递归的Karatsuba乘法不起作用？

Question

我试图通过递归调用实现Karatsuba增殖。下面的代码应该有效，但我总是得到错误的答案。有什么想法吗？

    public static long karatsuba(long x, long y){
        //base case:
        if (x < 10 || y < 10) return x * y;

        //length of digits:
        int xSize = String.valueOf(x).length();
        int ySize = String.valueOf(y).length();
        int N     = Math.max(xSize, ySize);

        //split each number in half (by length of digits):
        long numX_hi = Long.valueOf((String.valueOf(x).substring(0, N/2)));
        long numX_lo = Long.valueOf((String.valueOf(x).substring(N/2, xSize)));
        long numY_hi = Long.valueOf((String.valueOf(y).substring(0, N/2)));
        long numY_lo = Long.valueOf((String.valueOf(y).substring(N/2, ySize)));

        //solve multiplications recursively:
        long z0 = karatsuba(numX_lo,numY_lo);
        long z1 = karatsuba((numX_hi+numX_lo),(numY_hi+numY_lo));
        long z2 = karatsuba(numX_hi,numY_hi);

        //answer:
        return  (long)(z2 * Math.pow(10,N))  +  (long)((z1-z2-z0) * Math.pow(10,(N/2)))  +  (z0);
    }

下面是几个测试用例：

1) karatsuba(1234,5678) >>> 6952652

*应该是7006652

2) karatsuba(4589,7831) >>> 34649459

*应该是35936459

3) karatsuba(911,482) >>> 44722

*应该是472842

Answer 1

如果一个数字字符串的长度大于另一个数字字符串的两倍，则接受的解决方案将给出一个StringIndexOutOfBoundsException，因为splitX或splitY将为负数。

要防止此问题，必须捕获此异常，然后将halfN设置为Math.min(xSize，ySize)/2。以下是修正后的代码：

public static long karatsuba(long x, long y){
    //base case:
    if (x < 10 || y < 10) return x * y;

    //length of digits:
    int xSize = String.valueOf(x).length();
    int ySize = String.valueOf(y).length();

    int halfN = Math.max(xSize, ySize) / 2; // store N/2 instead of N
    if (halfN >= xSize || halfN >= ySize){
        halfN = Math.min(xSize, ySize) / 2; // prevents string index error
    }
    int splitX = xSize - halfN;  // count the split point from xSize down
    int splitY = ySize - halfN;  // count the split point from ySize down

    //split each number in half (by length of digits):
    long numX_hi = Long.valueOf((String.valueOf(x).substring(0, splitX)));
    long numX_lo = Long.valueOf((String.valueOf(x).substring(splitX)));
    long numY_hi = Long.valueOf((String.valueOf(y).substring(0, splitY)));
    long numY_lo = Long.valueOf((String.valueOf(y).substring(splitY)));

    //solve multiplications recursively:
    long z0 = karatsuba(numX_lo,numY_lo);
    long z1 = karatsuba((numX_hi+numX_lo),(numY_hi+numY_lo));
    long z2 = karatsuba(numX_hi,numY_hi);

    //answer:
    return  (long)(z2 * Math.pow(10,halfN*2))  +  (long)((z1-z2-z0) * Math.pow(10,halfN))  +  (z0);
}