = getLength(i.max(j));
BigInteger n = new BigInteger(length);
if (n.mod(Two).equals(One))
n = n.add(One);
BigInteger a = i.divide(Ten.pow(n.divide(Two).intValue()));
BigInteger b = i.mod(Ten.pow(n.divide(Two).intValue()));
BigInteger c = j.divide(Ten.pow(n.divide(Two).intValue()));
BigInteger d = j.mod(Ten.pow(n.divide(Two).intValue()));
BigInteger first = karatsuba3(a,c);
BigInteger second = karatsuba3(b,d);
BigInteger third = karatsuba3(a.add(b),c.add(d));
return ((first.multiply(Ten.pow(n.intValue()))).add ((((third.subtract(first)).subtract( second))).multiply(Ten.pow(n.divide((new BigInteger("2"))).intValue()))).add(second));
}
长代码 Karatsuba:
public static long karatsuba1(long i, long j){
if (i < 10 || j < 10)
return i*j;
double n = getLength(Math.max(i,j));
if (n%2 == 1)
n++;
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 = karatsuba1(a, c);
long second = karatsuba1(b, d);
long third = karatsuba1(a + b, c + d);
return ((long) ((first * Math.pow(10, n)) + ((third - first - second) * Math.pow(10, (n/2))) + second));
}
public static int getLength( long a){
String b = Long.toString(a);
return b.length();
}
Karasuba 与 BigInteger 代码:
public static BigInteger karatsuba3(BigInteger i, BigInteger j){
BigInteger Ten = new BigInteger("10");
if (i.compareTo(Ten) == -1 || j.compareTo(Ten) == -1)
return i.multiply(j);
String length = getLength(i.max(j));
BigInteger n = new BigInteger(length);
if (n.mod(new BigInteger("2")) == new BigInteger("1"))
n.add(new BigInteger ("1"));
BigInteger a = i.divide(Ten.xor(n.divide((new BigInteger("2")))));
BigInteger b = i.mod(Ten.xor(n.divide((new BigInteger("2")))));
BigInteger c = j.divide(Ten.xor(n.divide((new BigInteger("2")))));
BigInteger d = j.mod(Ten.xor(n.divide((new BigInteger("2")))));
BigInteger first = karatsuba3(a,c);
BigInteger second = karatsuba3(b,d);
BigInteger third = karatsuba3(a.add(b),c.add(d));
return ((first.multiply(Ten.xor(n))).add (((third.subtract(first).subtract( second)))).multiply(Ten.xor(n.divide((new BigInteger("2"))))).add(second));
}
public static String getLength( BigInteger a){
String b = a.toString();
return Integer.toString(b.length());
}