大数乘法 - Karatsuba算法

参考：https://blog.csdn.net/u010983881/article/details/77503519

/**
 * Karatsuba乘法
 */
public static long karatsuba(long num1, long num2){
    //递归终止条件
    if(num1 < 10 || num2 < 10) return num1 * num2;

    // 计算拆分长度
    int size1 = String.valueOf(num1).length();
    int size2 = String.valueOf(num2).length();
    int halfN = Math.max(size1, size2) / 2;

    /* 拆分为a, b, c, d */
    long a = Long.valueOf(String.valueOf(num1).substring(0, size1 - halfN));
    long b = Long.valueOf(String.valueOf(num1).substring(size1 - halfN));
    long c = Long.valueOf(String.valueOf(num2).substring(0, size2 - halfN));
    long d = Long.valueOf(String.valueOf(num2).substring(size2 - halfN));

    // 计算z2, z0, z1, 此处的乘法使用递归
    long z2 = karatsuba(a, c);
    long z0 = karatsuba(b, d);
    long z1 = karatsuba((a + b), (c + d)) - z0 - z2;

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